+@c PSPP - a program for statistical analysis.
+@c Copyright (C) 2017, 2020 Free Software Foundation, Inc.
+@c Permission is granted to copy, distribute and/or modify this document
+@c under the terms of the GNU Free Documentation License, Version 1.3
+@c or any later version published by the Free Software Foundation;
+@c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
+@c A copy of the license is included in the section entitled "GNU
+@c Free Documentation License".
+@c
@node Statistics
@chapter Statistics
-This chapter documents the statistical procedures that PSPP supports so
+This chapter documents the statistical procedures that @pspp{} supports so
far.
@menu
* DESCRIPTIVES:: Descriptive statistics.
* FREQUENCIES:: Frequency tables.
* EXAMINE:: Testing data for normality.
+* GRAPH:: Plot data.
* CORRELATIONS:: Correlation tables.
* CROSSTABS:: Crosstabulation tables.
-* FACTOR:: Factor analysis and Principal Components analysis
+* CTABLES:: Custom tables.
+* FACTOR:: Factor analysis and Principal Components analysis.
+* GLM:: Univariate Linear Models.
+* LOGISTIC REGRESSION:: Bivariate Logistic Regression.
+* MEANS:: Average values and other statistics.
* NPAR TESTS:: Nonparametric tests.
* T-TEST:: Test hypotheses about means.
* ONEWAY:: One way analysis of variance.
+* QUICK CLUSTER:: K-Means clustering.
* RANK:: Compute rank scores.
-* REGRESSION:: Linear regression.
* RELIABILITY:: Reliability analysis.
* ROC:: Receiver Operating Characteristic.
@end menu
@vindex DESCRIPTIVES
@display
DESCRIPTIVES
- /VARIABLES=var_list
+ /VARIABLES=@var{var_list}
/MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
/FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
/SAVE
@{A,D@}
@end display
-The @cmd{DESCRIPTIVES} procedure reads the active file and outputs
-descriptive
-statistics requested by the user. In addition, it can optionally
+The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
+linear descriptive statistics requested by the user. In addition, it can optionally
compute Z-scores.
-The VARIABLES subcommand, which is required, specifies the list of
-variables to be analyzed. Keyword VARIABLES is optional.
+The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
+variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
All other subcommands are optional:
-The MISSING subcommand determines the handling of missing variables. If
-INCLUDE is set, then user-missing values are included in the
-calculations. If NOINCLUDE is set, which is the default, user-missing
-values are excluded. If VARIABLE is set, then missing values are
-excluded on a variable by variable basis; if LISTWISE is set, then
+The @subcmd{MISSING} subcommand determines the handling of missing variables. If
+@subcmd{INCLUDE} is set, then user-missing values are included in the
+calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
+values are excluded. If @subcmd{VARIABLE} is set, then missing values are
+excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
the entire case is excluded whenever any value in that case has a
-system-missing or, if INCLUDE is set, user-missing value.
+system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
-The FORMAT subcommand affects the output format. Currently the
-LABELS/NOLABELS and NOINDEX/INDEX settings are not used. When SERIAL is
-set, both valid and missing number of cases are listed in the output;
-when NOSERIAL is set, only valid cases are listed.
+The @subcmd{FORMAT} subcommand has no effect. It is accepted for
+backward compatibility.
-The SAVE subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
+The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
the specified variables. The Z scores are saved to new variables.
Variable names are generated by trying first the original variable name
with Z prepended and truncated to a maximum of 8 characters, then the
names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
-variable names can be specified explicitly on VARIABLES in the variable
+variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
list by enclosing them in parentheses after each variable.
+When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
+treating temporary transformations as permanent.
-The STATISTICS subcommand specifies the statistics to be displayed:
+The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
@table @code
-@item ALL
+@item @subcmd{ALL}
All of the statistics below.
-@item MEAN
+@item @subcmd{MEAN}
Arithmetic mean.
-@item SEMEAN
+@item @subcmd{SEMEAN}
Standard error of the mean.
-@item STDDEV
+@item @subcmd{STDDEV}
Standard deviation.
-@item VARIANCE
+@item @subcmd{VARIANCE}
Variance.
-@item KURTOSIS
+@item @subcmd{KURTOSIS}
Kurtosis and standard error of the kurtosis.
-@item SKEWNESS
+@item @subcmd{SKEWNESS}
Skewness and standard error of the skewness.
-@item RANGE
+@item @subcmd{RANGE}
Range.
@item MINIMUM
Minimum value.
Standard error of the skewness.
@end table
-The SORT subcommand specifies how the statistics should be sorted. Most
-of the possible values should be self-explanatory. NAME causes the
+The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
+of the possible values should be self-explanatory. @subcmd{NAME} causes the
statistics to be sorted by name. By default, the statistics are listed
-in the order that they are specified on the VARIABLES subcommand. The A
-and D settings request an ascending or descending sort order,
-respectively.
+in the order that they are specified on the @subcmd{VARIABLES} subcommand.
+The @subcmd{A} and @subcmd{D} settings request an ascending or descending
+sort order, respectively.
+
+@subsection Descriptives Example
+
+The @file{physiology.sav} file contains various physiological data for a sample
+of persons. Running the @cmd{DESCRIPTIVES} command on the variables @exvar{height}
+and @exvar{temperature} with the default options allows one to see simple linear
+statistics for these two variables. In @ref{descriptives:ex}, these variables
+are specfied on the @subcmd{VARIABLES} subcommand and the @subcmd{SAVE} option
+has been used, to request that Z scores be calculated.
+
+After the command has completed, this example runs @cmd{DESCRIPTIVES} again, this
+time on the @exvar{zheight} and @exvar{ztemperature} variables,
+which are the two normalized (Z-score) variables generated by the
+first @cmd{DESCRIPTIVES} command.
+
+@float Example, descriptives:ex
+@psppsyntax {descriptives.sps}
+@caption {Running two @cmd{DESCRIPTIVES} commands, one with the @subcmd{SAVE} subcommand}
+@end float
+
+@float Screenshot, descriptives:scr
+@psppimage {descriptives}
+@caption {The Descriptives dialog box with two variables and Z-Scores option selected}
+@end float
+
+In @ref{descriptives:res}, we can see that there are 40 valid data for each of the variables
+and no missing values. The mean average of the height and temperature is 16677.12
+and 37.02 respectively. The descriptive statistics for temperature seem reasonable.
+However there is a very high standard deviation for @exvar{height} and a suspiciously
+low minimum. This is due to a data entry error in the
+data (@pxref{Identifying incorrect data}).
+
+In the second Descriptive Statistics command, one can see that the mean and standard
+deviation of both Z score variables is 0 and 1 respectively. All Z score statistics
+should have these properties since they are normalized versions of the original scores.
+
+@float Result, descriptives:res
+@psppoutput {descriptives}
+@caption {Descriptives statistics including two normalized variables (Z-scores)}
+@end float
@node FREQUENCIES
@section FREQUENCIES
@vindex FREQUENCIES
@display
FREQUENCIES
- /VARIABLES=var_list
- /FORMAT=@{TABLE,NOTABLE,LIMIT(limit)@}
+ /VARIABLES=@var{var_list}
+ /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
@{AVALUE,DVALUE,AFREQ,DFREQ@}
/MISSING=@{EXCLUDE,INCLUDE@}
/STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
SESKEWNESS,SEKURTOSIS,ALL,NONE@}
- /NTILES=ntiles
+ /NTILES=@var{ntiles}
/PERCENTILES=percent@dots{}
- /HISTOGRAM=[MINIMUM(x_min)] [MAXIMUM(x_max)]
- [@{FREQ[(y_max)],PERCENT[(y_max)]@}] [@{NONORMAL,NORMAL@}]
- /PIECHART=[MINIMUM(x_min)] [MAXIMUM(x_max)]
+ /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
+ [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
+ /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
[@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
+ /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
+ [@{FREQ,PERCENT@}]
+ /ORDER=@{ANALYSIS,VARIABLE@}
+
(These options are not currently implemented.)
- /BARCHART=@dots{}
/HBAR=@dots{}
/GROUPED=@dots{}
@end display
The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
variables.
@cmd{FREQUENCIES} can also calculate and display descriptive statistics
-(including median and mode) and percentiles,
-@cmd{FREQUENCIES} can also output
-histograms and pie charts.
+(including median and mode) and percentiles, and various graphical representations
+of the frequency distribution.
-The VARIABLES subcommand is the only required subcommand. Specify the
+The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
variables to be analyzed.
-The FORMAT subcommand controls the output format. It has several
-possible settings:
+The @subcmd{FORMAT} subcommand controls the output format. It has several
+possible settings:
-@itemize @bullet
+@itemize @subcmd{}
@item
-TABLE, the default, causes a frequency table to be output for every
-variable specified. NOTABLE prevents them from being output. LIMIT
+@subcmd{TABLE}, the default, causes a frequency table to be output for every
+variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
with a numeric argument causes them to be output except when there are
more than the specified number of values in the table.
@item
Normally frequency tables are sorted in ascending order by value. This
-is AVALUE. DVALUE tables are sorted in descending order by value.
-AFREQ and DFREQ tables are sorted in ascending and descending order,
+is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
+@subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
respectively, by frequency count.
@end itemize
-The MISSING subcommand controls the handling of user-missing values.
-When EXCLUDE, the default, is set, user-missing values are not included
-in frequency tables or statistics. When INCLUDE is set, user-missing
+The @subcmd{MISSING} subcommand controls the handling of user-missing values.
+When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
+in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
are included. System-missing values are never included in statistics,
but are listed in frequency tables.
-The available STATISTICS are the same as available in @cmd{DESCRIPTIVES}
-(@pxref{DESCRIPTIVES}), with the addition of MEDIAN, the data's median
+The available @subcmd{STATISTICS} are the same as available
+in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
+of @subcmd{MEDIAN}, the data's median
value, and MODE, the mode. (If there are multiple modes, the smallest
value is reported.) By default, the mean, standard deviation of the
mean, minimum, and maximum are reported for each variable.
@cindex percentiles
-PERCENTILES causes the specified percentiles to be reported.
+@subcmd{PERCENTILES} causes the specified percentiles to be reported.
The percentiles should be presented at a list of numbers between 0
-and 100 inclusive.
-The NTILES subcommand causes the percentiles to be reported at the
+and 100 inclusive.
+The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
boundaries of the data set divided into the specified number of ranges.
-For instance, @code{/NTILES=4} would cause quartiles to be reported.
+For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
-The HISTOGRAM subcommand causes the output to include a histogram for
+@cindex histogram
+The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
each specified numeric variable. The X axis by default ranges from
-the minimum to the maximum value observed in the data, but the MINIMUM
-and MAXIMUM keywords can set an explicit range. Specify NORMAL to
-superimpose a normal curve on the histogram. Histograms are not
-created for string variables.
-
-The PIECHART adds a pie chart for each variable to the data. Each
+the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
+and @subcmd{MAXIMUM} keywords can set an explicit range.
+@footnote{The number of
+bins is chosen according to the Freedman-Diaconis rule:
+@math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
+and @math{n} is the number of samples. Note that
+@cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
+Histograms are not created for string variables.
+
+Specify @subcmd{NORMAL} to superimpose a normal curve on the
+histogram.
+
+@cindex piechart
+The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
slice represents one value, with the size of the slice proportional to
the value's frequency. By default, all non-missing values are given
-slices. The MINIMUM and MAXIMUM keywords can be used to limit the
-displayed slices to a given range of values. The MISSING keyword adds
-slices for missing values.
-
-The FREQ and PERCENT options on HISTOGRAM and PIECHART are accepted
-but not currently honored.
+slices.
+The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
+displayed slices to a given range of values.
+The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
+piechart. This is the default.
+If instead, @subcmd{MISSING} is specified, then the pie chart includes
+a single slice representing all system missing and user-missing cases.
+
+@cindex bar chart
+The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
+The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
+categories whose counts which lie outside the specified limits.
+The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
+of each category, whereas the @subcmd{PERCENT} option displays relative
+percentages.
+
+The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
+@subcmd{PIECHART} are accepted but not currently honoured.
+
+The @subcmd{ORDER} subcommand is accepted but ignored.
+
+@subsection Frequencies Example
+
+@ref{frequencies:ex} runs a frequency analysis on the @exvar{sex}
+and @exvar{occupation} variables from the @file{personnel.sav} file.
+This is useful to get an general idea of the way in which these nominal
+variables are distributed.
+
+@float Example, frequencies:ex
+@psppsyntax {frequencies.sps}
+@caption {Running frequencies on the @exvar{sex} and @exvar{occupation} variables}
+@end float
+
+If you are using the graphic user interface, the dialog box is set up such that
+by default, several statistics are calculated. Some are not particularly useful
+for categorical variables, so you may want to disable those.
+
+@float Screenshot, frequencies:scr
+@psppimage {frequencies}
+@caption {The frequencies dialog box with the @exvar{sex} and @exvar{occupation} variables selected}
+@end float
+
+From @ref{frequencies:res} it is evident that there are 33 males, 21 females and
+2 persons for whom their sex has not been entered.
+
+One can also see how many of each occupation there are in the data.
+When dealing with string variables used as nominal values, running a frequency
+analysis is useful to detect data input entries. Notice that
+one @exvar{occupation} value has been mistyped as ``Scrientist''. This entry should
+be corrected, or marked as missing before using the data.
+
+@float Result, frequencies:res
+@psppoutput {frequencies}
+@caption {The relative frequencies of @exvar{sex} and @exvar{occupation}}
+@end float
@node EXAMINE
-@comment node-name, next, previous, up
@section EXAMINE
-@vindex EXAMINE
-@cindex Normality, testing for
+@vindex EXAMINE
+@cindex Exploratory data analysis
+@cindex normality, testing
@display
EXAMINE
- VARIABLES=var_list [BY factor_list ]
- /STATISTICS=@{DESCRIPTIVES, EXTREME[(n)], ALL, NONE@}
- /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, ALL, NONE@}
- /CINTERVAL n
+ VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
+ [BY @var{factor1} [BY @var{subfactor1}]
+ [ @var{factor2} [BY @var{subfactor2}]]
+ @dots{}
+ [ @var{factor3} [BY @var{subfactor3}]]
+ ]
+ /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
+ /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
+ /CINTERVAL @var{p}
/COMPARE=@{GROUPS,VARIABLES@}
- /ID=var_name
+ /ID=@var{identity_variable}
/@{TOTAL,NOTOTAL@}
- /PERCENTILE=[value_list]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
- /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
+ /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
+ /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
[@{NOREPORT,REPORT@}]
@end display
-The @cmd{EXAMINE} command is used to test how closely a distribution is to a
-normal distribution. It also shows you outliers and extreme values.
+The @cmd{EXAMINE} command is used to perform exploratory data analysis.
+In particular, it is useful for testing how closely a distribution follows a
+normal distribution, and for finding outliers and extreme values.
-The VARIABLES subcommand specifies the dependent variables and the
-independent variable to use as factors for the analysis. Variables
-listed before the first BY keyword are the dependent variables.
+The @subcmd{VARIABLES} subcommand is mandatory.
+It specifies the dependent variables and optionally variables to use as
+factors for the analysis.
+Variables listed before the first @subcmd{BY} keyword (if any) are the
+dependent variables.
The dependent variables may optionally be followed by a list of
-factors which tell PSPP how to break down the analysis for each
-dependent variable. The format for each factor is
+factors which tell @pspp{} how to break down the analysis for each
+dependent variable.
+
+Following the dependent variables, factors may be specified.
+The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
+The format for each factor is
@display
-var [BY var].
+@var{factorvar} [BY @var{subfactorvar}].
@end display
+Each unique combination of the values of @var{factorvar} and
+@var{subfactorvar} divide the dataset into @dfn{cells}.
+Statistics are calculated for each cell
+and for the entire dataset (unless @subcmd{NOTOTAL} is given).
+
+The @subcmd{STATISTICS} subcommand specifies which statistics to show.
+@subcmd{DESCRIPTIVES} produces a table showing some parametric and
+non-parametrics statistics.
+@subcmd{EXTREME} produces a table showing the extremities of each cell.
+A number in parentheses, @var{n} determines
+how many upper and lower extremities to show.
+The default number is 5.
+
+The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
+If @subcmd{TOTAL} appears, then statistics for the entire dataset
+as well as for each cell are produced.
+If @subcmd{NOTOTAL} appears, then statistics are produced only for the cells
+(unless no factor variables have been given).
+These subcommands have no effect if there have been no factor variables
+specified.
+
+@cindex boxplot
+@cindex histogram
+@cindex npplot
+@cindex spreadlevel plot
+The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
+Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
+@subcmd{SPREADLEVEL}.
+The first three can be used to visualise how closely each cell conforms to a
+normal distribution, whilst the spread vs.@: level plot can be useful to visualise
+how the variance differs between factors.
+Boxplots show you the outliers and extreme values.
+@footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
+bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
+Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
+
+The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
+median. It takes an optional parameter @var{t}, which specifies how the data
+should be transformed prior to plotting.
+The given value @var{t} is a power to which the data are raised. For example, if
+@var{t} is given as 2, then the square of the data is used.
+Zero, however is a special value. If @var{t} is 0 or
+is omitted, then data are transformed by taking its natural logarithm instead of
+raising to the power of @var{t}.
+
+@cindex Shapiro-Wilk
+When one or more plots are requested, @subcmd{EXAMINE} also performs the
+Shapiro-Wilk test for each category.
+There are however a number of provisos:
+@itemize
+@item All weight values must be integer.
+@item The cumulative weight value must be in the range [3, 5000]
+@end itemize
+The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
+useful there is more than one dependent variable and at least one factor.
