1 @c PSPP - a program for statistical analysis.
2 @c Copyright (C) 2017, 2020 Free Software Foundation, Inc.
3 @c Permission is granted to copy, distribute and/or modify this document
4 @c under the terms of the GNU Free Documentation License, Version 1.3
5 @c or any later version published by the Free Software Foundation;
6 @c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
7 @c A copy of the license is included in the section entitled "GNU
8 @c Free Documentation License".
13 This chapter documents the statistical procedures that @pspp{} supports so
17 * DESCRIPTIVES:: Descriptive statistics.
18 * FREQUENCIES:: Frequency tables.
19 * EXAMINE:: Testing data for normality.
21 * CORRELATIONS:: Correlation tables.
22 * CROSSTABS:: Crosstabulation tables.
23 * CTABLES:: Custom tables.
24 * FACTOR:: Factor analysis and Principal Components analysis.
25 * GLM:: Univariate Linear Models.
26 * LOGISTIC REGRESSION:: Bivariate Logistic Regression.
27 * MEANS:: Average values and other statistics.
28 * NPAR TESTS:: Nonparametric tests.
29 * T-TEST:: Test hypotheses about means.
30 * ONEWAY:: One way analysis of variance.
31 * QUICK CLUSTER:: K-Means clustering.
32 * RANK:: Compute rank scores.
33 * RELIABILITY:: Reliability analysis.
34 * ROC:: Receiver Operating Characteristic.
43 /VARIABLES=@var{var_list}
44 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
45 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
47 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
48 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
49 SESKEWNESS,SEKURTOSIS@}
50 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
51 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
55 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
56 linear descriptive statistics requested by the user. In addition, it can optionally
59 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
60 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
62 All other subcommands are optional:
64 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
65 @subcmd{INCLUDE} is set, then user-missing values are included in the
66 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
67 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
68 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
69 the entire case is excluded whenever any value in that case has a
70 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
72 The @subcmd{FORMAT} subcommand has no effect. It is accepted for
73 backward compatibility.
75 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
76 the specified variables. The Z scores are saved to new variables.
77 Variable names are generated by trying first the original variable name
78 with Z prepended and truncated to a maximum of 8 characters, then the
79 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
80 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
81 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
82 list by enclosing them in parentheses after each variable.
83 When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
84 treating temporary transformations as permanent.
86 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
90 All of the statistics below.
94 Standard error of the mean.
97 @item @subcmd{VARIANCE}
99 @item @subcmd{KURTOSIS}
100 Kurtosis and standard error of the kurtosis.
101 @item @subcmd{SKEWNESS}
102 Skewness and standard error of the skewness.
112 Mean, standard deviation of the mean, minimum, maximum.
114 Standard error of the kurtosis.
116 Standard error of the skewness.
119 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
120 of the possible values should be self-explanatory. @subcmd{NAME} causes the
121 statistics to be sorted by name. By default, the statistics are listed
122 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
123 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
124 sort order, respectively.
126 @subsection Descriptives Example
128 The @file{physiology.sav} file contains various physiological data for a sample
129 of persons. Running the @cmd{DESCRIPTIVES} command on the variables @exvar{height}
130 and @exvar{temperature} with the default options allows one to see simple linear
131 statistics for these two variables. In @ref{descriptives:ex}, these variables
132 are specfied on the @subcmd{VARIABLES} subcommand and the @subcmd{SAVE} option
133 has been used, to request that Z scores be calculated.
135 After the command has completed, this example runs @cmd{DESCRIPTIVES} again, this
136 time on the @exvar{zheight} and @exvar{ztemperature} variables,
137 which are the two normalized (Z-score) variables generated by the
138 first @cmd{DESCRIPTIVES} command.
140 @float Example, descriptives:ex
141 @psppsyntax {descriptives.sps}
142 @caption {Running two @cmd{DESCRIPTIVES} commands, one with the @subcmd{SAVE} subcommand}
145 @float Screenshot, descriptives:scr
146 @psppimage {descriptives}
147 @caption {The Descriptives dialog box with two variables and Z-Scores option selected}
150 In @ref{descriptives:res}, we can see that there are 40 valid data for each of the variables
151 and no missing values. The mean average of the height and temperature is 16677.12
152 and 37.02 respectively. The descriptive statistics for temperature seem reasonable.
153 However there is a very high standard deviation for @exvar{height} and a suspiciously
154 low minimum. This is due to a data entry error in the
155 data (@pxref{Identifying incorrect data}).
157 In the second Descriptive Statistics command, one can see that the mean and standard
158 deviation of both Z score variables is 0 and 1 respectively. All Z score statistics
159 should have these properties since they are normalized versions of the original scores.
161 @float Result, descriptives:res
162 @psppoutput {descriptives}
163 @caption {Descriptives statistics including two normalized variables (Z-scores)}
172 /VARIABLES=@var{var_list}
173 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
174 @{AVALUE,DVALUE,AFREQ,DFREQ@}
175 /MISSING=@{EXCLUDE,INCLUDE@}
176 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
177 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
178 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
180 /PERCENTILES=percent@dots{}
181 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
182 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
183 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
184 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
185 /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
187 /ORDER=@{ANALYSIS,VARIABLE@}
190 (These options are not currently implemented.)
