-@node Statistics, Utilities, Conditionals and Looping, Top
+@node Statistics
@chapter Statistics
This chapter documents the statistical procedures that PSPP supports so
far.
-@c If you add any new commands, then don't forget to remove the entry in
-@c not-implemented.texi
-
@menu
* DESCRIPTIVES:: Descriptive statistics.
* FREQUENCIES:: Frequency tables.
* EXAMINE:: Testing data for normality.
* CROSSTABS:: Crosstabulation tables.
+* NPAR TESTS:: Nonparametric tests.
* T-TEST:: Test hypotheses about means.
* ONEWAY:: One way analysis of variance.
* RANK:: Compute rank scores.
* REGRESSION:: Linear regression.
+* RELIABILITY:: Reliability analysis.
+* ROC:: Receiver Operating Characteristic.
@end menu
-@node DESCRIPTIVES, FREQUENCIES, Statistics, Statistics
+@node DESCRIPTIVES
@section DESCRIPTIVES
@vindex DESCRIPTIVES
and D settings request an ascending or descending sort order,
respectively.
-@node FREQUENCIES, EXAMINE, DESCRIPTIVES, Statistics
+@node FREQUENCIES
@section FREQUENCIES
@vindex FREQUENCIES
SESKEWNESS,SEKURTOSIS,ALL,NONE@}
/NTILES=ntiles
/PERCENTILES=percent@dots{}
+ /HISTOGRAM=[MINIMUM(x_min)] [MAXIMUM(x_max)]
+ [@{FREQ,PCNT@}] [@{NONORMAL,NORMAL@}]
+ /PIECHART=[MINIMUM(x_min)] [MAXIMUM(x_max)] @{NOMISSING,MISSING@}
(These options are not currently implemented.)
/BARCHART=@dots{}
- /HISTOGRAM=@dots{}
/HBAR=@dots{}
/GROUPED=@dots{}
-
-(Integer mode.)
- /VARIABLES=var_list (low,high)@dots{}
@end display
The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
@cmd{FREQUENCIES} can also calculate and display descriptive statistics
(including median and mode) and percentiles.
-In the future, @cmd{FREQUENCIES} will also support graphical output in the
-form of bar charts and histograms. In addition, it will be able to
-support percentiles for grouped data.
+@cmd{FREQUENCIES} also support graphical output in the form of
+histograms and pie charts. In the future, it will be able to produce
+bar charts and output percentiles for grouped data.
The VARIABLES subcommand is the only required subcommand. Specify the
-variables to be analyzed. In most cases, this is all that is required.
-This is known as @dfn{general mode}.
-
-Occasionally, one may want to invoke a special mode called @dfn{integer
-mode}. Normally, in general mode, PSPP will automatically determine
-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 a
-range of data values in parentheses, separated by a comma. 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.
+variables to be analyzed.
The FORMAT subcommand controls the output format. It has several
possible settings:
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.
The percentiles should be presented at a list of numbers between 0
and 100 inclusive.
boundaries of the data set divided into the specified number of ranges.
For instance, @code{/NTILES=4} would cause quartiles to be reported.
-
-@node EXAMINE, CROSSTABS, FREQUENCIES, Statistics
+The 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. The Y axis by default is
+labeled in frequencies; use the PERCENT keyword to causes it to be
+labeled in percent of the total observed count. 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
+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.
+
+@node EXAMINE
@comment node-name, next, previous, up
@section EXAMINE
@vindex EXAMINE
/PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, ALL, NONE@}
/CINTERVAL n
/COMPARE=@{GROUPS,VARIABLES@}
- /ID=@{case_number, var_name@}
+ /ID=var_name
/@{TOTAL,NOTOTAL@}
/PERCENTILE=[value_list]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
/MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
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%.
+@cindex percentiles
The 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
large quantity of output.
-@node CROSSTABS, T-TEST, EXAMINE, Statistics
+@node CROSSTABS
@section CROSSTABS
@vindex CROSSTABS
subcommand.
In general mode, numeric and string variables may be specified on
-TABLES. Although long string variables are allowed, only their
-initial short-string parts are used. In integer mode, only numeric
-variables are allowed.
+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 @asis
@item CHISQ
+@cindex chisquare
+@cindex chi-square
+
Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
correction, linear-by-linear association.
@item PHI
Fixes for any of these deficiencies would be welcomed.
-@node T-TEST, ONEWAY, CROSSTABS, Statistics
+@node NPAR TESTS
+@section NPAR TESTS
+
+@vindex NPAR TESTS
+@cindex nonparametric tests
+
+@display
+NPAR TESTS
+
+ nonparametric test subcommands
+ .
+ .
+ .
+
+ [ /STATISTICS=@{DESCRIPTIVES@} ]
+
+ [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
+
+ [ /METHOD=EXACT [ TIMER [(n)] ] ]
+@end display
+
+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
+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
+is used.
+
+
+@menu
+* BINOMIAL:: Binomial Test
+* CHISQUARE:: Chisquare Test
+* WILCOXON:: Wilcoxon Signed Ranks Test
+* SIGN:: The Sign Test
+@end menu
+
+
+@node BINOMIAL
+@subsection Binomial test
+@vindex BINOMIAL
+@cindex binomial test
+
+@display
+ [ /BINOMIAL[(p)]=var_list[(value1[, value2)] ] ]
+@end display
+
+The /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 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.
+
+If two values appear after the variable list, then they will be 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
+values, take no part in the test for that variable.
+
+If no values appear, then the variable must assume dichotomous
+values.
+If more than two distinct, non-missing values for a variable
+under test are encountered then an error occurs.