+If
+@subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
+each of which contain boxplots for all the cells.
+If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
+each containing one boxplot per dependent variable.
+If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
+@subcmd{/COMPARE=GROUPS} were given.
-The STATISTICS subcommand specifies the analysis to be done.
-DESCRIPTIVES will produce a table showing some parametric and
-non-parametrics statistics. EXTREME produces a table showing extreme
-values of the dependent variable. A number in parentheses determines
-how many upper and lower extremes to show. The default number is 5.
-
-
-The PLOT subcommand specifies which plots are to be produced if any.
+The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
+@subcmd{/STATISTICS=EXTREME} has been given.
+If given, it should provide the name of a variable which is to be used
+to labels extreme values and outliers.
+Numeric or string variables are permissible.
+If the @subcmd{ID} subcommand is not given, then the case number is used for
+labelling.
-The COMPARE subcommand is only relevant if producing boxplots, and it is only
-useful there is more than one dependent variable and at least one factor. If
-/COMPARE=GROUPS is specified, then one plot per dependent variable is produced,
-containing boxplots for all the factors.
-If /COMPARE=VARIABLES is specified, then one plot per factor is produced, each
-each containing one boxplot per dependent variable.
-If the /COMPARE subcommand is ommitted, then PSPP uses the default value of
-/COMPARE=GROUPS.
-
-The ID subcommand also pertains to boxplots. If given, it must
-specify a variable name. Outliers and extreme cases plotted in
-boxplots will be labelled with the case from that variable. Numeric or
-string variables are permissible. If the ID subcommand is not given,
-then the casenumber will be used for labelling.
-
-The CINTERVAL subcommand specifies the confidence interval to use in
-calculation of the descriptives command. The default it 95%.
+The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
+calculation of the descriptives command. The default is 95%.
@cindex percentiles
-The PERCENTILES subcommand specifies which percentiles are to be calculated,
+The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
and which algorithm to use for calculating them. The default is to
calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
-HAVERAGE algorithm.
+@subcmd{HAVERAGE} algorithm.
-The TOTAL and NOTOTAL subcommands are mutually exclusive. If NOTOTAL
-is given and factors have been specified in the VARIABLES subcommand,
-then then statistics for the unfactored dependent variables are
+The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
+is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
+then statistics for the unfactored dependent variables are
produced in addition to the factored variables. If there are no
-factors specified then TOTAL and NOTOTAL have no effect.
+factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
+
+
+The following example generates descriptive statistics and histograms for
+two variables @var{score1} and @var{score2}.
+Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
+Therefore, the descriptives and histograms are generated for each
+distinct value
+of @var{gender} @emph{and} for each distinct combination of the values
+of @var{gender} and @var{race}.
+Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
+@var{score1} and @var{score2} covering the whole dataset are not produced.
+@example
+EXAMINE @var{score1} @var{score2} BY
+ @var{gender}
+ @var{gender} BY @var{culture}
+ /STATISTICS = DESCRIPTIVES
+ /PLOT = HISTOGRAM
+ /NOTOTAL.
+@end example
+
+Here is a second example showing how the @cmd{examine} command can be used to find extremities.
+@example
+EXAMINE @var{height} @var{weight} BY
+ @var{gender}
+ /STATISTICS = EXTREME (3)
+ /PLOT = BOXPLOT
+ /COMPARE = GROUPS
+ /ID = @var{name}.
+@end example
+In this example, we look at the height and weight of a sample of individuals and
+how they differ between male and female.
+A table showing the 3 largest and the 3 smallest values of @exvar{height} and
+@exvar{weight} for each gender, and for the whole dataset as are shown.
+In addition, the @subcmd{/PLOT} subcommand requests boxplots.
+Because @subcmd{/COMPARE = GROUPS} was specified, boxplots for male and female are
+shown in juxtaposed in the same graphic, allowing us to easily see the difference between
+the genders.
+Since the variable @var{name} was specified on the @subcmd{ID} subcommand,
+values of the @var{name} variable are used to label the extreme values.
@strong{Warning!}
-If many dependent variable are given, or factors are given for which
-there are many distinct values, then @cmd{EXAMINE} will produce a very
+If you specify many dependent variables or factor variables
+for which there are many distinct values, then @cmd{EXAMINE} will produce a very
large quantity of output.
+@node GRAPH
+@section GRAPH
+
+@vindex GRAPH
+@cindex Exploratory data analysis
+@cindex normality, testing
+
+@display
+GRAPH
+ /HISTOGRAM [(NORMAL)]= @var{var}
+ /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
+ /BAR = @{@var{summary-function}(@var{var1}) | @var{count-function}@} BY @var{var2} [BY @var{var3}]
+ [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
+ [@{NOREPORT,REPORT@}]
+
+@end display
+
+The @cmd{GRAPH} command produces graphical plots of data. Only one of the subcommands
+@subcmd{HISTOGRAM}, @subcmd{BAR} or @subcmd{SCATTERPLOT} can be specified, @i{i.e.} only one plot
+can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
+
+@menu
+* SCATTERPLOT:: Cartesian Plots
+* HISTOGRAM:: Histograms
+* BAR CHART:: Bar Charts
+@end menu
+
+@node SCATTERPLOT
+@subsection Scatterplot
+@cindex scatterplot
+
+The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the
+data.
+@cmd{GRAPH} uses the third variable @var{var3}, if specified, to determine
+the colours and/or markers for the plot.
+The following is an example for producing a scatterplot.
+
+@example
+GRAPH
+ /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
+@end example
+
+This example produces a scatterplot where @var{height} is plotted versus @var{weight}. Depending
+on the value of the @var{gender} variable, the colour of the datapoint is different. With
+this plot it is possible to analyze gender differences for @var{height} versus @var{weight} relation.
+
+@node HISTOGRAM
+@subsection Histogram
+@cindex histogram
+
+The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
+the histogram plot.
+The keyword @subcmd{NORMAL} may be specified in parentheses, to indicate that the ideal normal curve
+should be superimposed over the histogram.
+For an alternative method to produce histograms @pxref{EXAMINE}. The
+following example produces a histogram plot for the variable @var{weight}.
+
+@example
+GRAPH
+ /HISTOGRAM = @var{weight}.
+@end example
+
+@node BAR CHART
+@subsection Bar Chart
+@cindex bar chart
+
+The subcommand @subcmd{BAR} produces a bar chart.
+This subcommand requires that a @var{count-function} be specified (with no arguments) or a @var{summary-function} with a variable @var{var1} in parentheses.
+Following the summary or count function, the keyword @subcmd{BY} should be specified and then a catagorical variable, @var{var2}.
+The values of the variable @var{var2} determine the labels of the bars to be plotted.
+Optionally a second categorical variable @var{var3} may be specified in which case a clustered (grouped) bar chart is produced.
+
+Valid count functions are
+@table @subcmd
+@item COUNT
+The weighted counts of the cases in each category.
+@item PCT
+The weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
+@item CUFREQ
+The cumulative weighted counts of the cases in each category.
+@item CUPCT
+The cumulative weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
+@end table
+
+The summary function is applied to @var{var1} across all cases in each category.
+The recognised summary functions are:
+@table @subcmd
+@item SUM
+The sum.
+@item MEAN
+The arithmetic mean.
+@item MAXIMUM
+The maximum value.
+@item MINIMUM
+The minimum value.
+@end table
+
+The following examples assume a dataset which is the results of a survey.
+Each respondent has indicated annual income, their sex and city of residence.
+One could create a bar chart showing how the mean income varies between of residents of different cities, thus:
+@example
+GRAPH /BAR = MEAN(@var{income}) BY @var{city}.
+@end example
+
+This can be extended to also indicate how income in each city differs between the sexes.
+@example
+GRAPH /BAR = MEAN(@var{income}) BY @var{city} BY @var{sex}.
+@end example
+
+One might also want to see how many respondents there are from each city. This can be achieved as follows:
+@example
+GRAPH /BAR = COUNT BY @var{city}.
+@end example
+
+Bar charts can also be produced using the @ref{FREQUENCIES} and @ref{CROSSTABS} commands.
+
@node CORRELATIONS
@section CORRELATIONS
@vindex CORRELATIONS
@display
CORRELATIONS
- /VARIABLES = varlist [ WITH varlist ]
+ /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
[
.
.
.
- /VARIABLES = varlist [ WITH varlist ]
- /VARIABLES = varlist [ WITH varlist ]
+ /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
+ /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
]
[ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
[ /STATISTICS=DESCRIPTIVES XPROD ALL]
[ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
-@end display
+@end display
@cindex correlation
The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
for a set of variables. The significance of the coefficients are also given.
-At least one VARIABLES subcommand is required. If the WITH keyword is used, then a non-square
-correlation table will be produced.
-The variables preceding WITH, will be used as the rows of the table, and the variables following
-will be the columns of the table.
-If no WITH subcommand is given, then a square, symmetrical table using all variables is produced.
+At least one @subcmd{VARIABLES} subcommand is required. If you specify the @subcmd{WITH}
+keyword, then a non-square correlation table is produced.
+The variables preceding @subcmd{WITH}, are used as the rows of the table,
+and the variables following @subcmd{WITH} are used as the columns of the table.
+If no @subcmd{WITH} subcommand is specified, then @cmd{CORRELATIONS} produces a
+square, symmetrical table using all variables.
-
-The @cmd{MISSING} subcommand determines the handling of missing variables.
-If INCLUDE is set, then user-missing values are included in the
+The @cmd{MISSING} subcommand determines the handling of missing variables.
+If @subcmd{INCLUDE} is set, then user-missing values are included in the
calculations, but system-missing values are not.
-If EXCLUDE is set, which is the default, user-missing
-values are excluded as well as system-missing values.
-This is the default.
+If @subcmd{EXCLUDE} is set, which is the default, user-missing
+values are excluded as well as system-missing values.
-If LISTWISE is set, then the entire case is excluded from analysis
+If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
whenever any variable specified in any @cmd{/VARIABLES} subcommand
-contains a missing value.
-If PAIRWISE is set, then a case is considered missing only if either of the
+contains a missing value.
+If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
values for the particular coefficient are missing.
-The default is PAIRWISE.
+The default is @subcmd{PAIRWISE}.
-The PRINT subcommand is used to control how the reported significance values are printed.
-If the TWOTAIL option is used, then a two-tailed test of significance is
-printed. If the ONETAIL option is given, then a one-tailed test is used.
-The default is TWOTAIL.
+The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
+If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
+printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
+The default is @subcmd{TWOTAIL}.
-If the NOSIG option is specified, then correlation coefficients with significance less than
+If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
0.05 are highlighted.
-If SIG is specified, then no highlighting is performed. This is the default.
+If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
@cindex covariance
-The STATISTICS subcommand requests additional statistics to be displayed. The keyword
-DESCRIPTIVES requests that the mean, number of non-missing cases, and the non-biased
+The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
+@subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
estimator of the standard deviation are displayed.
-These statistics will be displayed in a separated table, for all the variables listed
-in any /VARIABLES subcommand.
-The XPROD keyword requests cross-product deviations and covariance estimators to
+These statistics are displayed in a separated table, for all the variables listed
+in any @subcmd{/VARIABLES} subcommand.
+The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
be displayed for each pair of variables.
-The keyword ALL is the union of DESCRIPTIVES and XPROD.
+The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
@node CROSSTABS
@section CROSSTABS
@vindex CROSSTABS
@display
CROSSTABS
- /TABLES=var_list BY var_list [BY var_list]@dots{}
+ /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
/MISSING=@{TABLE,INCLUDE,REPORT@}
- /WRITE=@{NONE,CELLS,ALL@}
/FORMAT=@{TABLES,NOTABLES@}
- @{LABELS,NOLABELS,NOVALLABS@}
- @{PIVOT,NOPIVOT@}
@{AVALUE,DVALUE@}
- @{NOINDEX,INDEX@}
- @{BOX,NOBOX@}
/CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
ASRESIDUAL,ALL,NONE@}
+ /COUNT=@{ASIS,CASE,CELL@}
+ @{ROUND,TRUNCATE@}
/STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
KAPPA,ETA,CORR,ALL,NONE@}
-
+ /BARCHART
+
(Integer mode.)
- /VARIABLES=var_list (low,high)@dots{}
+ /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
@end display
The @cmd{CROSSTABS} procedure displays crosstabulation
each cell in the crosstabulation tables. In addition, a number of
statistics can be calculated for each table itself.
-The TABLES subcommand is used to specify the tables to be reported. Any
+The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
number of dimensions is permitted, and any number of variables per
-dimension is allowed. The TABLES subcommand may be repeated as many
+dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
times as needed. This is the only required subcommand in @dfn{general
-mode}.
+mode}.
Occasionally, one may want to invoke a special mode called @dfn{integer
-mode}. Normally, in general mode, PSPP automatically determines
+mode}. Normally, in general mode, @pspp{} automatically determines
what values occur in the data. In integer mode, the user specifies the
range of values that the data assumes. To invoke this mode, specify the
-VARIABLES subcommand, giving a range of data values in parentheses for
-each variable to be used on the TABLES subcommand. Data values inside
+@subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
+each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
the range are truncated to the nearest integer, then assigned to that
value. If values occur outside this range, they are discarded. When it
-is present, the VARIABLES subcommand must precede the TABLES
+is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
subcommand.
In general mode, numeric and string variables may be specified on
TABLES. In integer mode, only numeric variables are allowed.
-The MISSING subcommand determines the handling of user-missing values.
-When set to TABLE, the default, missing values are dropped on a table by
-table basis. When set to INCLUDE, user-missing values are included in
-tables and statistics. When set to REPORT, which is allowed only in
+The @subcmd{MISSING} subcommand determines the handling of user-missing values.
+When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
+table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
+tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
integer mode, user-missing values are included in tables but marked with
-an @samp{M} (for ``missing'') and excluded from statistical
-calculations.
+a footnote and excluded from statistical calculations.
-Currently the WRITE subcommand is ignored.
-
-The FORMAT subcommand controls the characteristics of the
+The @subcmd{FORMAT} subcommand controls the characteristics of the
crosstabulation tables to be displayed. It has a number of possible
settings:
+@itemize @w{}
+@item
+@subcmd{TABLES}, the default, causes crosstabulation tables to be output.
+@subcmd{NOTABLES}, which is equivalent to @code{CELLS=NONE}, suppresses them.
+
+@item
+@subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
+@subcmd{DVALUE} asserts a descending sort order.
+@end itemize
+
+The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
+crosstabulation table. The possible settings are:
+
+@table @asis
+@item COUNT
+Frequency count.
+@item ROW
+Row percent.
+@item COLUMN
+Column percent.
+@item TOTAL
+Table percent.
+@item EXPECTED
+Expected value.
+@item RESIDUAL
+Residual.
+@item SRESIDUAL
+Standardized residual.
+@item ASRESIDUAL
+Adjusted standardized residual.
+@item ALL
+All of the above.
+@item NONE
+Suppress cells entirely.
+@end table
+
+@samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
+@subcmd{COLUMN}, and @subcmd{TOTAL}.
+If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
+is selected.
+
+By default, crosstabulation and statistics use raw case weights,
+without rounding. Use the @subcmd{/COUNT} subcommand to perform
+rounding: CASE rounds the weights of individual weights as cases are
+read, CELL rounds the weights of cells within each crosstabulation
+table after it has been constructed, and ASIS explicitly specifies the
+default non-rounding behavior. When rounding is requested, ROUND, the
+default, rounds to the nearest integer and TRUNCATE rounds toward
+zero.
+
+The @subcmd{STATISTICS} subcommand selects statistics for computation:
+
+@table @asis
+@item CHISQ
+@cindex chi-square
+
+Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
+correction, linear-by-linear association.
+@item PHI
+Phi.
+@item CC
+Contingency coefficient.
+@item LAMBDA
+Lambda.
+@item UC
+Uncertainty coefficient.
+@item BTAU
+Tau-b.
+@item CTAU
+Tau-c.
+@item RISK
+Risk estimate.
+@item GAMMA
+Gamma.
+@item D
+Somers' D.
+@item KAPPA
+Cohen's Kappa.
+@item ETA
+Eta.
+@item CORR
+Spearman correlation, Pearson's r.
+@item ALL
+All of the above.
+@item NONE
+No statistics.
+@end table
+
+Selected statistics are only calculated when appropriate for the
+statistic. Certain statistics require tables of a particular size, and
+some statistics are calculated only in integer mode.
+
+@samp{/STATISTICS} without any settings selects CHISQ. If the
+@subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
+
+@cindex bar chart
+The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
+variables on each table.
+If a table has more than two variables, the counts for the third and subsequent levels
+are aggregated and the chart is produced as if there were only two variables.
+
+
+@strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
+following limitations:
+
@itemize @bullet
@item
-TABLES, the default, causes crosstabulation tables to be output.
-NOTABLES suppresses them.
+Significance of some symmetric and directional measures is not calculated.
+@item
+Asymptotic standard error is not calculated for
+Goodman and Kruskal's tau or symmetric Somers' d.
+@item
+Approximate T is not calculated for symmetric uncertainty coefficient.
+@end itemize
+
+Fixes for any of these deficiencies would be welcomed.
+
+@subsection Crosstabs Example
+
+@cindex chi-square test of independence
+
+A researcher wishes to know if, in an industry, a person's sex is related to
+the person's occupation. To investigate this, she has determined that the
+@file{personnel.sav} is a representative, randomly selected sample of persons.
+The researcher's null hypothesis is that a person's sex has no relation to a
+person's occupation. She uses a chi-squared test of independence to investigate
+the hypothesis.