195 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
197 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
198 (including median and mode) and percentiles, and various graphical representations
199 of the frequency distribution.
201 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
202 variables to be analyzed.
204 The @subcmd{FORMAT} subcommand controls the output format. It has several
209 @subcmd{TABLE}, the default, causes a frequency table to be output for every
210 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
211 with a numeric argument causes them to be output except when there are
212 more than the specified number of values in the table.
215 Normally frequency tables are sorted in ascending order by value. This
216 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
217 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
218 respectively, by frequency count.
221 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
222 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
223 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
224 are included. System-missing values are never included in statistics,
225 but are listed in frequency tables.
227 The available @subcmd{STATISTICS} are the same as available
228 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
229 of @subcmd{MEDIAN}, the data's median
230 value, and MODE, the mode. (If there are multiple modes, the smallest
231 value is reported.) By default, the mean, standard deviation of the
232 mean, minimum, and maximum are reported for each variable.
235 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
236 The percentiles should be presented at a list of numbers between 0
238 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
239 boundaries of the data set divided into the specified number of ranges.
240 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
243 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
244 each specified numeric variable. The X axis by default ranges from
245 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
246 and @subcmd{MAXIMUM} keywords can set an explicit range.
247 @footnote{The number of
248 bins is chosen according to the Freedman-Diaconis rule:
249 @math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
250 and @math{n} is the number of samples. Note that
251 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
252 Histograms are not created for string variables.
254 Specify @subcmd{NORMAL} to superimpose a normal curve on the
258 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
259 slice represents one value, with the size of the slice proportional to
260 the value's frequency. By default, all non-missing values are given
262 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
263 displayed slices to a given range of values.
264 The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
265 piechart. This is the default.
266 If instead, @subcmd{MISSING} is specified, then the pie chart includes
267 a single slice representing all system missing and user-missing cases.
270 The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
271 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
272 categories whose counts which lie outside the specified limits.
273 The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
274 of each category, whereas the @subcmd{PERCENT} option displays relative
277 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
278 @subcmd{PIECHART} are accepted but not currently honoured.
280 The @subcmd{ORDER} subcommand is accepted but ignored.
282 @subsection Frequencies Example
284 @ref{frequencies:ex} runs a frequency analysis on the @exvar{sex}
285 and @exvar{occupation} variables from the @file{personnel.sav} file.
286 This is useful to get an general idea of the way in which these nominal
287 variables are distributed.
289 @float Example, frequencies:ex
290 @psppsyntax {frequencies.sps}
291 @caption {Running frequencies on the @exvar{sex} and @exvar{occupation} variables}
294 If you are using the graphic user interface, the dialog box is set up such that
295 by default, several statistics are calculated. Some are not particularly useful
296 for categorical variables, so you may want to disable those.
298 @float Screenshot, frequencies:scr
299 @psppimage {frequencies}
300 @caption {The frequencies dialog box with the @exvar{sex} and @exvar{occupation} variables selected}
303 From @ref{frequencies:res} it is evident that there are 33 males, 21 females and
304 2 persons for whom their sex has not been entered.
306 One can also see how many of each occupation there are in the data.
307 When dealing with string variables used as nominal values, running a frequency
308 analysis is useful to detect data input entries. Notice that
309 one @exvar{occupation} value has been mistyped as ``Scrientist''. This entry should
310 be corrected, or marked as missing before using the data.
312 @float Result, frequencies:res
313 @psppoutput {frequencies}
314 @caption {The relative frequencies of @exvar{sex} and @exvar{occupation}}
321 @cindex Exploratory data analysis
322 @cindex normality, testing
326 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
327 [BY @var{factor1} [BY @var{subfactor1}]
328 [ @var{factor2} [BY @var{subfactor2}]]
330 [ @var{factor3} [BY @var{subfactor3}]]
332 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
333 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
335 /COMPARE=@{GROUPS,VARIABLES@}
336 /ID=@var{identity_variable}
338 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
339 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
340 [@{NOREPORT,REPORT@}]
344 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
345 In particular, it is useful for testing how closely a distribution follows a
346 normal distribution, and for finding outliers and extreme values.
348 The @subcmd{VARIABLES} subcommand is mandatory.
349 It specifies the dependent variables and optionally variables to use as
350 factors for the analysis.
351 Variables listed before the first @subcmd{BY} keyword (if any) are the
353 The dependent variables may optionally be followed by a list of
354 factors which tell @pspp{} how to break down the analysis for each
357 Following the dependent variables, factors may be specified.
358 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
359 The format for each factor is
361 @var{factorvar} [BY @var{subfactorvar}].
363 Each unique combination of the values of @var{factorvar} and
364 @var{subfactorvar} divide the dataset into @dfn{cells}.
365 Statistics are calculated for each cell
366 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
368 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
369 @subcmd{DESCRIPTIVES} produces a table showing some parametric and
370 non-parametrics statistics.