+
+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.
+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.
+
+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
+@vindex CHISQUARE
+@cindex chisquare test
+
+
+@display
+ [ /CHISQUARE=var_list[(lo,hi)] [/EXPECTED=@{EQUAL|f1, f2 @dots{} 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.
+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.
+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}
+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
+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
+
+@display
+ [ /WILCOXON varlist [ WITH varlist [ (PAIRED) ]]]
+@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.
+
+If the @code{WITH} keyword is omitted, then tests for all
+combinations of the listed variables are performed.
+If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
+is also given, then the number of variables preceding @code{WITH}
+must be the same as the number following it.
+In this case, tests for each respective pair of variables are
+performed.
+If the @code{WITH} keyword is given, but the
+@code{(PAIRED)} keyword is omitted, then tests for each combination
+of variable preceding @code{WITH} against variable following
+@code{WITH} are performed.
+
+
+@node SIGN
+@subsection Sign Test
+@vindex SIGN
+@cindex sign test
+
+@display
+ [ /SIGN varlist [ WITH varlist [ (PAIRED) ]]]
+@end display
+
+The /SIGN subcommand tests for differences between medians of the
+variables listed.
+The test does not make any assumptions about the
+distribution of the data.
+
+If the @code{WITH} keyword is omitted, then tests for all
+combinations of the listed variables are performed.
+If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
+is also given, then the number of variables preceding @code{WITH}
+must be the same as the number following it.
+In this case, tests for each respective pair of variables are
+performed.
+If the @code{WITH} keyword is given, but the
+@code{(PAIRED)} keyword is omitted, then tests for each combination
+of variable preceding @code{WITH} against variable following
+@code{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@}
* Paired Samples Mode:: Testing two interdependent groups for equal mean
@end menu
-@node One Sample Mode, Independent Samples Mode, T-TEST, T-TEST
+@node One Sample Mode
@subsection One Sample Mode
The @cmd{TESTVAL} subcommand invokes the One Sample mode.
In this mode, you must also use the @cmd{/VARIABLES} subcommand to
tell PSPP which variables you wish to test.
-@node Independent Samples Mode, Paired Samples Mode, One Sample Mode, T-TEST
+@node Independent Samples Mode
@comment node-name, next, previous, up
@subsection Independent Samples Mode
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
-less than or equal to this value belong to the first group, and cases
-greater than this value belong to the second group.
+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
the independent variable are excluded on a listwise basis, regardless
of whether @cmd{/MISSING=LISTWISE} was specified.
-@node Paired Samples Mode, , Independent Samples Mode, T-TEST
+@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 the @code{WITH} keyword is omitted, then tables for all
+If the @code{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
@code{WITH} are generated.
-@node ONEWAY, RANK, T-TEST, Statistics
+@node ONEWAY
@comment node-name, next, previous, up
@section ONEWAY
ONEWAY
[/VARIABLES = ] var_list BY var
/MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
- /CONTRASTS= value1 [, value2] ... [,valueN]
+ /CONTRAST= value1 [, value2] ... [,valueN]
/STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
@end display
variables and their groups.
@end itemize
-The @code{CONTRASTS} subcommand is used when you anticipate certain
+The @code{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.
groups (or values of the independent variable).
If the total sum of the coefficients are not zero, then PSPP will
display a warning, but will proceed with the analysis.
-The @code{CONTRASTS} subcommand may be given up to 10 times in order
+The @code{CONTRAST} subcommand may be given up to 10 times in order
to specify different contrast tests.
-@setfilename ignored
-@node RANK, REGRESSION, ONEWAY, Statistics
+@node RANK
@comment node-name, next, previous, up
@section RANK
@vindex RANK
-@cindex RANK
-
@display
RANK
[VARIABLES=] var_list [@{A,D@}] [BY var_list]
INCLUDE means they are to be included. The default is EXCLUDE.
@include regression.texi
+
+
+@node RELIABILITY
+@section RELIABILITY
+
+@vindex RELIABILITY
+@display
+RELIABILITY
+ /VARIABLES=var_list
+ /SCALE (@var{name}) = @{var_list, ALL@}
+ /MODEL=@{ALPHA, SPLIT[(N)]@}
+ /SUMMARY=@{TOTAL,ALL@}
+ /MISSING=@{EXCLUDE,INCLUDE@}
+@end display
+
+@cindex Cronbach's Alpha
+The @cmd{RELIABILTY} command performs reliablity analysis on the data.
+
+The 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
+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
+scale, or one half minus one if there are an odd number of variables.
+The default model is 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.
+
+The SUMMARY subcommand determines the type of summary analysis to be performed.
+Currently there is only one type: SUMMARY=TOTAL, which displays per-item
+analysis tested against the totals.
+
+
+
+@node ROC
+@section ROC
+
+@vindex ROC
+@cindex Receiver Operating Characterstic
+@cindex Area under curve
+
+@display
+ROC @var{var_list} BY @var{state_var} (@var{state_value})
+ /PLOT @{ CURVE [(REFERENCE)], NONE @}
+ /PRINT = [ SE ] [ COORDINATES ]
+ /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
+ [ TESTPOS (@{LARGE,SMALL@}) ]
+ [ CI (@var{confidence}) ]
+ [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
+ /MISSING=@{EXCLUDE,INCLUDE@}
+@end display
+
+
+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,
+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,
+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.
+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 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 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 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
+exponential distribution estimate.
+The 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.
+
+@item The CUTOFF parameter is for compatibility and is ignored.
+@end itemize
+
+The 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
+excluded.
+
+
projects / pspp-builds.git / blobdiff