+
+@float Example, crosstabs:ex
+@psppsyntax {crosstabs.sps}
+@caption {Running crosstabs on the @exvar{sex} and @exvar{occupation} variables}
+@end float
+
+The syntax in @ref{crosstabs:ex} conducts a chi-squared test of independence.
+The line @code{/tables = occupation by sex} indicates that @exvar{occupation}
+and @exvar{sex} are the variables to be tabulated. To do this using the @gui{}
+you must place these variable names respectively in the @samp{Row} and
+@samp{Column} fields as shown in @ref{crosstabs:scr}.
+
+@float Screenshot, crosstabs:scr
+@psppimage {crosstabs}
+@caption {The Crosstabs dialog box with the @exvar{sex} and @exvar{occupation} variables selected}
+@end float
+
+Similarly, the @samp{Cells} button shows a dialog box to select the @code{count}
+and @code{expected} options. All other cell options can be deselected for this
+test.
+
+You would use the @samp{Format} and @samp{Statistics} buttons to select options
+for the @subcmd{FORMAT} and @subcmd{STATISTICS} subcommands. In this example,
+the @samp{Statistics} requires only the @samp{Chisq} option to be checked. All
+other options should be unchecked. No special settings are required from the
+@samp{Format} dialog.
+
+As shown in @ref{crosstabs:res} @cmd{CROSSTABS} generates a contingency table
+containing the observed count and the expected count of each sex and each
+occupation. The expected count is the count which would be observed if the
+null hypothesis were true.
+
+The significance of the Pearson Chi-Square value is very much larger than the
+normally accepted value of 0.05 and so one cannot reject the null hypothesis.
+Thus the researcher must conclude that a person's sex has no relation to the
+person's occupation.
+
+@float Results, crosstabs:res
+@psppoutput {crosstabs}
+@caption {The results of a test of independence between @exvar{sex} and @exvar{occupation}}
+@end float
+
+@node CTABLES
+@section CTABLES
+
+@vindex CTABLES
+@cindex custom tables
+@cindex tables, custom
+
+@code{CTABLES} has the following overall syntax. At least one
+@code{TABLE} subcommand is required:
+
+@display
+@t{CTABLES}
+ @dots{}@i{global subcommands}@dots{}
+ [@t{/TABLE} @i{axis} [@t{BY} @i{axis} [@t{BY} @i{axis}]]
+ @dots{}@i{per-table subcommands}@dots{}]@dots{}
+@end display
+
+@noindent
+where each @i{axis} may be empty or take one of the following forms:
+
+@display
+@i{variable}
+@i{variable} @t{[}@{@t{C} @math{|} @t{S}@}@t{]}
+@i{axis} + @i{axis}
+@i{axis} > @i{axis}
+(@i{axis})
+@i{axis} @t{[}@i{summary} [@i{string}] [@i{format}]@t{]}
+@end display
+
+The following subcommands precede the first @code{TABLE} subcommand
+and apply to all of the output tables. All of these subcommands are
+optional:
+
+@display
+@t{/FORMAT}
+ [@t{MINCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
+ [@t{MAXCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
+ [@t{UNITS=}@{@t{POINTS} @math{|} @t{INCHES} @math{|} @t{CM}@}]
+ [@t{EMPTY=}@{@t{ZERO} @math{|} @t{BLANK} @math{|} @i{string}@}]
+ [@t{MISSING=}@i{string}]
+@t{/VLABELS}
+ @t{VARIABLES=}@i{variables}
+ @t{DISPLAY}=@{@t{DEFAULT} @math{|} @t{NAME} @math{|} @t{LABEL} @math{|} @t{BOTH} @math{|} @t{NONE}@}
+@ignore @c not yet implemented
+@t{/MRSETS COUNTDUPLICATES=}@{@t{YES} @math{|} @t{NO}@}
+@end ignore
+@t{/SMISSING} @{@t{VARIABLE} @math{|} @t{LISTWISE}@}
+@t{/PCOMPUTE} @t{&}@i{postcompute}@t{=EXPR(}@i{expression}@t{)}
+@t{/PPROPERTIES} @t{&}@i{postcompute}@dots{}
+ [@t{LABEL=}@i{string}]
+ [@t{FORMAT=}[@i{summary} @i{format}]@dots{}]
+ [@t{HIDESOURCECATS=}@{@t{NO} @math{|} @t{YES}@}
+@t{/WEIGHT VARIABLE=}@i{variable}
+@t{/HIDESMALLCOUNTS COUNT=@i{count}}
+@end display
+
+The following subcommands follow @code{TABLE} and apply only to the
+previous @code{TABLE}. All of these subcommands are optional:
+
+@display
+@t{/SLABELS}
+ [@t{POSITION=}@{@t{COLUMN} @math{|} @t{ROW} @math{|} @t{LAYER}@}]
+ [@t{VISIBLE=}@{@t{YES} @math{|} @t{NO}@}]
+@t{/CLABELS} @{@t{AUTO} @math{|} @{@t{ROWLABELS}@math{|}@t{COLLABELS}@}@t{=}@{@t{OPPOSITE}@math{|}@t{LAYER}@}@}
+@t{/CATEGORIES} @t{VARIABLES=}@i{variables}
+ @{@t{[}@i{value}@t{,} @i{value}@dots{}@t{]}
+ @math{|} [@t{ORDER=}@{@t{A} @math{|} @t{D}@}]
+ [@t{KEY=}@{@t{VALUE} @math{|} @t{LABEL} @math{|} @i{summary}@t{(}@i{variable}@t{)}@}]
+ [@t{MISSING=}@{@t{EXCLUDE} @math{|} @t{INCLUDE}@}]@}
+ [@t{TOTAL=}@{@t{NO} @math{|} @t{YES}@} [@t{LABEL=}@i{string}] [@t{POSITION=}@{@t{AFTER} @math{|} @t{BEFORE}@}]]
+ [@t{EMPTY=}@{@t{INCLUDE} @math{|} @t{EXCLUDE}@}]
+@t{/TITLES}
+ [@t{TITLE=}@i{string}@dots{}]
+ [@t{CAPTION=}@i{string}@dots{}]
+ [@t{CORNER=}@i{string}@dots{}]
+@ignore @c not yet implemented
+@t{/CRITERIA CILEVEL=}@i{percentage}
+@t{/SIGTEST TYPE=CHISQUARE}
+ [@t{ALPHA=}@i{siglevel}]
+ [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
+ [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
+@t{/COMPARETEST TYPE=}@{@t{PROP} @math{|} @t{MEAN}@}
+ [@t{ALPHA=}@i{value}[@t{,} @i{value}]]
+ [@t{ADJUST=}@{@t{BONFERRONI} @math{|} @t{BH} @math{|} @t{NONE}@}]
+ [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
+ [@t{MEANSVARIANCE=}@{@t{ALLCATS} @math{|} @t{TESTEDCATS}@}]
+ [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
+ [@t{MERGE=}@{@t{NO} @math{|} @t{YES}@}]
+ [@t{STYLE=}@{@t{APA} @math{|} @t{SIMPLE}@}]
+ [@t{SHOWSIG=}@{@t{NO} @math{|} @t{YES}@}]
+@end ignore
+@end display
+
+The @code{CTABLES} (aka ``custom tables'') command produces
+multi-dimensional tables from categorical and scale data. It offers
+many options for data summarization and formatting.
+
+This section's examples use data from the 2008 (USA) National Survey
+of Drinking and Driving Attitudes and Behaviors, a public domain data
+set from the (USA) National Highway Traffic Administration and
+available at @url{https://data.transportation.gov}. @pspp{} includes
+this data set, with a slightly modified dictionary, as
+@file{examples/nhtsa.sav}.
+
+@node CTABLES Basics
+@subsection Basics
+
+The only required subcommand is @code{TABLE}, which specifies the
+variables to include along each axis:
+@display
+@t{/TABLE} @i{rows} [@t{BY} @i{columns} [@t{BY} @i{layers}]]
+@end display
+@noindent
+In @code{TABLE}, each of @var{rows}, @var{columns}, and @var{layers}
+is either empty or an axis expression that specifies one or more
+variables. At least one must specify an axis expression.
+
+@menu
+* CTABLES Categorical Variable Basics::
+* CTABLES Scalar Variable Basics::
+* CTABLES Overriding Measurement Level::
+@end menu
+
+@node CTABLES Categorical Variable Basics
+@subsubsection Categorical Variables
+
+An axis expression that names a categorical variable divides the data
+into cells according to the values of that variable. When all the
+variables named on @code{TABLE} are categorical, by default each cell
+displays the number of cases that it contains, so specifying a single
+variable yields a frequency table, much like the output of the
+@code{FREQUENCIES} command (@pxref{FREQUENCIES}):
+
+@example
+CTABLES /TABLE=AgeGroup.
+@end example
+@psppoutput {ctables1}
+
+@noindent
+Specifying a row and a column categorical variable yields a
+crosstabulation, much like the output of the @code{CROSSTABS} command
+(@pxref{CROSSTABS}):
+
+@example
+CTABLES /TABLE=AgeGroup BY qns3a.
+@end example
+@psppoutput {ctables2}
+
+@noindent
+The @samp{>} ``nesting'' operator nests multiple variables on a single
+axis, e.g.:
+
+@example
+CTABLES /TABLE qn105ba BY AgeGroup > qns3a.
+@end example
+@psppoutput {ctables3}
+
+@noindent
+The @samp{+} ``stacking'' operator allows a single output table to
+include multiple data analyses. With @samp{+}, @code{CTABLES} divides
+the output table into multiple @dfn{sections}, each of which includes
+an analysis of the full data set. For example, the following command
+separately tabulates age group and driving frequency by gender:
+
+@example
+CTABLES /TABLE AgeGroup + qn1 BY qns3a.
+@end example
+@psppoutput {ctables4}
+
+@noindent
+When @samp{+} and @samp{>} are used together, @samp{>} binds more
+tightly. Use parentheses to override operator precedence. Thus:
+
+@example
+CTABLES /TABLE qn26 + qn27 > qns3a.
+CTABLES /TABLE (qn26 + qn27) > qns3a.
+@end example
+@psppoutput {ctables5}
+
+@node CTABLES Scalar Variable Basics
+@subsubsection Scalar Variables
+
+For a categorical variable, @code{CTABLES} divides the table into a
+cell per category. For a scalar variable, @code{CTABLES} instead
+calculates a summary measure, by default the mean, of the values that
+fall into a cell. For example, if the only variable specified is a
+scalar variable, then the output is a single cell that holds the mean
+of all of the data:
+
+@example
+CTABLES /TABLE qnd1.
+@end example
+@psppoutput {ctables6}
+
+A scalar variable may nest with categorical variables. The following
+example shows the mean age of survey respondents across gender and
+language groups:
+
+@example
+CTABLES /TABLE qns3a > qnd1 BY region.
+@end example
+@psppoutput {ctables7}
+
+The order of nesting of scalar and categorical variables affects table
+labeling, but it does not affect the data displayed in the table. The
+following example shows how the output changes when the nesting order
+of the scalar and categorical variable are interchanged:
+
+@example
+CTABLES /TABLE qnd1 > qns3a BY region.
+@end example
+@psppoutput {ctables8}
+
+Only a single scalar variable may appear in each section; that is, a
+scalar variable may not nest inside a scalar variable directly or
+indirectly. Scalar variables may only appear on one axis within
+@code{TABLE}.
+
+@node CTABLES Overriding Measurement Level
+@subsubsection Overriding Measurement Level
+
+By default, @code{CTABLES} uses a variable's measurement level to
+decide whether to treat it as categorical or scalar. Variables
+assigned the nominal or ordinal measurement level are treated as
+categorical, and scalar variables are treated as scalar.
+
+When @pspp{} reads data from a file in an external format, such as a
+text file, variables' measurement levels are often unknown. If
+@code{CTABLES} runs when a variable has an unknown measurement level,
+it makes an initial pass through the data to guess measurement levels
+using the rules described earlier in this manual (@pxref{Measurement
+Level}). Use the @code{VARIABLE LEVEL} command to set or change a
+variable's measurement level (@pxref{VARIABLE LEVEL}).
+
+To treat a variable as categorical or scalar only for one use on
+@code{CTABLES}, add @samp{[C]} or @samp{[S]}, respectively, after the
+variable name. The following example shows the output when variable
+@code{qn20} is analyzed as scalar (the default for its measurement
+level) and as categorical:
+
+@example
+CTABLES
+ /TABLE qn20 BY qns3a
+ /TABLE qn20 [C] BY qns3a.
+@end example
+@psppoutput {ctables9}
+
+@ignore
+@node CTABLES Multiple Response Sets
+@subsubheading Multiple Response Sets
+
+The @code{CTABLES} command does not yet support multiple response
+sets.
+@end ignore
+
+@node CTABLES Data Summarization
+@subsection Data Summarization
+
+The @code{CTABLES} command allows the user to control how the data are
+summarized with @dfn{summary specifications}, syntax that lists one or
+more summary function names, optionally separated by commas, and which
+are enclosed in square brackets following a variable name on the
+@code{TABLE} subcommand. When all the variables are categorical,
+summary specifications can be given for the innermost nested variables
+on any one axis. When a scalar variable is present, only the scalar
+variable may have summary specifications.
+
+The following example includes a summary specification for column and
+row percentages for categorical variables, and mean and median for a
+scalar variable:
+
+@example
+CTABLES
+ /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a
+ /TABLE=AgeGroup [COLPCT, ROWPCT] BY qns3a.
+@end example
+@psppoutput {ctables10}
+
+A summary specification may override the default label and format by
+appending a string or format specification or both (in that order) to
+the summary function name. For example:
+
+@example
+CTABLES /TABLE=AgeGroup [COLPCT 'Gender %' PCT5.0,
+ ROWPCT 'Age Group %' PCT5.0]
+ BY qns3a.
+@end example
+@psppoutput {ctables11}
+
+@c TODO special CTABLES formats
+In addition to the standard formats, @code{CTABLES} allows the user to
+specify the following special formats:
+
+@multitable {@code{NEGPAREN@i{w}.@i{d}}} {Encloses all numbers in parentheses.} {@t{(42.96%)}} {@t{(-42.96%)}}
+@item @code{NEGPAREN@i{w}.@i{d}}
+@tab Encloses negative numbers in parentheses.
+@tab @t{@w{ }42.96}
+@tab @t{@w{ }(42.96)}
+
+@item @code{NEQUAL@i{w}.@i{d}}
+@tab Adds a @code{N=} prefix.
+@tab @t{@w{ }N=42.96}
+@tab @t{@w{ }N=-42.96}
+
+@item @code{@code{PAREN@i{w}.@i{d}}}
+@tab Encloses all numbers in parentheses.
+@tab @t{@w{ }(42.96)}
+@tab @t{@w{ }(-42.96)}
+
+@item @code{PCTPAREN@i{w}.@i{d}}
+@tab Encloses all numbers in parentheses with a @samp{%} suffix.
+@tab @t{@w{ }(42.96%)}
+@tab @t{(-42.96%)}
+@end multitable
+
+Parentheses provide a shorthand to apply summary specifications to
+multiple variables. For example, both of these commands:
+
+@example
+CTABLES /TABLE=AgeGroup[COLPCT] + qns1[COLPCT] BY qns3a.
+CTABLES /TABLE=(AgeGroup + qns1)[COLPCT] BY qns3a.
+@end example
+
+@noindent
+produce the same output shown below:
+
+@psppoutput {ctables12}
+
+The following sections list the available summary functions. After
+each function's name is given its default label and format. If no
+format is listed, then the default format is the print format for the
+variable being summarized.
+
+@menu
+* CTABLES Summary Functions for Individual Cells::
+* CTABLES Summary Functions for Groups of Cells::
+* CTABLES Summary Functions for Adjusted Weights::
+* CTABLES Unweighted Summary Functions::
+@end menu
+
+@node CTABLES Summary Functions for Individual Cells
+@subsubsection Summary Functions for Individual Cells
+
+This section lists the summary functions that consider only an
+individual cell in @code{CTABLES}. Only one such summary function,
+@code{COUNT}, may be applied to both categorical and scale variables:
+
+@table @asis
+@item @code{COUNT} (``Count'', F40.0)
+The sum of weights in a cell.
+
+If @code{CATEGORIES} for one or more of the variables in a table
+include missing values (@pxref{CTABLES Per-Variable Category
+Options}), then some or all of the categories for a cell might be
+missing values. @code{COUNT} counts data included in a cell
+regardless of whether its categories are missing.
+@end table
+
+The following summary functions apply only to scale variables or
+totals and subtotals for categorical variables. Be cautious about
+interpreting the summary value in the latter case, because it is not
+necessarily meaningful; however, the mean of a Likert scale, etc.@:
+may have a straightforward interpreation.
+
+@table @asis
+@item @code{MAXIMUM} (``Maximum'')
+The largest value.
+
+@item @code{MEAN} (``Mean'')
+The mean.
+
+@item @code{MEDIAN} (``Median'')
+The median value.
+
+@item @code{MINIMUM} (``Minimum'')
+The smallest value.
+
+@item @code{MISSING} (``Missing'')
+Sum of weights of user- and system-missing values.
+
+@item @code{MODE} (``Mode'')
+The highest-frequency value. Ties are broken by taking the smallest mode.
+
+@item @code{PTILE} @i{n} (``Percentile @i{n}'')
+The @var{n}th percentile, where @math{0 @leq{} @var{n} @leq{} 100}.
+
+@item @code{RANGE} (``Range'')
+The maximum minus the minimum.
+
+@item @code{SEMEAN} (``Std Error of Mean'')
+The standard error of the mean.
+
+@item @code{STDDEV} (``Std Deviation'')
+The standard deviation.
+
+@item @code{SUM} (``Sum'')
+The sum.
+
+@item @code{TOTALN} (``Total N'', F40.0)
+The sum of weights in a cell.
+
+For scale data, @code{COUNT} and @code{TOTALN} are the same.
+
+For categorical data, @code{TOTALN} counts missing values in excluded
+categories, that is, user-missing values not in an explicit category
+list on @code{CATEGORIES} (@pxref{CTABLES Per-Variable Category
+Options}), or user-missing values excluded because
+@code{MISSING=EXCLUDE} is in effect on @code{CATEGORIES}, or
+system-missing values. @code{COUNT} does not count these.
+
+@item @code{VALIDN} (``Valid N'', F40.0)
+The sum of valid count weights in included categories.
+
+@code{VALIDN} does not count missing values regardless of whether they
+are in included categories via @code{CATEGORIES}. @code{VALIDN} does
+not count valid values that are in excluded categories.
+
+@item @code{VARIANCE} (``Variance'')
+The variance.
+@end table
+
+@node CTABLES Summary Functions for Groups of Cells
+@subsubsection Summary Functions for Groups of Cells
+
+These summary functions summarize over multiple cells within an area
+of the output chosen by the user and specified as part of the function
+name. The following basic @var{area}s are supported, in decreasing
+order of size:
+
+@table @code
+@item TABLE
+A @dfn{section}. Stacked variables divide sections of the output from
+each other. sections may span multiple layers.
+
+@item LAYER
+A section within a single layer.
+
+@item SUBTABLE
+A @dfn{subtable}, whose contents are the cells that pair an innermost
+row variable and an innermost column variable within a single layer.
+@end table
+
+The following shows how the output for the table expression @code{qn61
+> qn57 BY qnd7a > qn86 + qn64b BY qns3a}@footnote{This is not
+necessarily a meaningful table, so for clarity variable labels are
+omitted.} is divided up into @code{TABLE}, @code{LAYER}, and
+@code{SUBTABLE} areas. Each unique value for Table ID is one section,
+and similarly for Layer ID and Subtable ID. Thus, this output has two
+@code{TABLE} areas (one for @code{qnd7a} and one for @code{qn64b}),
+four @code{LAYER} areas (for those two variables, per layer), and 12
+@code{SUBTABLE} areas.
+@psppoutput {ctables22}
+
+@code{CTABLES} also supports the following @var{area}s that further
+divide a subtable or a layer within a section:
+
+@table @code
+@item LAYERROW
+@itemx LAYERCOL
+A row or column, respectively, in one layer of a section.
+
+@item ROW
+@itemx COL
+A row or column, respectively, in a subtable.
+@end table
+
+The following summary functions for groups of cells are available for
+each @var{area} described above, for both categorical and scale
+variables:
+
+@table @asis
+@item @code{@i{area}PCT} or @code{@i{area}PCT.COUNT} (``@i{Area} %'', PCT40.1)
+A percentage of total counts within @var{area}.
+
+@item @code{@i{area}PCT.VALIDN} (``@i{Area} Valid N %'', PCT40.1)
+A percentage of total counts for valid values within @var{area}.
+
+@item @code{@i{area}PCT.TOTALN} (``@i{Area} Total N %'', PCT40.1)
+A percentage of total counts for all values within @var{area}.
+@end table
+
+Scale variables and totals and subtotals for categorical variables may
+use the following additional group cell summary function:
+
+@table @asis
+@item @code{@i{area}PCT.SUM} (``@i{Area} Sum %'', PCT40.1)
+Percentage of the sum of the values within @var{area}.
+@end table
+
+@node CTABLES Summary Functions for Adjusted Weights
+@subsubsection Summary Functions for Adjusted Weights
+
+If the @code{WEIGHT} subcommand specified an adjustment weight
+variable, then the following summary functions use its value instead
+of the dictionary weight variable. Otherwise, they are equivalent to
+the summary function without the @samp{E}-prefix:
+
+@itemize @bullet
+@item
+@code{ECOUNT} (``Adjusted Count'', F40.0)
+
+@item
+@code{ETOTALN} (``Adjusted Total N'', F40.0)
+
+@item
+@code{EVALIDN} (``Adjusted Valid N'', F40.0)
+@end itemize
+
+@node CTABLES Unweighted Summary Functions
+@subsubsection Unweighted Summary Functions
+
+The following summary functions with a @samp{U}-prefix are equivalent
+to the same ones without the prefix, except that they use unweighted
+counts:
+
+@itemize @bullet
+@item
+@code{UCOUNT} (``Unweighted Count'', F40.0)
+
+@item
+@code{U@i{area}PCT} or @code{U@i{area}PCT.COUNT} (``Unweighted @i{Area} %'', PCT40.1)
+
+@item
+@code{U@i{area}PCT.VALIDN} (``Unweighted @i{Area} Valid N %'', PCT40.1)
+
+@item
+@code{U@i{area}PCT.TOTALN} (``Unweighted @i{Area} Total N %'', PCT40.1)
+
+@item
+@code{UMEAN} (``Unweighted Mean'')
+
+@item
+@code{UMEDIAN} (``Unweighted Median'')
+
+@item
+@code{UMISSING} (``Unweighted Missing'')
+
+@item
+@code{UMODE} (``Unweight Mode'')
+
+@item
+@code{U@i{area}PCT.SUM} (``Unweighted @i{Area} Sum %'', PCT40.1)
+
+@item
+@code{UPTILE} @i{n} (``Unweighted Percentile @i{n}'')
+
+@item
+@code{USEMEAN} (``Unweighted Std Error of Mean'')
@item
-LABELS, the default, allows variable labels and value labels to appear
-in the output. NOLABELS suppresses them. NOVALLABS displays variable
-labels but suppresses value labels.
+@code{USTDDEV} (``Unweighted Std Deviation'')
@item
-PIVOT, the default, causes each TABLES subcommand to be displayed in a
-pivot table format. NOPIVOT causes the old-style crosstabulation format
-to be used.
+@code{USUM} (``Unweighted Sum'')
@item
-AVALUE, the default, causes values to be sorted in ascending order.
-DVALUE asserts a descending sort order.
+@code{UTOTALN} (``Unweighted Total N'', F40.0)
@item
-INDEX/NOINDEX is currently ignored.
+@code{UVALIDN} (``Unweighted Valid N'', F40.0)
@item
-BOX/NOBOX is currently ignored.
+@code{UVARIANCE} (``Unweighted Variance'', F40.0)
@end itemize
-The CELLS subcommand controls the contents of each cell in the displayed
-crosstabulation table. The possible settings are:
+@node CTABLES Statistics Positions and Labels
+@subsection Statistics Positions and Labels
+
+@display
+@t{/SLABELS}
+ [@t{POSITION=}@{@t{COLUMN} @math{|} @t{ROW} @math{|} @t{LAYER}@}]
+ [@t{VISIBLE=}@{@t{YES} @math{|} @t{NO}@}]
+@end display
+
+The @code{SLABELS} subcommand controls the position and visibility of
+summary statistics for the @code{TABLE} subcommand that it follows.
+
+@code{POSITION} sets the axis on which summary statistics appear.
+With @t{POSITION=COLUMN}, which is the default, each summary statistic
+appears in a column. For example:
+
+@example
+CTABLES /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a.
+@end example
+@psppoutput {ctables13}
+
+@noindent
+With @t{POSITION=ROW}, each summary statistic appears in a row, as
+shown below:
+
+@example
+CTABLES /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a /SLABELS POSITION=ROW.
+@end example
+@psppoutput {ctables14}
+
+@noindent
+@t{POSITION=LAYER} is also available to place each summary statistic in
+a separate layer.
+
+Labels for summary statistics are shown by default. Use
+@t{VISIBLE=NO} to suppress them. Because unlabeled data can cause
+confusion, it should only be considered if the meaning of the data is
+evident, as in a simple case like this:
+
+@example
+CTABLES /TABLE=AgeGroup [TABLEPCT] /SLABELS VISIBLE=NO.
+@end example
+@psppoutput {ctables15}
+
+@node CTABLES Category Label Positions
+@subsection Category Label Positions
+
+@display
+@t{/CLABELS} @{@t{AUTO} @math{|} @{@t{ROWLABELS}@math{|}@t{COLLABELS}@}@t{=}@{@t{OPPOSITE}@math{|}@t{LAYER}@}@}
+@end display
+
+The @code{CLABELS} subcommand controls the position of category labels
+for the @code{TABLE} subcommand that it follows. By default, or if
+@t{AUTO} is specified, category labels for a given variable nest
+inside the variable's label on the same axis. For example, the
+command below results in age categories nesting within the age group
+variable on the rows axis and gender categories within the gender
+variable on the columns axis:
+
+@example
+CTABLES /TABLE AgeGroup BY qns3a.
+@end example
+@psppoutput {ctables16}
+
+@t{ROWLABELS=OPPOSITE} or @t{COLLABELS=OPPOSITE} move row or column
+variable category labels, respectively, to the opposite axis. The
+setting affects only the innermost variable on the given axis. For
+example:
+
+@example
+CTABLES /TABLE AgeGroup BY qns3a /CLABELS ROWLABELS=OPPOSITE.
+CTABLES /TABLE AgeGroup BY qns3a /CLABELS COLLABELS=OPPOSITE.
+@end example
+@psppoutput {ctables17}
+
+@t{ROWLABELS=LAYER} or @t{COLLABELS=LAYER} move the innermost row or
+column variable category labels, respectively, to the layer axis.
+
+Only one axis's labels may be moved, whether to the opposite axis or
+to the layer axis.
+
+@c TODO Moving category labels for stacked variables
+
+@subsubheading Effect on Summary Statistics
+
+@code{CLABELS} primarily affects the appearance of tables, not the
+data displayed in them. However, @code{CTABLES} can affect the values
+displayed for statistics that summarize areas of a table, since it can
+change the definitions of these areas.
+
+For example, consider the following syntax and output:
+
+@example
+CTABLES /TABLE AgeGroup BY qns3a [ROWPCT, COLPCT].
+@end example
+@psppoutput {ctables23}
+
+@noindent
+Using @code{COLLABELS=OPPOSITE} changes the definitions of rows and
+columns, so that column percentages display what were previously row
+percentages and the new row percentages become meaningless (because
+there is only one cell per row):
+
+@example
+CTABLES
+ /TABLE AgeGroup BY qns3a [ROWPCT, COLPCT]
+ /CLABELS COLLABELS=OPPOSITE.
+@end example
+@psppoutput {ctables24}
+
+@node CTABLES Per-Variable Category Options
+@subsection Per-Variable Category Options
+
+@display
+@t{/CATEGORIES} @t{VARIABLES=}@i{variables}
+ @{@t{[}@i{value}@t{,} @i{value}@dots{}@t{]}
+ @math{|} [@t{ORDER=}@{@t{A} @math{|} @t{D}@}]
+ [@t{KEY=}@{@t{VALUE} @math{|} @t{LABEL} @math{|} @i{summary}@t{(}@i{variable}@t{)}@}]
+ [@t{MISSING=}@{@t{EXCLUDE} @math{|} @t{INCLUDE}@}]@}
+ [@t{TOTAL=}@{@t{NO} @math{|} @t{YES}@} [@t{LABEL=}@i{string}] [@t{POSITION=}@{@t{AFTER} @math{|} @t{BEFORE}@}]]
+ [@t{EMPTY=}@{@t{INCLUDE} @math{|} @t{EXCLUDE}@}]
+@end display
+
+The @code{CATEGORIES} subcommand specifies, for one or more
+categorical variables, the categories to include and exclude, the sort
+order for included categories, and treatment of missing values. It
+also controls the totals and subtotals to display. It may be
+specified any number of times, each time for a different set of
+variables. @code{CATEGORIES} applies to the table produced by the
+@code{TABLE} subcommand that it follows.
+
+@code{CATEGORIES} does not apply to scalar variables.
+
+@t{VARIABLES} is required and must list the variables for the subcommand
+to affect.
+
+There are two way to specify the Categories to include and their sort
+order:
@table @asis
-@item COUNT
-Frequency count.
-@item ROW
-Row percent.
-@item COLUMN
-Column percent.
+@item Explicit categories.
+@anchor{CTABLES Explicit Category List}
+To explicitly specify categories to include, list the categories
+within square brackets in the desired sort order. Use spaces or
+commas to separate values. Categories not covered by the list are
+excluded from analysis.
+
+Each element of the list takes one of the following forms:
+
+@table @t
+@item @i{number}
+@itemx '@i{string}'
+A numeric or string category value, for variables that have the
+corresponding type.
+
+@item '@i{date}'
+@itemx '@i{time}'
+A date or time category value, for variables that have a date or time
+print format.
+
+@item @i{min} THRU @i{max}
+@itemx LO THRU @i{max}
+@itemx @i{min} THRU HI
+A range of category values, where @var{min} and @var{max} each takes
+one of the forms above, in increasing order.
+
+@item MISSING
+All user-missing values. (To match individual user-missing values,
+specify their category values.)
+
+@item OTHERNM
+Any non-missing value not covered by any other element of the list
+(regardless of where @t{OTHERNM} is placed in the list).
+
+@item &@i{postcompute}
+A computed category name (@pxref{CTABLES Computed Categories}).
+@end table
+
+Additional forms, described later, allow for subtotals.
+If multiple elements of the list cover a given category, the last one
+in the list takes precedence.
+
+@item Implicit categories.
+Without an explicit list of categories, @pspp{} sorts
+categories automatically.
+
+The @code{KEY} setting specifies the sort key. By default, or with
+@code{KEY=VALUE}, categories are sorted by default. Categories may
+also be sorted by value label, with @code{KEY=LABEL}, or by the value
+of a summary function, e.g.@: @code{KEY=COUNT}.
+@ignore @c Not yet implemented
+For summary functions, a variable name may be specified in
+parentheses, e.g.@: @code{KEY=MAXIUM(qnd1)}, and this is required for
+functions that apply only to scalar variables. The @code{PTILE}
+function also requires a percentage argument, e.g.@:
+@code{KEY=PTILE(qnd1, 90)}. Only summary functions used in the table
+may be used, except that @code{COUNT} is always allowed.
+@end ignore
+
+By default, or with @code{ORDER=A}, categories are sorted in ascending
+order. Specify @code{ORDER=D} to sort in descending order.
+
+User-missing values are excluded by default, or with
+@code{MISSING=EXCLUDE}. Specify @code{MISSING=INCLUDE} to include
+user-missing values. The system-missing value is always excluded.
+@end table
+
+@subsubheading Totals and Subtotals
+
+@code{CATEGORIES} also controls display of totals and subtotals.
+Totals are not displayed with @code{TOTAL=NO}, which is also the
+default. Specify @code{TOTAL=YES} to display a total. By default,
+the total is labeled ``Total''; use @code{LABEL="@i{label}"} to
+override it.
+
+Subtotals are also not displayed by default. To add one or more
+subtotals, use an explicit category list and insert @code{SUBTOTAL} or
+@code{HSUBTOTAL} in the position or positions where the subtotal
+should appear. With @code{SUBTOTAL}, the subtotal becomes an extra
+row or column or layer; @code{HSUBTOTAL} additionally hides the
+categories that make up the subtotal. Either way, the default label
+is ``Subtotal'', use @code{SUBTOTAL="@i{label}"} or
+@code{HSUBTOTAL="@i{label}"} to specify a custom label.
+
+By default, or with @code{POSITION=AFTER}, totals are displayed in the
+output after the last category and subtotals apply to categories that
+precede them. With @code{POSITION=BEFORE}, totals come before the
+first category and subtotals apply to categories that follow them.
+
+Only categorical variables may have totals and subtotals. Scalar
+variables may be ``totaled'' indirectly by enabling totals and
+subtotals on a categorical variable within which the scalar variable is
+summarized.
+
+@c TODO Specifying summaries for totals and subtotals
+
+@subsubheading Categories Without Values
+
+Some categories might not be included in the data set being analyzed.
+For example, our example data set has no cases in the ``15 or
+younger'' age group. By default, or with @code{EMPTY=INCLUDE},
+@pspp{} includes these empty categories in output tables. To exclude
+them, specify @code{EMPTY=EXCLUDE}.
+
+For implicit categories, empty categories potentially include all the
+values with value labels for a given variable; for explicit
+categories, they include all the values listed individually and all
+values with value labels that are covered by ranges or @code{MISSING}
+or @code{OTHERNM}.
+
+@node CTABLES Titles
+@subsection Titles
+
+@display
+@t{/TITLES}
+ [@t{TITLE=}@i{string}@dots{}]
+ [@t{CAPTION=}@i{string}@dots{}]
+ [@t{CORNER=}@i{string}@dots{}]
+@end display
+
+@c TODO Describe substitution variables
+
+The @code{TITLES} subcommand sets the title, caption, and corner text
+for the table output for the previous @code{TABLE} subcommand. The
+title appears above the table, the caption below the table, and the
+corner text appears in the table's upper left corner. By default, the
+title is ``Custom Tables'' and the caption and corner text are empty.
+With some table output styles, the corner text is not displayed.
+
+@node CTABLES Table Formatting
+@subsection Table Formatting
+
+@display
+@t{/FORMAT}
+ [@t{MINCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
+ [@t{MAXCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
+ [@t{UNITS=}@{@t{POINTS} @math{|} @t{INCHES} @math{|} @t{CM}@}]
+ [@t{EMPTY=}@{@t{ZERO} @math{|} @t{BLANK} @math{|} @i{string}@}]
+ [@t{MISSING=}@i{string}]
+@end display
+
+The @code{FORMAT} subcommand, which must precede the first
+@code{TABLE} subcommand, controls formatting for all the output
+tables. @code{FORMAT} and all of its settings are optional.
+
+Use @code{MINCOLWIDTH} and @code{MAXCOLWIDTH} to control the minimum
+or maximum width of columns in output tables. By default, with
+@code{DEFAULT}, column width varies based on content. Otherwise,
+specify a number for either or both of these settings. If both are
+specified, @code{MAXCOLWIDTH} must be greater than or equal to
+@code{MINCOLWIDTH}. The default unit, or with @code{UNITS=POINTS}, is
+points (1/72 inch), or specify @code{UNITS=INCHES} to use inches or
+@code{UNITS=CM} for centimeters.
+
+By default, or with @code{EMPTY=ZERO}, zero values are displayed in
+their usual format. Use @code{EMPTY=BLANK} to use an empty cell
+instead, or @code{EMPTY="@i{string}"} to use the specified string.
+
+By default, missing values are displayed as @samp{.}, the same as in
+other tables. Specify @code{MISSING="@i{string}"} to instead use a
+custom string.
+
+@node CTABLES Display of Variable Labels
+@subsection Display of Variable Labels
+
+@display
+@t{/VLABELS}
+ @t{VARIABLES=}@i{variables}
+ @t{DISPLAY}=@{@t{DEFAULT} @math{|} @t{NAME} @math{|} @t{LABEL} @math{|} @t{BOTH} @math{|} @t{NONE}@}
+@end display
+
+The @code{VLABELS} subcommand, which must precede the first
+@code{TABLE} subcommand, controls display of variable labels in all
+the output tables. @code{VLABELS} is optional. It may appear
+multiple times to adjust settings for different variables.
+
+@code{VARIABLES} and @code{DISPLAY} are required. The value of
+@code{DISPLAY} controls how variable labels are displayed for the
+variables listed on @code{VARIABLES}. The supported values are:
+
+@table @code
+@item DEFAULT
+Use the setting from @code{SET TVARS} (@pxref{SET TVARS}).
+
+@item NAME
+Show only a variable name.
+
+@item LABEL
+Show only a variable label.
+
+@item BOTH
+Show variable name and label.
+
+@item NONE
+Show nothing.
+@end table
+
+@node CTABLES Missing Value Treatment
+@subsection Missing Value Treatment
+
+@display
+@t{/SMISSING} @{@t{VARIABLE} @math{|} @t{LISTWISE}@}
+@end display
+
+The @code{SMISSING} subcommand, which must precede the first
+@code{TABLE} subcommand, controls treatment of missing values for
+scalar variables in producing all the output tables. @code{SMISSING}
+is optional.
+
+With @code{SMISSING=VARIABLE}, which is the default, missing values
+are excluded on a variable-by-variable basis. With
+@code{SMISSING=LISTWISE}, when stacked scalar variables are nested
+together with a categorical variable, a missing value for any of the
+scalar variables causes the case to be excluded for all of them.
+
+As an example, consider the following dataset, in which @samp{x} is a
+categorical variable and @samp{y} and @samp{z} are scale:
+
+@psppoutput{ctables18}
+
+@noindent
+With the default missing-value treatment, @samp{x}'s mean is 20, based
+on the values 10, 20, and 30, and @samp{y}'s mean is 50, based on 40,
+50, and 60:
+
+@example
+CTABLES /TABLE (y + z) > x.
+@end example
+@psppoutput{ctables19}
+
+@noindent
+By adding @code{SMISSING=LISTWISE}, only cases where @samp{y} and
+@samp{z} are both non-missing are considered, so @samp{x}'s mean
+becomes 15, as the average of 10 and 20, and @samp{y}'s mean becomes
+55, the average of 50 and 60:
+
+@example
+CTABLES /SMISSING LISTWISE /TABLE (y + z) > x.
+@end example
+@psppoutput{ctables20}
+
+@noindent
+Even with @code{SMISSING=LISTWISE}, if @samp{y} and @samp{z} are
+separately nested with @samp{x}, instead of using a single @samp{>}
+operator, missing values revert to being considered on a
+variable-by-variable basis:
+
+@example
+CTABLES /SMISSING LISTWISE /TABLE (y > x) + (z > x).
+@end example
+@psppoutput{ctables21}
+
+@node CTABLES Computed Categories
+@subsection Computed Categories
+
+@display
+@t{/PCOMPUTE} @t{&}@i{postcompute}@t{=EXPR(}@i{expression}@t{)}
+@end display
+
+@dfn{Computed categories}, also called @dfn{postcomputes}, are
+categories created using arithmetic on categories obtained from the
+data. The @code{PCOMPUTE} subcommand defines computed categories,
+which can then be used in two places: on @code{CATEGORIES} within an
+explicit category list (@pxref{CTABLES Explicit Category List}), and on
+the @code{PPROPERTIES} subcommand to define further properties for a
+given postcompute.
+
+@code{PCOMPUTE} must precede the first @code{TABLE} command. It is
+optional and it may be used any number of times to define multiple
+postcomputes.
+
+Each @code{PCOMPUTE} defines one postcompute. Its syntax consists of
+a name to identify the postcompute as a @pspp{} identifier prefixed by
+@samp{&}, followed by @samp{=} and a postcompute expression enclosed
+in @code{EXPR(@dots{})}. A postcompute expression consists of:
+
+@table @t
+@item [@i{category}]
+This form evaluates to the summary statistic for @i{category}, e.g.@:
+@code{[1]} evaluates to the value of the summary statistic associated
+with category 1. The @i{category} may be a number, a quoted string,
+or a quoted time or date value. All of the categories for a given
+postcompute must have the same form. The category must appear in all
+the @code{CATEGORIES} list in which the postcompute is used.
+
+@item [@i{min} THRU @i{max}]
+@itemx [LO THRU @i{max}]
+@itemx [@i{min} THRU HI]
+@itemx MISSING
+@itemx OTHERNM
+These forms evaluate to the summary statistics for a category
+specified with the same syntax, as described in previous section
+(@pxref{CTABLES Explicit Category List}). The category must appear in
+all the @code{CATEGORIES} list in which the postcompute is used.
+
+@item SUBTOTAL
+The summary statistic for the subtotal category. This form is allowed
+only if the @code{CATEGORIES} lists that include this postcompute have
+exactly one subtotal.
+
+@item SUBTOTAL[@i{index}]
+The summary statistic for subtotal category @i{index}, where 1 is the
+first subtotal, 2 is the second, and so on. This form may be used for
+@code{CATEGORIES} lists with any number of subtotals.
+
@item TOTAL
-Table percent.
-@item EXPECTED
-Expected value.
-@item RESIDUAL
-Residual.
-@item SRESIDUAL
-Standardized residual.
-@item ASRESIDUAL
-Adjusted standardized residual.
-@item ALL
-All of the above.
-@item NONE
-Suppress cells entirely.
+The summary statistic for the total. The @code{CATEGORIES} lsits that
+include this postcompute must have a total enabled.
+
+@item @i{a} + @i{b}
+@itemx @i{a} - @i{b}
+@itemx @i{a} * @i{b}
+@itemx @i{a} / @i{b}
+@itemx @i{a} ** @i{b}
+These forms perform arithmetic on the values of postcompute
+expressions @i{a} and @i{b}. The usual operator precedence rules
+apply.
+
+@item @i{number}
+Numeric constants may be used in postcompute expressions.
+
+@item (@i{a})
+Parentheses override operator precedence.
@end table
-@samp{/CELLS} without any settings specified requests COUNT, ROW,
-COLUMN, and TOTAL. If CELLS is not specified at all then only COUNT
-will be selected.
+A postcompute is not associated with any particular variable.
+Instead, it may be referenced within @code{CATEGORIES} for any
+suitable variable (e.g.@: only a string variable is suitable for a
+postcompute expression that refers to a string category, only a
+variable with subtotals for an expression that refers to subtotals,
+@dots{}).
-The STATISTICS subcommand selects statistics for computation:
+Normally a named postcompute is defined only once, but if a later
+@code{PCOMPUTE} redefines a postcompute with the same name as an
+earlier one, the later one take precedence.
-@table @asis
-@item CHISQ
-@cindex chisquare
-@cindex chi-square
+@node CTABLES Computed Category Properties
+@subsection Computed Category Properties
-Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
-correction, linear-by-linear association.
-@item PHI
-Phi.
-@item CC
-Contingency coefficient.
-@item LAMBDA
-Lambda.
-@item UC
-Uncertainty coefficient.
-@item BTAU
-Tau-b.
-@item CTAU
-Tau-c.
-@item RISK
-Risk estimate.
-@item GAMMA
-Gamma.
-@item D
-Somers' D.
-@item KAPPA
-Cohen's Kappa.
-@item ETA
-Eta.
-@item CORR
-Spearman correlation, Pearson's r.
-@item ALL
-All of the above.
-@item NONE
-No statistics.
-@end table
+@display
+@t{/PPROPERTIES} @t{&}@i{postcompute}@dots{}
+ [@t{LABEL=}@i{string}]
+ [@t{FORMAT=}[@i{summary} @i{format}]@dots{}]
+ [@t{HIDESOURCECATS=}@{@t{NO} @math{|} @t{YES}@}
+@end display
-Selected statistics are only calculated when appropriate for the
-statistic. Certain statistics require tables of a particular size, and
-some statistics are calculated only in integer mode.
+The @code{PPROPERTIES} subcommand, which must appear before
+@code{TABLE}, sets properties for one or more postcomputes defined on
+prior @code{PCOMPUTE} subcommands. The subcommand syntax begins with
+the list of postcomputes, each prefixed with @samp{&} as specified on
+@code{PCOMPUTE}.
-@samp{/STATISTICS} without any settings selects CHISQ. If the
-STATISTICS subcommand is not given, no statistics are calculated.
+All of the settings on @code{PPROPERTIES} are optional. Use
+@code{LABEL} to set the label shown for the postcomputes in table
+output. The default label for a postcompute is the expression used to
+define it.
-@strong{Please note:} Currently the implementation of CROSSTABS has the
-followings bugs:
+The @code{FORMAT} setting sets summary statistics and display formats
+for the postcomputes.
-@itemize @bullet
-@item
-Pearson's R (but not Spearman) is off a little.
-@item
-T values for Spearman's R and Pearson's R are wrong.
-@item
-Significance of symmetric and directional measures is not calculated.
-@item
-Asymmetric ASEs and T values for lambda are wrong.
-@item
-ASE of Goodman and Kruskal's tau is not calculated.
-@item
-ASE of symmetric somers' d is wrong.
-@item
-Approximate T of uncertainty coefficient is wrong.
-@end itemize
+By default, or with @code{HIDESOURCECATS=NO}, categories referred to
+by computed categories are displayed like other categories. Use
+@code{HIDESOURCECATS=YES} to hide them.
-Fixes for any of these deficiencies would be welcomed.
+@node CTABLES Base Weight
+@subsection Base Weight
+
+@display
+@t{/WEIGHT VARIABLE=}@i{variable}
+@end display
+
+The @code{WEIGHT} subcommand is optional and must appear before
+@code{TABLE}. If it appears, it must name a numeric variable, known
+as the @dfn{effective base weight} or @dfn{adjustment weight}. The
+effective base weight variable stands in for the dictionary's weight
+variable (@pxref{WEIGHT}), if any, in most calculations in
+@code{CTABLES}. The only exceptions are the @code{COUNT},
+@code{TOTALN}, and @code{VALIDN} summary functions, which use the
+dictionary weight instead.
+
+Weights obtained from the @pspp{} dictionary are rounded to the
+nearest integer at the case level. Effective base weights are not
+rounded. Regardless of the weighting source, @pspp{} does not analyze
+cases with zero, missing, or negative effective weights.
+
+@node CTABLES Hiding Small Counts
+@subsection Hiding Small Counts
+
+@display
+@t{/HIDESMALLCOUNTS COUNT=@i{count}}
+@end display
+
+The @code{HIDESMALLCOUNTS} subcommand is optional. If it specified,
+then count values in output tables less than the value of @i{count}
+are shown as @code{<@i{count}} instead of their true values. The
+value of @i{count} must be an integer and must be at least 2. Case
+weights are considered for deciding whether to hide a count.
@node FACTOR
@section FACTOR
@cindex data reduction
@display
-FACTOR VARIABLES=var_list
+FACTOR @{
+ VARIABLES=@var{var_list},
+ MATRIX IN (@{CORR,COV@}=@{*,@var{file_spec}@})
+ @}
[ /METHOD = @{CORRELATION, COVARIANCE@} ]
- [ /EXTRACTION=@{PC, PAF@}]
+ [ /ANALYSIS=@var{var_list} ]
- [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
+ [ /EXTRACTION=@{PC, PAF@}]
- [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [SIG] [ALL] [DEFAULT] ]
+ [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
+
+ [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [AIC] [SIG] [ALL] [DEFAULT] ]
[ /PLOT=[EIGEN] ]
[ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
@end display
-The FACTOR command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
+The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
common factors in the data or for data reduction purposes.
-The VARIABLES subcommand is required. It lists the variables which are to partake in the analysis.
-
-The /EXTRACTION subcommand is used to specify the way in which factors (components) are extracted from the data.
-If PC is specified, then Principal Components Analysis is used. If PAF is specified, then Principal Axis Factoring is
-used. By default Principal Components Analysis will be used.
-
-The /ROTATION subcommand is used to specify the method by which the extracted solution will be rotated.
-Three methods are available: VARIMAX (which is the default), EQUAMAX, and QUARTIMAX.
-If don't want any rotation to be performed, the word NOROTATE will prevent the command from performing any
-rotation on the data. Oblique rotations are not supported.
-
-The /METHOD subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
+The @subcmd{VARIABLES} subcommand is required (unless the @subcmd{MATRIX IN}
+subcommand is used).
+It lists the variables which are to partake in the analysis. (The @subcmd{ANALYSIS}
+subcommand may optionally further limit the variables that
+participate; it is useful primarily in conjunction with @subcmd{MATRIX IN}.)
+
+If @subcmd{MATRIX IN} instead of @subcmd{VARIABLES} is specified, then the analysis
+is performed on a pre-prepared correlation or covariance matrix file instead of on
+individual data cases. Typically the matrix file will have been generated by
+@cmd{MATRIX DATA} (@pxref{MATRIX DATA}) or provided by a third party.
+If specified, @subcmd{MATRIX IN} must be followed by @samp{COV} or @samp{CORR},
+then by @samp{=} and @var{file_spec} all in parentheses.
+@var{file_spec} may either be an asterisk, which indicates the currently loaded
+dataset, or it may be a file name to be loaded. @xref{MATRIX DATA}, for the expected
+format of the file.
+
+The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors
+(components) are extracted from the data.
+If @subcmd{PC} is specified, then Principal Components Analysis is used.
+If @subcmd{PAF} is specified, then Principal Axis Factoring is
+used. By default Principal Components Analysis is used.
+
+The @subcmd{/ROTATION} subcommand is used to specify the method by which the
+extracted solution is rotated. Three orthogonal rotation methods are available:
+@subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
+There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
+Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
+The default value of @var{k} is 5.
+If you don't want any rotation to be performed, the word @subcmd{NOROTATE}
+prevents the command from performing any rotation on the data.
+
+The @subcmd{/METHOD} subcommand should be used to determine whether the
+covariance matrix or the correlation matrix of the data is
to be analysed. By default, the correlation matrix is analysed.
-The /PRINT subcommand may be used to select which features of the analysis are reported:
+The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
@itemize
-@item UNIVARIATE
+@item @subcmd{UNIVARIATE}
A table of mean values, standard deviations and total weights are printed.
-@item INITIAL
+@item @subcmd{INITIAL}
Initial communalities and eigenvalues are printed.
-@item EXTRACTION
+@item @subcmd{EXTRACTION}
Extracted communalities and eigenvalues are printed.
-@item ROTATION
+@item @subcmd{ROTATION}
Rotated communalities and eigenvalues are printed.
-@item CORRELATION
+@item @subcmd{CORRELATION}
The correlation matrix is printed.
-@item COVARIANCE
+@item @subcmd{COVARIANCE}
The covariance matrix is printed.
-@item DET
+@item @subcmd{DET}
The determinant of the correlation or covariance matrix is printed.
-@item SIG
+@item @subcmd{AIC}
+ The anti-image covariance and anti-image correlation matrices are printed.
+@item @subcmd{KMO}
+ The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
+@item @subcmd{SIG}
The significance of the elements of correlation matrix is printed.
-@item ALL
+@item @subcmd{ALL}
All of the above are printed.
-@item DEFAULT
- Identical to INITIAL and EXTRACTION.
+@item @subcmd{DEFAULT}
+ Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
@end itemize
-If /PLOT=EIGEN is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualising
+If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues is
+printed. This can be useful for visualizing the factors and deciding
which factors (components) should be retained.
-The /FORMAT subcommand determined how data are to be displayed in loading matrices. If SORT is specified, then the variables
-are sorted in descending order of significance. If BLANK(@var{n}) is specified, then coefficients whose absolute value is less
-than @var{n} will not be printed. If the keyword DEFAULT is given, or if no /FORMAT subcommand is given, then no sorting is
-performed, and all coefficients will be printed.
-
-The /CRITERIA subcommand is used to specify how the number of extracted factors (components) are chosen. If FACTORS(@var{n}) is
-specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the MINEIGEN setting will
-be used. MINEIGEN(@var{l}) requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
-The default value of @var{l} is 1. The ECONVERGE and ITERATE settings have effect only when iterative algorithms for factor
-extraction (such as Principal Axis Factoring) are used. ECONVERGE(@var{delta}) specifies that iteration should cease when
-the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
-default value of @var{delta} is 0.001.
-The ITERATE(@var{m}) setting sets the maximum number of iterations to @var{m}. The default value of @var{m} is 25.
-
-The @cmd{MISSING} subcommand determines the handling of missing variables.
-If INCLUDE is set, then user-missing values are included in the
+The @subcmd{/FORMAT} subcommand determined how data are to be
+displayed in loading matrices. If @subcmd{SORT} is specified, then
+the variables are sorted in descending order of significance. If
+@subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute
+value is less than @var{n} are not printed. If the keyword
+@subcmd{DEFAULT} is specified, or if no @subcmd{/FORMAT} subcommand is
+specified, then no sorting is performed, and all coefficients are printed.
+
+You can use the @subcmd{/CRITERIA} subcommand to specify how the number of
+extracted factors (components) are chosen. If @subcmd{FACTORS(@var{n})} is
+specified, where @var{n} is an integer, then @var{n} factors are
+extracted. Otherwise, the @subcmd{MINEIGEN} setting is used.
+@subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues
+are greater than or equal to @var{l} are extracted. The default value
+of @var{l} is 1. The @subcmd{ECONVERGE} setting has effect only when
+using iterative algorithms for factor extraction (such as Principal Axis
+Factoring). @subcmd{ECONVERGE(@var{delta})} specifies that
+iteration should cease when the maximum absolute value of the
+communality estimate between one iteration and the previous is less
+than @var{delta}. The default value of @var{delta} is 0.001.
+
+The @subcmd{ITERATE(@var{m})} may appear any number of times and is
+used for two different purposes. It is used to set the maximum number
+of iterations (@var{m}) for convergence and also to set the maximum
+number of iterations for rotation.
+Whether it affects convergence or rotation depends upon which
+subcommand follows the @subcmd{ITERATE} subcommand.
+If @subcmd{EXTRACTION} follows, it affects convergence.
+If @subcmd{ROTATION} follows, it affects rotation.
+If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a
+@subcmd{ITERATE} subcommand, then the entire subcommand is ignored.
+The default value of @var{m} is 25.
+
+The @cmd{MISSING} subcommand determines the handling of missing
+variables. If @subcmd{INCLUDE} is set, then user-missing values are
+included in the calculations, but system-missing values are not.
+If @subcmd{EXCLUDE} is set, which is the default, user-missing
+values are excluded as well as system-missing values. This is the
+default. If @subcmd{LISTWISE} is set, then the entire case is excluded
+from analysis whenever any variable specified in the @cmd{VARIABLES}
+subcommand contains a missing value.
+
+If @subcmd{PAIRWISE} is set, then a case is considered missing only if
+either of the values for the particular coefficient are missing.
+The default is @subcmd{LISTWISE}.
+
+@node GLM
+@section GLM
+
+@vindex GLM
+@cindex univariate analysis of variance
+@cindex fixed effects
+@cindex factorial anova
+@cindex analysis of variance
+@cindex ANOVA
+
+
+@display
+GLM @var{dependent_vars} BY @var{fixed_factors}
+ [/METHOD = SSTYPE(@var{type})]
+ [/DESIGN = @var{interaction_0} [@var{interaction_1} [... @var{interaction_n}]]]
+ [/INTERCEPT = @{INCLUDE|EXCLUDE@}]
+ [/MISSING = @{INCLUDE|EXCLUDE@}]
+@end display
+
+The @cmd{GLM} procedure can be used for fixed effects factorial Anova.
+
+The @var{dependent_vars} are the variables to be analysed.
+You may analyse several variables in the same command in which case they should all
+appear before the @code{BY} keyword.
+
+The @var{fixed_factors} list must be one or more categorical variables. Normally it
+does not make sense to enter a scalar variable in the @var{fixed_factors} and doing
+so may cause @pspp{} to do a lot of unnecessary processing.
+
+The @subcmd{METHOD} subcommand is used to change the method for producing the sums of
+squares. Available values of @var{type} are 1, 2 and 3. The default is type 3.
+
+You may specify a custom design using the @subcmd{DESIGN} subcommand.
+The design comprises a list of interactions where each interaction is a
+list of variables separated by a @samp{*}. For example the command
+@display
+GLM subject BY sex age_group race
+ /DESIGN = age_group sex group age_group*sex age_group*race
+@end display
+@noindent specifies the model @math{subject = age_group + sex + race + age_group*sex + age_group*race}.
+If no @subcmd{DESIGN} subcommand is specified, then the default is all possible combinations
+of the fixed factors. That is to say
+@display
+GLM subject BY sex age_group race
+@end display
+implies the model
+@math{subject = age_group + sex + race + age_group*sex + age_group*race + sex*race + age_group*sex*race}.
+
+
+The @subcmd{MISSING} subcommand determines the handling of missing
+variables.
+If @subcmd{INCLUDE} is set then, for the purposes of GLM analysis,
+only system-missing values are considered
+to be missing; user-missing values are not regarded as missing.
+If @subcmd{EXCLUDE} is set, which is the default, then user-missing
+values are considered to be missing as well as system-missing values.
+A case for which any dependent variable or any factor
+variable has a missing value is excluded from the analysis.
+
+@node LOGISTIC REGRESSION
+@section LOGISTIC REGRESSION
+
+@vindex LOGISTIC REGRESSION
+@cindex logistic regression
+@cindex bivariate logistic regression
+
+@display
+LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
+
+ [/CATEGORICAL = @var{categorical_predictors}]
+
+ [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
+
+ [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
+
+ [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
+ [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
+ [CUT(@var{cut_point})]]
+
+ [/MISSING = @{INCLUDE|EXCLUDE@}]
+@end display
+
+Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
+variable in terms of one or more predictor variables.
+
+The minimum command is
+@example
+LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
+@end example
+Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
+are the predictor variables whose coefficients the procedure estimates.
+
+By default, a constant term is included in the model.
+Hence, the full model is
+@math{
+{\bf y}
+= b_0 + b_1 {\bf x_1}
++ b_2 {\bf x_2}
++ \dots
++ b_n {\bf x_n}
+}
+
+Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
+Simple variables as well as interactions between variables may be listed here.
+
+If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
+@subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
+
+An iterative Newton-Raphson procedure is used to fit the model.
+The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
+and other parameters.
+The value of @var{cut_point} is used in the classification table. It is the
+threshold above which predicted values are considered to be 1. Values
+of @var{cut_point} must lie in the range [0,1].
+During iterations, if any one of the stopping criteria are satisfied, the procedure is
+considered complete.
+The stopping criteria are:
+@itemize
+@item The number of iterations exceeds @var{max_iterations}.
+ The default value of @var{max_iterations} is 20.
+@item The change in the all coefficient estimates are less than @var{min_delta}.
+The default value of @var{min_delta} is 0.001.
+@item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
+The default value of @var{min_delta} is zero.
+This means that this criterion is disabled.
+@item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
+In other words, the probabilities are close to zero or one.
+The default value of @var{min_epsilon} is 0.00000001.
+@end itemize
+
+
+The @subcmd{PRINT} subcommand controls the display of optional statistics.
+Currently there is one such option, @subcmd{CI}, which indicates that the
+confidence interval of the odds ratio should be displayed as well as its value.
+@subcmd{CI} should be followed by an integer in parentheses, to indicate the
+confidence level of the desired confidence interval.
+
+The @subcmd{MISSING} subcommand determines the handling of missing
+variables.
+If @subcmd{INCLUDE} is set, then user-missing values are included in the
calculations, but system-missing values are not.
-If EXCLUDE is set, which is the default, user-missing
-values are excluded as well as system-missing values.
+If @subcmd{EXCLUDE} is set, which is the default, user-missing
+values are excluded as well as system-missing values.
This is the default.
-If LISTWISE is set, then the entire case is excluded from analysis
-whenever any variable specified in the @cmd{VARIABLES} subcommand
-contains a missing value.
-If PAIRWISE is set, then a case is considered missing only if either of the
-values for the particular coefficient are missing.
-The default is LISTWISE.
-
+
+@node MEANS
+@section MEANS
+
+@vindex MEANS
+@cindex means
+
+@display
+MEANS [TABLES =]
+ @{@var{var_list}@}
+ [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
+
+ [ /@{@var{var_list}@}
+ [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
+
+ [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
+ [VARIANCE] [KURT] [SEKURT]
+ [SKEW] [SESKEW] [FIRST] [LAST]
+ [HARMONIC] [GEOMETRIC]
+ [DEFAULT]
+ [ALL]
+ [NONE] ]
+
+ [/MISSING = [INCLUDE] [DEPENDENT]]
+@end display
+
+You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
+statistics, either for the dataset as a whole or for categories of data.
+
+The simplest form of the command is
+@example
+MEANS @var{v}.
+@end example
+@noindent which calculates the mean, count and standard deviation for @var{v}.
+If you specify a grouping variable, for example
+@example
+MEANS @var{v} BY @var{g}.
+@end example
+@noindent then the means, counts and standard deviations for @var{v} after having
+been grouped by @var{g} are calculated.
+Instead of the mean, count and standard deviation, you could specify the statistics
+in which you are interested:
+@example
+MEANS @var{x} @var{y} BY @var{g}
+ /CELLS = HARMONIC SUM MIN.
+@end example
+This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
+grouped by @var{g}.
+
+The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
+are:
+@itemize
+@item @subcmd{MEAN}
+@cindex arithmetic mean
+ The arithmetic mean.
+@item @subcmd{COUNT}
+ The count of the values.
+@item @subcmd{STDDEV}
+ The standard deviation.
+@item @subcmd{SEMEAN}
+ The standard error of the mean.
+@item @subcmd{SUM}
+ The sum of the values.
+@item @subcmd{MIN}
+ The minimum value.
+@item @subcmd{MAX}
+ The maximum value.
+@item @subcmd{RANGE}
+ The difference between the maximum and minimum values.
+@item @subcmd{VARIANCE}
+ The variance.
+@item @subcmd{FIRST}
+ The first value in the category.
+@item @subcmd{LAST}
+ The last value in the category.
+@item @subcmd{SKEW}
+ The skewness.
+@item @subcmd{SESKEW}
+ The standard error of the skewness.
+@item @subcmd{KURT}
+ The kurtosis
+@item @subcmd{SEKURT}
+ The standard error of the kurtosis.
+@item @subcmd{HARMONIC}
+@cindex harmonic mean
+ The harmonic mean.
+@item @subcmd{GEOMETRIC}
+@cindex geometric mean
+ The geometric mean.
+@end itemize
+
+In addition, three special keywords are recognized:
+@itemize
+@item @subcmd{DEFAULT}
+ This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
+@item @subcmd{ALL}
+ All of the above statistics are calculated.
+@item @subcmd{NONE}
+ No statistics are calculated (only a summary is shown).
+@end itemize
+
+
+More than one @dfn{table} can be specified in a single command.
+Each table is separated by a @samp{/}. For
+example
+@example
+MEANS TABLES =
+ @var{c} @var{d} @var{e} BY @var{x}
+ /@var{a} @var{b} BY @var{x} @var{y}
+ /@var{f} BY @var{y} BY @var{z}.
+@end example
+has three tables (the @samp{TABLE =} is optional).
+The first table has three dependent variables @var{c}, @var{d} and @var{e}
+and a single categorical variable @var{x}.
+The second table has two dependent variables @var{a} and @var{b},
+and two categorical variables @var{x} and @var{y}.
+The third table has a single dependent variables @var{f}
+and a categorical variable formed by the combination of @var{y} and @var{z}.
+
+
+By default values are omitted from the analysis only if missing values
+(either system missing or user missing)
+for any of the variables directly involved in their calculation are
+encountered.
+This behaviour can be modified with the @subcmd{/MISSING} subcommand.
+Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
+
+@subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
+variables or in the categorical variables should be taken at their face
+value, and not excluded.
+
+@subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
+variables should be taken at their face value, however cases which
+have user missing values for the categorical variables should be omitted
+from the calculation.
+
+@subsection Example Means
+
+The dataset in @file{repairs.sav} contains the mean time between failures (@exvar{mtbf})
+for a sample of artifacts produced by different factories and trialed under
+different operating conditions.
+Since there are four combinations of categorical variables, by simply looking
+at the list of data, it would be hard to how the scores vary for each category.
+@ref{means:ex} shows one way of tabulating the @exvar{mtbf} in a way which is
+easier to understand.
+
+@float Example, means:ex
+@psppsyntax {means.sps}
+@caption {Running @cmd{MEANS} on the @exvar{mtbf} score with categories @exvar{factory} and @exvar{environment}}
+@end float
+
+The results are shown in @ref{means:res}. The figures shown indicate the mean,
+standard deviation and number of samples in each category.
+These figures however do not indicate whether the results are statistically
+significant. For that, you would need to use the procedures @cmd{ONEWAY}, @cmd{GLM} or
+@cmd{T-TEST} depending on the hypothesis being tested.
+
+@float Result, means:res
+@psppoutput {means}
+@caption {The @exvar{mtbf} categorised by @exvar{factory} and @exvar{environment}}
+@end float
+
+Note that there is no limit to the number of variables for which you can calculate
+statistics, nor to the number of categorical variables per layer, nor the number
+of layers.
+However, running @cmd{MEANS} on a large numbers of variables, or with categorical variables
+containing a large number of distinct values may result in an extremely large output, which
+will not be easy to interpret.
+So you should consider carefully which variables to select for participation in the analysis.
@node NPAR TESTS
@section NPAR TESTS
@vindex NPAR TESTS
@cindex nonparametric tests
-@display
+@display
NPAR TESTS
-
+
nonparametric test subcommands
.
.
.
-
+
[ /STATISTICS=@{DESCRIPTIVES@} ]
[ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
- [ /METHOD=EXACT [ TIMER [(n)] ] ]
+ [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
@end display
-NPAR TESTS performs nonparametric tests.
-Non parametric tests make very few assumptions about the distribution of the
+@cmd{NPAR TESTS} performs nonparametric tests.
+Non parametric tests make very few assumptions about the distribution of the
data.
One or more tests may be specified by using the corresponding subcommand.
-If the /STATISTICS subcommand is also specified, then summary statistics are
+If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
produces for each variable that is the subject of any test.
Certain tests may take a long time to execute, if an exact figure is required.
Therefore, by default asymptotic approximations are used unless the
-subcommand /METHOD=EXACT is specified.
-Exact tests give more accurate results, but may take an unacceptably long
-time to perform. If the TIMER keyword is used, it sets a maximum time,
-after which the test will be abandoned, and a warning message printed.
-The time, in minutes, should be specified in parentheses after the TIMER keyword.
-If the TIMER keyword is given without this figure, then a default value of 5 minutes
+subcommand @subcmd{/METHOD=EXACT} is specified.
+Exact tests give more accurate results, but may take an unacceptably long
+time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
+after which the test is abandoned, and a warning message printed.
+The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
+If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
is used.
@menu
* BINOMIAL:: Binomial Test
-* CHISQUARE:: Chisquare Test
-* WILCOXON:: Wilcoxon Signed Ranks Test
+* CHISQUARE:: Chi-square Test
+* COCHRAN:: Cochran Q Test
+* FRIEDMAN:: Friedman Test
+* KENDALL:: Kendall's W Test
+* KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
+* KRUSKAL-WALLIS:: Kruskal-Wallis Test
+* MANN-WHITNEY:: Mann Whitney U Test
+* MCNEMAR:: McNemar Test
+* MEDIAN:: Median Test
+* RUNS:: Runs Test
* SIGN:: The Sign Test
+* WILCOXON:: Wilcoxon Signed Ranks Test
@end menu
@vindex BINOMIAL
@cindex binomial test
-@display
- [ /BINOMIAL[(p)]=var_list[(value1[, value2)] ] ]
-@end display
+@display
+ [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
+@end display
-The /BINOMIAL subcommand compares the observed distribution of a dichotomous
+The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
variable with that of a binomial distribution.
-The variable @var{p} specifies the test proportion of the binomial
-distribution.
+The variable @var{p} specifies the test proportion of the binomial
+distribution.
The default value of 0.5 is assumed if @var{p} is omitted.
If a single value appears after the variable list, then that value is
used as the threshold to partition the observed values. Values less
than or equal to the threshold value form the first category. Values
-greater than the threshold form the second category.
+greater than the threshold form the second category.
-If two values appear after the variable list, then they will be used
+If two values appear after the variable list, then they are used
as the values which a variable must take to be in the respective
-category.
-Cases for which a variable takes a value equal to neither of the specified
+category.
+Cases for which a variable takes a value equal to neither of the specified
values, take no part in the test for that variable.
If no values appear, then the variable must assume dichotomous
If the test proportion is equal to 0.5, then a two tailed test is
reported. For any other test proportion, a one tailed test is
-reported.
+reported.
For one tailed tests, if the test proportion is less than
or equal to the observed proportion, then the significance of
observing the observed proportion or more is reported.
If the test proportion is more than the observed proportion, then the
significance of observing the observed proportion or less is reported.
That is to say, the test is always performed in the observed
-direction.
+direction.
-PSPP uses a very precise approximation to the gamma function to
+@pspp{} uses a very precise approximation to the gamma function to
compute the binomial significance. Thus, exact results are reported
even for very large sample sizes.
-
@node CHISQUARE
-@subsection Chisquare Test
+@subsection Chi-square Test
@vindex CHISQUARE
-@cindex chisquare test
+@cindex chi-square test
@display
- [ /CHISQUARE=var_list[(lo,hi)] [/EXPECTED=@{EQUAL|f1, f2 @dots{} fn@}] ]
-@end display
+ [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
+@end display
-The /CHISQUARE subcommand produces a chi-square statistic for the differences
-between the expected and observed frequencies of the categories of a variable.
-Optionally, a range of values may appear after the variable list.
+The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
+between the expected and observed frequencies of the categories of a variable.
+Optionally, a range of values may appear after the variable list.
If a range is given, then non integer values are truncated, and values
outside the specified range are excluded from the analysis.
-The /EXPECTED subcommand specifies the expected values of each
-category.
+The @subcmd{/EXPECTED} subcommand specifies the expected values of each
+category.
There must be exactly one non-zero expected value, for each observed
-category, or the EQUAL keywork must be specified.
-You may use the notation @var{n}*@var{f} to specify @var{n}
+category, or the @subcmd{EQUAL} keyword must be specified.
+You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
consecutive expected categories all taking a frequency of @var{f}.
The frequencies given are proportions, not absolute frequencies. The
sum of the frequencies need not be 1.
-If no /EXPECTED subcommand is given, then then equal frequencies
+If no @subcmd{/EXPECTED} subcommand is given, then equal frequencies
are expected.
-@node WILCOXON
-@subsection Wilcoxon Matched Pairs Signed Ranks Test
-@comment node-name, next, previous, up
-@vindex WILCOXON
-@cindex wilcoxon matched pairs signed ranks test
+@subsubsection Chi-square Example
+
+A researcher wishes to investigate whether there are an equal number of
+persons of each sex in a population. The sample chosen for invesigation
+is that from the @file {physiology.sav} dataset. The null hypothesis for
+the test is that the population comprises an equal number of males and females.
+The analysis is performed as shown in @ref{chisquare:ex}.
+
+@float Example, chisquare:ex
+@psppsyntax {chisquare.sps}
+@caption {Performing a chi-square test to check for equal distribution of sexes}
+@end float
+
+There is only one test variable, @i{viz:} @exvar{sex}. The other variables in the dataset
+are ignored.
+
+@float Screenshot, chisquare:scr
+@psppimage {chisquare}
+@caption {Performing a chi-square test using the graphic user interface}
+@end float
+
+In @ref{chisquare:res} the summary box shows that in the sample, there are more males
+than females. However the significance of chi-square result is greater than 0.05
+--- the most commonly accepted p-value --- and therefore
+there is not enough evidence to reject the null hypothesis and one must conclude
+that the evidence does not indicate that there is an imbalance of the sexes
+in the population.
+
+@float Result, chisquare:res
+@psppoutput {chisquare}
+@caption {The results of running a chi-square test on @exvar{sex}}
+@end float
+
+
+@node COCHRAN
+@subsection Cochran Q Test
+@vindex Cochran
+@cindex Cochran Q test
+@cindex Q, Cochran Q
@display
- [ /WILCOXON varlist [ WITH varlist [ (PAIRED) ]]]
+ [ /COCHRAN = @var{var_list} ]
@end display
-The /WILCOXON subcommand tests for differences between medians of the
-variables listed.
-The test does not make any assumptions about the variances of the samples.
-It does however assume that the distribution is symetrical.
+The Cochran Q test is used to test for differences between three or more groups.
+The data for @var{var_list} in all cases must assume exactly two
+distinct values (other than missing values).
+
+The value of Q is displayed along with its Asymptotic significance
+based on a chi-square distribution.
+
+@node FRIEDMAN
+@subsection Friedman Test
+@vindex FRIEDMAN
+@cindex Friedman test
+
+@display
+ [ /FRIEDMAN = @var{var_list} ]
+@end display
+
+The Friedman test is used to test for differences between repeated measures when
+there is no indication that the distributions are normally distributed.
+
+A list of variables which contain the measured data must be given. The procedure
+prints the sum of ranks for each variable, the test statistic and its significance.
+
+@node KENDALL
+@subsection Kendall's W Test
+@vindex KENDALL
+@cindex Kendall's W test
+@cindex coefficient of concordance
+
+@display
+ [ /KENDALL = @var{var_list} ]
+@end display
+
+The Kendall test investigates whether an arbitrary number of related samples come from the
+same population.
+It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
+It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
+unity indicates complete agreement.
+
+
+@node KOLMOGOROV-SMIRNOV
+@subsection Kolmogorov-Smirnov Test
+@vindex KOLMOGOROV-SMIRNOV
+@vindex K-S
+@cindex Kolmogorov-Smirnov test
+
+@display
+ [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
+@end display
+
+The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
+drawn from a particular distribution. Four distributions are supported, @i{viz:}
+Normal, Uniform, Poisson and Exponential.
+
+Ideally you should provide the parameters of the distribution against
+which you wish to test the data. For example, with the normal
+distribution the mean (@var{mu})and standard deviation (@var{sigma})
+should be given; with the uniform distribution, the minimum
+(@var{min})and maximum (@var{max}) value should be provided.
+However, if the parameters are omitted they are imputed from the
+data. Imputing the parameters reduces the power of the test so should
+be avoided if possible.
+
+In the following example, two variables @var{score} and @var{age} are
+tested to see if they follow a normal distribution with a mean of 3.5
+and a standard deviation of 2.0.
+@example
+ NPAR TESTS
+ /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
+@end example
+If the variables need to be tested against different distributions, then a separate
+subcommand must be used. For example the following syntax tests @var{score} against
+a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
+is tested against a normal distribution of mean 40 and standard deviation 1.5.
+@example
+ NPAR TESTS
+ /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
+ /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
+@end example
+
+The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
+
+@node KRUSKAL-WALLIS
+@subsection Kruskal-Wallis Test
+@vindex KRUSKAL-WALLIS
+@vindex K-W
+@cindex Kruskal-Wallis test
+
+@display
+ [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
+@end display
+
+The Kruskal-Wallis test is used to compare data from an
+arbitrary number of populations. It does not assume normality.
+The data to be compared are specified by @var{var_list}.
+The categorical variable determining the groups to which the
+data belongs is given by @var{var}. The limits @var{lower} and
+@var{upper} specify the valid range of @var{var}.
+If @var{upper} is smaller than @var{lower}, the PSPP will assume their values
+to be reversed. Any cases for which @var{var} falls outside
+[@var{lower}, @var{upper}] are ignored.
+
+The mean rank of each group as well as the chi-squared value and
+significance of the test are printed.
+The abbreviated subcommand @subcmd{K-W} may be used in place of
+@subcmd{KRUSKAL-WALLIS}.
+
+
+@node MANN-WHITNEY
+@subsection Mann-Whitney U Test
+@vindex MANN-WHITNEY
+@vindex M-W
+@cindex Mann-Whitney U test
+@cindex U, Mann-Whitney U
+
+@display
+ [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
+@end display
+
+The Mann-Whitney subcommand is used to test whether two groups of data
+come from different populations. The variables to be tested should be
+specified in @var{var_list} and the grouping variable, that determines
+to which group the test variables belong, in @var{var}.
+@var{Var} may be either a string or an alpha variable.
+@var{Group1} and @var{group2} specify the
+two values of @var{var} which determine the groups of the test data.
+Cases for which the @var{var} value is neither @var{group1} or
+@var{group2} are ignored.
+
+The value of the Mann-Whitney U statistic, the Wilcoxon W, and the
+significance are printed.
+You may abbreviated the subcommand @subcmd{MANN-WHITNEY} to
+@subcmd{M-W}.
+
+
+@node MCNEMAR
+@subsection McNemar Test
+@vindex MCNEMAR
+@cindex McNemar test
+
+@display
+ [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
+@end display
+
+Use McNemar's test to analyse the significance of the difference between
+pairs of correlated proportions.
If the @code{WITH} keyword is omitted, then tests for all
combinations of the listed variables are performed.
of variable preceding @code{WITH} against variable following
@code{WITH} are performed.
+The data in each variable must be dichotomous. If there are more
+than two distinct variables an error will occur and the test will
+not be run.
+
+@node MEDIAN
+@subsection Median Test
+@vindex MEDIAN
+@cindex Median test
+
+@display
+ [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
+@end display
+
+The median test is used to test whether independent samples come from
+populations with a common median.
+The median of the populations against which the samples are to be tested
+may be given in parentheses immediately after the
+@subcmd{/MEDIAN} subcommand. If it is not given, the median is imputed from the
+union of all the samples.
+
+The variables of the samples to be tested should immediately follow the @samp{=} sign. The
+keyword @code{BY} must come next, and then the grouping variable. Two values
+in parentheses should follow. If the first value is greater than the second,
+then a 2 sample test is performed using these two values to determine the groups.
+If however, the first variable is less than the second, then a @i{k} sample test is
+conducted and the group values used are all values encountered which lie in the
+range [@var{value1},@var{value2}].
+
+
+@node RUNS
+@subsection Runs Test
+@vindex RUNS
+@cindex runs test
+
+@display
+ [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
+@end display
+
+The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
+
+It works by examining the number of times a variable's value crosses a given threshold.
+The desired threshold must be specified within parentheses.
+It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
+Following the threshold specification comes the list of variables whose values are to be
+tested.
+
+The subcommand shows the number of runs, the asymptotic significance based on the
+length of the data.
@node SIGN
@subsection Sign Test
@cindex sign test
@display
- [ /SIGN varlist [ WITH varlist [ (PAIRED) ]]]
+ [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
@end display
-The /SIGN subcommand tests for differences between medians of the
+The @subcmd{/SIGN} subcommand tests for differences between medians of the
variables listed.
The test does not make any assumptions about the
distribution of the data.
of variable preceding @code{WITH} against variable following
@code{WITH} are performed.
+@node WILCOXON
+@subsection Wilcoxon Matched Pairs Signed Ranks Test
+@vindex WILCOXON
+@cindex wilcoxon matched pairs signed ranks test
+
+@display
+ [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
+@end display
+
+The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
+variables listed.
+The test does not make any assumptions about the variances of the samples.
+It does however assume that the distribution is symmetrical.
+
+If the @subcmd{WITH} keyword is omitted, then tests for all
+combinations of the listed variables are performed.
+If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
+is also given, then the number of variables preceding @subcmd{WITH}
+must be the same as the number following it.
+In this case, tests for each respective pair of variables are
+performed.
+If the @subcmd{WITH} keyword is given, but the
+@subcmd{(PAIRED)} keyword is omitted, then tests for each combination
+of variable preceding @subcmd{WITH} against variable following
+@subcmd{WITH} are performed.
+
@node T-TEST
-@comment node-name, next, previous, up
@section T-TEST
@vindex T-TEST
@display
T-TEST
/MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
- /CRITERIA=CIN(confidence)
+ /CRITERIA=CI(@var{confidence})
(One Sample mode.)
- TESTVAL=test_value
- /VARIABLES=var_list
+ TESTVAL=@var{test_value}
+ /VARIABLES=@var{var_list}
(Independent Samples mode.)
- GROUPS=var(value1 [, value2])
- /VARIABLES=var_list
+ GROUPS=var(@var{value1} [, @var{value2}])
+ /VARIABLES=@var{var_list}
(Paired Samples mode.)
- PAIRS=var_list [WITH var_list [(PAIRED)] ]
+ PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
@end display
-The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
-means.
+The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
+means.
It operates in one of three modes:
@itemize
@item One Sample mode.
Each of these modes are described in more detail below.
There are two optional subcommands which are common to all modes.
-The @cmd{/CRITERIA} subcommand tells PSPP the confidence interval used
+The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
in the tests. The default value is 0.95.
The @cmd{MISSING} subcommand determines the handling of missing
-variables.
-If INCLUDE is set, then user-missing values are included in the
+variables.
+If @subcmd{INCLUDE} is set, then user-missing values are included in the
calculations, but system-missing values are not.
-If EXCLUDE is set, which is the default, user-missing
-values are excluded as well as system-missing values.
+If @subcmd{EXCLUDE} is set, which is the default, user-missing
+values are excluded as well as system-missing values.
This is the default.
-If LISTWISE is set, then the entire case is excluded from analysis
-whenever any variable specified in the @cmd{/VARIABLES}, @cmd{/PAIRS} or
-@cmd{/GROUPS} subcommands contains a missing value.
-If ANALYSIS is set, then missing values are excluded only in the analysis for
+If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
+whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
+@subcmd{/GROUPS} subcommands contains a missing value.
+If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
which they would be needed. This is the default.
@menu
-* One Sample Mode:: Testing against a hypothesised mean
+* One Sample Mode:: Testing against a hypothesized mean
* Independent Samples Mode:: Testing two independent groups for equal mean
* Paired Samples Mode:: Testing two interdependent groups for equal mean
@end menu
@node One Sample Mode
@subsection One Sample Mode
-The @cmd{TESTVAL} subcommand invokes the One Sample mode.
-This mode is used to test a population mean against a hypothesised
-mean.
-The value given to the @cmd{TESTVAL} subcommand is the value against
+The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
+This mode is used to test a population mean against a hypothesized
+mean.
+The value given to the @subcmd{TESTVAL} subcommand is the value against
which you wish to test.
-In this mode, you must also use the @cmd{/VARIABLES} subcommand to
-tell PSPP which variables you wish to test.
+In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
+tell @pspp{} which variables you wish to test.
+
+@subsubsection Example - One Sample T-test
+
+A researcher wishes to know whether the weight of persons in a population
+is different from the national average.
+The samples are drawn from the population under investigation and recorded
+in the file @file{physiology.sav}.
+From the Department of Health, she
+knows that the national average weight of healthy adults is 76.8kg.
+Accordingly the @subcmd{TESTVAL} is set to 76.8.
+The null hypothesis therefore is that the mean average weight of the
+population from which the sample was drawn is 76.8kg.
+
+As previously noted (@pxref{Identifying incorrect data}), one
+sample in the dataset contains a weight value
+which is clearly incorrect. So this is excluded from the analysis
+using the @cmd{SELECT} command.
+
+@float Example, one-sample-t:ex
+@psppsyntax {one-sample-t.sps}
+@caption {Running a one sample T-Test after excluding all non-positive values}
+@end float
+
+@float Screenshot, one-sample-t:scr
+@psppimage {one-sample-t}
+@caption {Using the One Sample T-Test dialog box to test @exvar{weight} for a mean of 76.8kg}
+@end float
+
+
+@ref{one-sample-t:res} shows that the mean of our sample differs from the test value
+by -1.40kg. However the significance is very high (0.610). So one cannot
+reject the null hypothesis, and must conclude there is not enough evidence
+to suggest that the mean weight of the persons in our population is different
+from 76.8kg.
+
+@float Results, one-sample-t:res
+@psppoutput {one-sample-t}
+@caption {The results of a one sample T-test of @exvar{weight} using a test value of 76.8kg}
+@end float
@node Independent Samples Mode
-@comment node-name, next, previous, up
@subsection Independent Samples Mode
-The @cmd{GROUPS} subcommand invokes Independent Samples mode or
-`Groups' mode.
+The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
+`Groups' mode.
This mode is used to test whether two groups of values have the
same population mean.
-In this mode, you must also use the @cmd{/VARIABLES} subcommand to
-tell PSPP the dependent variables you wish to test.
+In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
+tell @pspp{} the dependent variables you wish to test.
-The variable given in the @cmd{GROUPS} subcommand is the independent
+The variable given in the @subcmd{GROUPS} subcommand is the independent
variable which determines to which group the samples belong.
The values in parentheses are the specific values of the independent
variable for each group.
-If the parentheses are omitted and no values are given, the default values
+If the parentheses are omitted and no values are given, the default values
of 1.0 and 2.0 are assumed.
-If the independent variable is numeric,
+If the independent variable is numeric,
it is acceptable to specify only one value inside the parentheses.
If you do this, cases where the independent variable is
greater than or equal to this value belong to the first group, and cases
less than this value belong to the second group.
-When using this form of the @cmd{GROUPS} subcommand, missing values in
+When using this form of the @subcmd{GROUPS} subcommand, missing values in
the independent variable are excluded on a listwise basis, regardless
-of whether @cmd{/MISSING=LISTWISE} was specified.
+of whether @subcmd{/MISSING=LISTWISE} was specified.
+
+@subsubsection Example - Independent Samples T-test
+
+A researcher wishes to know whether within a population, adult males
+are taller than adult females.
+The samples are drawn from the population under investigation and recorded
+in the file @file{physiology.sav}.
+
+As previously noted (@pxref{Identifying incorrect data}), one
+sample in the dataset contains a height value
+which is clearly incorrect. So this is excluded from the analysis
+using the @cmd{SELECT} command.
+
+
+@float Example, indepdendent-samples-t:ex
+@psppsyntax {independent-samples-t.sps}
+@caption {Running a independent samples T-Test after excluding all observations less than 200kg}
+@end float
+
+
+The null hypothesis is that both males and females are on average
+of equal height.
+
+@float Screenshot, independent-samples-t:scr
+@psppimage {independent-samples-t}
+@caption {Using the Independent Sample T-test dialog, to test for differences of @exvar{height} between values of @exvar{sex}}
+@end float
+In this case, the grouping variable is @exvar{sex}, so this is entered
+as the variable for the @subcmd{GROUP} subcommand. The group values are 0 (male) and
+1 (female).
+
+If you are running the proceedure using syntax, then you need to enter
+the values corresponding to each group within parentheses.
+If you are using the graphic user interface, then you have to open
+the ``Define Groups'' dialog box and enter the values corresponding
+to each group as shown in @ref{define-groups-t:scr}. If, as in this case, the dataset has defined value
+labels for the group variable, then you can enter them by label
+or by value.
+
+@float Screenshot, define-groups-t:scr
+@psppimage {define-groups-t}
+@caption {Setting the values of the grouping variable for an Independent Samples T-test}
+@end float
+
+From @ref{independent-samples-t:res}, one can clearly see that the @emph{sample} mean height
+is greater for males than for females. However in order to see if this
+is a significant result, one must consult the T-Test table.
+
+The T-Test table contains two rows; one for use if the variance of the samples
+in each group may be safely assumed to be equal, and the second row
+if the variances in each group may not be safely assumed to be equal.
+
+In this case however, both rows show a 2-tailed significance less than 0.001 and
+one must therefore reject the null hypothesis and conclude that within
+the population the mean height of males and of females are unequal.
+
+@float Result, independent-samples-t:res
+@psppoutput {independent-samples-t}
+@caption {The results of an independent samples T-test of @exvar{height} by @exvar{sex}}
+@end float
+
@node Paired Samples Mode
-@comment node-name, next, previous, up
@subsection Paired Samples Mode
The @cmd{PAIRS} subcommand introduces Paired Samples mode.
Use this mode when repeated measures have been taken from the same
samples.
-If the @code{WITH} keyword is omitted, then tables for all
+If the @subcmd{WITH} keyword is omitted, then tables for all
combinations of variables given in the @cmd{PAIRS} subcommand are
-generated.
-If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
-is also given, then the number of variables preceding @code{WITH}
+generated.
+If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
+is also given, then the number of variables preceding @subcmd{WITH}
must be the same as the number following it.
In this case, tables for each respective pair of variables are
generated.
-In the event that the @code{WITH} keyword is given, but the
-@code{(PAIRED)} keyword is omitted, then tables for each combination
-of variable preceding @code{WITH} against variable following
-@code{WITH} are generated.
+In the event that the @subcmd{WITH} keyword is given, but the
+@subcmd{(PAIRED)} keyword is omitted, then tables for each combination
+of variable preceding @subcmd{WITH} against variable following
+@subcmd{WITH} are generated.
@node ONEWAY
-@comment node-name, next, previous, up
@section ONEWAY
@vindex ONEWAY
@display
ONEWAY
- [/VARIABLES = ] var_list BY var
+ [/VARIABLES = ] @var{var_list} BY @var{var}
/MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
- /CONTRAST= value1 [, value2] ... [,valueN]
+ /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
/STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
-
+ /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
@end display
The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
variables factored by a single independent variable.
It is used to compare the means of a population
-divided into more than two groups.
+divided into more than two groups.
-The variables to be analysed should be given in the @code{VARIABLES}
-subcommand.
-The list of variables must be followed by the @code{BY} keyword and
+The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
+subcommand.
+The list of variables must be followed by the @subcmd{BY} keyword and
the name of the independent (or factor) variable.
-You can use the @code{STATISTICS} subcommand to tell PSPP to display
-ancilliary information. The options accepted are:
+You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
+ancillary information. The options accepted are:
@itemize
@item DESCRIPTIVES
Displays descriptive statistics about the groups factored by the independent
variables and their groups.
@end itemize
-The @code{CONTRAST} subcommand is used when you anticipate certain
+The @subcmd{CONTRAST} subcommand is used when you anticipate certain
differences between the groups.
The subcommand must be followed by a list of numerals which are the
coefficients of the groups to be tested.
The number of coefficients must correspond to the number of distinct
groups (or values of the independent variable).
-If the total sum of the coefficients are not zero, then PSPP will
+If the total sum of the coefficients are not zero, then @pspp{} will
display a warning, but will proceed with the analysis.
-The @code{CONTRAST} subcommand may be given up to 10 times in order
+The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
to specify different contrast tests.
+The @subcmd{MISSING} subcommand defines how missing values are handled.
+If @subcmd{LISTWISE} is specified then cases which have missing values for
+the independent variable or any dependent variable are ignored.
+If @subcmd{ANALYSIS} is specified, then cases are ignored if the independent
+variable is missing or if the dependent variable currently being
+analysed is missing. The default is @subcmd{ANALYSIS}.
+A setting of @subcmd{EXCLUDE} means that variables whose values are
+user-missing are to be excluded from the analysis. A setting of
+@subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
+
+Using the @code{POSTHOC} subcommand you can perform multiple
+pairwise comparisons on the data. The following comparison methods
+are available:
+@itemize
+@item @subcmd{LSD}
+Least Significant Difference.
+@item @subcmd{TUKEY}
+Tukey Honestly Significant Difference.
+@item @subcmd{BONFERRONI}
+Bonferroni test.
+@item @subcmd{SCHEFFE}
+Scheff@'e's test.
+@item @subcmd{SIDAK}
+Sidak test.
+@item @subcmd{GH}
+The Games-Howell test.
+@end itemize
+
+@noindent
+Use the optional syntax @code{ALPHA(@var{value})} to indicate that
+@cmd{ONEWAY} should perform the posthoc tests at a confidence level of
+@var{value}. If @code{ALPHA(@var{value})} is not specified, then the
+confidence level used is 0.05.
+
+@node QUICK CLUSTER
+@section QUICK CLUSTER
+@vindex QUICK CLUSTER
+
+@cindex K-means clustering
+@cindex clustering
+
+@display
+QUICK CLUSTER @var{var_list}
+ [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
+ [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
+ [/PRINT=@{INITIAL@} @{CLUSTER@}]
+ [/SAVE[=[CLUSTER[(@var{membership_var})]] [DISTANCE[(@var{distance_var})]]]
+@end display
+
+The @cmd{QUICK CLUSTER} command performs k-means clustering on the
+dataset. This is useful when you wish to allocate cases into clusters
+of similar values and you already know the number of clusters.
+
+The minimum specification is @samp{QUICK CLUSTER} followed by the names
+of the variables which contain the cluster data. Normally you will also
+want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
+number of clusters. If this is not specified, then @var{k} defaults to 2.
+
+If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
+the initial clusters is used. This will provide for faster execution but
+less well separated initial clusters and hence possibly an inferior final
+result.
+
+
+@cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
+The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
+During classification, @pspp{} will continue iterating until until @var{max_iter}
+iterations have been done or the convergence criterion (see below) is fulfilled.
+The default value of @var{max_iter} is 2.
+
+If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
+no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
+is ignored.
+
+The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
+to set the convergence criterion. The value of convergence criterion is @var{epsilon}
+times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
+the mean cluster distance between one iteration and the next
+is less than the convergence criterion. The default value of @var{epsilon} is zero.
+
+The @subcmd{MISSING} subcommand determines the handling of missing variables.
+If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
+value and not as missing values.
+If @subcmd{EXCLUDE} is set, which is the default, user-missing
+values are excluded as well as system-missing values.
+
+If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
+whenever any of the clustering variables contains a missing value.
+If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
+clustering variables contain missing values. Otherwise it is clustered
+on the basis of the non-missing values.
+The default is @subcmd{LISTWISE}.
+
+The @subcmd{PRINT} subcommand requests additional output to be printed.
+If @subcmd{INITIAL} is set, then the initial cluster memberships will
+be printed.
+If @subcmd{CLUSTER} is set, the cluster memberships of the individual
+cases are displayed (potentially generating lengthy output).
+
+You can specify the subcommand @subcmd{SAVE} to ask that each case's cluster membership
+and the euclidean distance between the case and its cluster center be saved to
+a new variable in the active dataset. To save the cluster membership use the
+@subcmd{CLUSTER} keyword and to save the distance use the @subcmd{DISTANCE} keyword.
+Each keyword may optionally be followed by a variable name in parentheses to specify
+the new variable which is to contain the saved parameter. If no variable name is specified,
+then PSPP will create one.
@node RANK
-@comment node-name, next, previous, up
@section RANK
@vindex RANK
@display
RANK
- [VARIABLES=] var_list [@{A,D@}] [BY var_list]
+ [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
/TIES=@{MEAN,LOW,HIGH,CONDENSE@}
/FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
/PRINT[=@{YES,NO@}
/MISSING=@{EXCLUDE,INCLUDE@}
- /RANK [INTO var_list]
- /NTILES(k) [INTO var_list]
- /NORMAL [INTO var_list]
- /PERCENT [INTO var_list]
- /RFRACTION [INTO var_list]
- /PROPORTION [INTO var_list]
- /N [INTO var_list]
- /SAVAGE [INTO var_list]
+ /RANK [INTO @var{var_list}]
+ /NTILES(k) [INTO @var{var_list}]
+ /NORMAL [INTO @var{var_list}]
+ /PERCENT [INTO @var{var_list}]
+ /RFRACTION [INTO @var{var_list}]
+ /PROPORTION [INTO @var{var_list}]
+ /N [INTO @var{var_list}]
+ /SAVAGE [INTO @var{var_list}]
@end display
The @cmd{RANK} command ranks variables and stores the results into new
-variables.
+variables.
-The VARIABLES subcommand, which is mandatory, specifies one or
-more variables whose values are to be ranked.
+The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
+more variables whose values are to be ranked.
After each variable, @samp{A} or @samp{D} may appear, indicating that
the variable is to be ranked in ascending or descending order.
Ascending is the default.
-If a BY keyword appears, it should be followed by a list of variables
-which are to serve as group variables.
+If a @subcmd{BY} keyword appears, it should be followed by a list of variables
+which are to serve as group variables.
In this case, the cases are gathered into groups, and ranks calculated
for each group.
-The TIES subcommand specifies how tied values are to be treated. The
+The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
default is to take the mean value of all the tied cases.
-The FRACTION subcommand specifies how proportional ranks are to be
-calculated. This only has any effect if NORMAL or PROPORTIONAL rank
+The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
+calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
functions are requested.
-The PRINT subcommand may be used to specify that a summary of the rank
+The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
variables created should appear in the output.
-The function subcommands are RANK, NTILES, NORMAL, PERCENT, RFRACTION,
-PROPORTION and SAVAGE. Any number of function subcommands may appear.
+The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
+@subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
If none are given, then the default is RANK.
-The NTILES subcommand must take an integer specifying the number of
+The @subcmd{NTILES} subcommand must take an integer specifying the number of
partitions into which values should be ranked.
-Each subcommand may be followed by the INTO keyword and a list of
+Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
variables which are the variables to be created and receive the rank
scores. There may be as many variables specified as there are
-variables named on the VARIABLES subcommand. If fewer are specified,
+variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
then the variable names are automatically created.
-The MISSING subcommand determines how user missing values are to be
-treated. A setting of EXCLUDE means that variables whose values are
+The @subcmd{MISSING} subcommand determines how user missing values are to be
+treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
user-missing are to be excluded from the rank scores. A setting of
-INCLUDE means they are to be included. The default is EXCLUDE.
+@subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
@include regression.texi
@vindex RELIABILITY
@display
RELIABILITY
- /VARIABLES=var_list
- /SCALE (@var{name}) = @{var_list, ALL@}
- /MODEL=@{ALPHA, SPLIT[(N)]@}
+ /VARIABLES=@var{var_list}
+ /SCALE (@var{name}) = @{@var{var_list}, ALL@}
+ /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
/SUMMARY=@{TOTAL,ALL@}
/MISSING=@{EXCLUDE,INCLUDE@}
@end display
@cindex Cronbach's Alpha
-The @cmd{RELIABILTY} command performs reliablity analysis on the data.
+The @cmd{RELIABILITY} command performs reliability analysis on the data.
-The VARIABLES subcommand is required. It determines the set of variables
+The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
upon which analysis is to be performed.
-The SCALE subcommand determines which variables reliability is to be
-calculated for. If it is omitted, then analysis for all variables named
-in the VARIABLES subcommand will be used.
-Optionally, the @var{name} parameter may be specified to set a string name
+The @subcmd{SCALE} subcommand determines the variables for which
+reliability is to be calculated. If @subcmd{SCALE} is omitted, then analysis for
+all variables named in the @subcmd{VARIABLES} subcommand are used.
+Optionally, the @var{name} parameter may be specified to set a string name
for the scale.
-The MODEL subcommand determines the type of analysis. If ALPHA is specified,
-then Cronbach's Alpha is calculated for the scale. If the model is SPLIT,
-then the variables are divided into 2 subsets. An optional parameter
-@var{N} may be given, to specify how many variables to be in the first subset.
-If @var{N} is omitted, then it defaults to one half of the variables in the
+The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
+then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
+then the variables are divided into 2 subsets. An optional parameter
+@var{n} may be given, to specify how many variables to be in the first subset.
+If @var{n} is omitted, then it defaults to one half of the variables in the
scale, or one half minus one if there are an odd number of variables.
-The default model is ALPHA.
+The default model is @subcmd{ALPHA}.
-By default, any cases with user missing, or system missing values for
-any variables given
-in the VARIABLES subcommand will be omitted from analysis.
-The MISSING subcommand determines whether user missing values are to
-be included or excluded in the analysis.
+By default, any cases with user missing, or system missing values for
+any variables given in the @subcmd{VARIABLES} subcommand are omitted
+from the analysis. The @subcmd{MISSING} subcommand determines whether
+user missing values are included or excluded in the analysis.
-The SUMMARY subcommand determines the type of summary analysis to be performed.
-Currently there is only one type: SUMMARY=TOTAL, which displays per-item
+The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
+Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
analysis tested against the totals.
+@subsection Example - Reliability
+
+Before analysing the results of a survey -- particularly for a multiple choice survey --
+it is desireable to know whether the respondents have considered their answers
+or simply provided random answers.
+
+In the following example the survey results from the file @file{hotel.sav} are used.
+All five survey questions are included in the reliability analysis.
+However, before running the analysis, the data must be preprocessed.
+An examination of the survey questions reveals that two questions, @i{viz:} v3 and v5
+are negatively worded, whereas the others are positively worded.
+All questions must be based upon the same scale for the analysis to be meaningful.
+One could use the @cmd{RECODE} command (@pxref{RECODE}), however a simpler way is
+to use @cmd{COMPUTE} (@pxref{COMPUTE}) and this is what is done in @ref{reliability:ex}.
+
+@float Example, reliability:ex
+@psppsyntax {reliability.sps}
+@caption {Investigating the reliability of survey responses}
+@end float
+
+In this case, all variables in the data set are used. So we can use the special
+keyword @samp{ALL} (@pxref{BNF}).
+
+@float Screenshot, reliability:src
+@psppimage {reliability}
+@caption {Reliability dialog box with all variables selected}
+@end float
+
+@ref{reliability:res} shows that Cronbach's Alpha is 0.11 which is a value normally considered too
+low to indicate consistency within the data. This is possibly due to the small number of
+survey questions. The survey should be redesigned before serious use of the results are
+applied.
+
+@float Result, reliability:res
+@psppoutput {reliability}
+@caption {The results of the reliability command on @file{hotel.sav}}
+@end float
@node ROC
@section ROC
@vindex ROC
-@cindex Receiver Operating Characterstic
+@cindex Receiver Operating Characteristic
@cindex Area under curve
@display
@end display
-The @cmd{ROC} command is used to plot the receiver operating characteristic curve
+The @cmd{ROC} command is used to plot the receiver operating characteristic curve
of a dataset, and to estimate the area under the curve.
This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
The mandatory @var{var_list} is the list of predictor variables.
-The variable @var{state_var} is the variable whose values represent the actual states,
+The variable @var{state_var} is the variable whose values represent the actual states,
and @var{state_value} is the value of this variable which represents the positive state.
-The optional subcommand PLOT is used to determine if and how the ROC curve is drawn.
-The keyword CURVE means that the ROC curve should be drawn, and the optional keyword REFERENCE,
+The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
+The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
-If the keyword NONE is given, then no ROC curve is drawn.
+If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
By default, the curve is drawn with no reference line.
-The optional subcommand PRINT determines which additional tables should be printed.
-Two additional tables are available.
-The SE keyword says that standard error of the area under the curve should be printed as well as
-the area itself.
-In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
-printed.
-The COORDINATES keyword says that a table of coordinates of the ROC curve should be printed.
+The optional subcommand @subcmd{PRINT} determines which additional
+tables should be printed. Two additional tables are available. The
+@subcmd{SE} keyword says that standard error of the area under the
+curve should be printed as well as the area itself. In addition, a
+p-value for the null hypothesis that the area under the curve equals
+0.5 is printed. The @subcmd{COORDINATES} keyword says that a
+table of coordinates of the @subcmd{ROC} curve should be printed.
-The CRITERIA subcommand has four optional parameters:
+The @subcmd{CRITERIA} subcommand has four optional parameters:
@itemize @bullet
-@item The TESTPOS parameter may be LARGE or SMALL.
-LARGE is the default, and says that larger values in the predictor variables are to be
-considered positive. SMALL indicates that smaller values should be considered positive.
+@item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
+@subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
+considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
-@item The CI parameter specifies the confidence interval that should be printed.
-It has no effect if the SE keyword in the PRINT subcommand has not been given.
+@item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
+It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
-@item The DISTRIBUTION parameter determines the method to be used when estimating the area
-under the curve.
-There are two possibilities, @i{viz}: FREE and NEGEXPO.
-The FREE method uses a non-parametric estimate, and the NEGEXPO method a bi-negative
+@item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
+under the curve.
+There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
+The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
exponential distribution estimate.
-The NEGEXPO method should only be used when the number of positive actual states is
+The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
equal to the number of negative actual states.
-The default is FREE.
+The default is @subcmd{FREE}.
-@item The CUTOFF parameter is for compatibility and is ignored.
+@item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
@end itemize
-The MISSING subcommand determines whether user missing values are to
+The @subcmd{MISSING} subcommand determines whether user missing values are to
be included or excluded in the analysis. The default behaviour is to
exclude them.
-Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
-or if the variable @var{state_var} is missing, then the entire case will be
+Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
+or if the variable @var{state_var} is missing, then the entire case is
excluded.
-
+@c LocalWords: subcmd subcommand
projects / pspp / blobdiff