371 @subcmd{EXTREME} produces a table showing the extremities of each cell.
372 A number in parentheses, @var{n} determines
373 how many upper and lower extremities to show.
374 The default number is 5.
376 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
377 If @subcmd{TOTAL} appears, then statistics for the entire dataset
378 as well as for each cell are produced.
379 If @subcmd{NOTOTAL} appears, then statistics are produced only for the cells
380 (unless no factor variables have been given).
381 These subcommands have no effect if there have been no factor variables
387 @cindex spreadlevel plot
388 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
389 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
390 @subcmd{SPREADLEVEL}.
391 The first three can be used to visualise how closely each cell conforms to a
392 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
393 how the variance differs between factors.
394 Boxplots show you the outliers and extreme values.
395 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
396 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
397 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
399 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
400 median. It takes an optional parameter @var{t}, which specifies how the data
401 should be transformed prior to plotting.
402 The given value @var{t} is a power to which the data are raised. For example, if
403 @var{t} is given as 2, then the square of the data is used.
404 Zero, however is a special value. If @var{t} is 0 or
405 is omitted, then data are transformed by taking its natural logarithm instead of
406 raising to the power of @var{t}.
409 When one or more plots are requested, @subcmd{EXAMINE} also performs the
410 Shapiro-Wilk test for each category.
411 There are however a number of provisos:
413 @item All weight values must be integer.
414 @item The cumulative weight value must be in the range [3, 5000]
417 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
418 useful there is more than one dependent variable and at least one factor.
420 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
421 each of which contain boxplots for all the cells.
422 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
423 each containing one boxplot per dependent variable.
424 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
425 @subcmd{/COMPARE=GROUPS} were given.
427 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
428 @subcmd{/STATISTICS=EXTREME} has been given.
429 If given, it should provide the name of a variable which is to be used
430 to labels extreme values and outliers.
431 Numeric or string variables are permissible.
432 If the @subcmd{ID} subcommand is not given, then the case number is used for
435 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
436 calculation of the descriptives command. The default is 95%.
439 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
440 and which algorithm to use for calculating them. The default is to
441 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
442 @subcmd{HAVERAGE} algorithm.
444 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
445 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
446 then statistics for the unfactored dependent variables are
447 produced in addition to the factored variables. If there are no
448 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
451 The following example generates descriptive statistics and histograms for
452 two variables @var{score1} and @var{score2}.
453 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
454 Therefore, the descriptives and histograms are generated for each
456 of @var{gender} @emph{and} for each distinct combination of the values
457 of @var{gender} and @var{race}.
458 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
459 @var{score1} and @var{score2} covering the whole dataset are not produced.
461 EXAMINE @var{score1} @var{score2} BY
463 @var{gender} BY @var{culture}
464 /STATISTICS = DESCRIPTIVES
469 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
471 EXAMINE @var{height} @var{weight} BY
473 /STATISTICS = EXTREME (3)
478 In this example, we look at the height and weight of a sample of individuals and
479 how they differ between male and female.
480 A table showing the 3 largest and the 3 smallest values of @exvar{height} and
481 @exvar{weight} for each gender, and for the whole dataset as are shown.
482 In addition, the @subcmd{/PLOT} subcommand requests boxplots.
483 Because @subcmd{/COMPARE = GROUPS} was specified, boxplots for male and female are
484 shown in juxtaposed in the same graphic, allowing us to easily see the difference between
486 Since the variable @var{name} was specified on the @subcmd{ID} subcommand,
487 values of the @var{name} variable are used to label the extreme values.
490 If you specify many dependent variables or factor variables
491 for which there are many distinct values, then @cmd{EXAMINE} will produce a very
492 large quantity of output.
498 @cindex Exploratory data analysis
499 @cindex normality, testing
503 /HISTOGRAM [(NORMAL)]= @var{var}
504 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
505 /BAR = @{@var{summary-function}(@var{var1}) | @var{count-function}@} BY @var{var2} [BY @var{var3}]
506 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
507 [@{NOREPORT,REPORT@}]
511 The @cmd{GRAPH} command produces graphical plots of data. Only one of the subcommands
512 @subcmd{HISTOGRAM}, @subcmd{BAR} or @subcmd{SCATTERPLOT} can be specified, @i{i.e.} only one plot
513 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
516 * SCATTERPLOT:: Cartesian Plots
517 * HISTOGRAM:: Histograms
518 * BAR CHART:: Bar Charts
522 @subsection Scatterplot
525 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the
527 @cmd{GRAPH} uses the third variable @var{var3}, if specified, to determine
528 the colours and/or markers for the plot.
529 The following is an example for producing a scatterplot.
533 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
536 This example produces a scatterplot where @var{height} is plotted versus @var{weight}. Depending
537 on the value of the @var{gender} variable, the colour of the datapoint is different. With
538 this plot it is possible to analyze gender differences for @var{height} versus @var{weight} relation.
541 @subsection Histogram
544 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
546 The keyword @subcmd{NORMAL} may be specified in parentheses, to indicate that the ideal normal curve
547 should be superimposed over the histogram.
548 For an alternative method to produce histograms @pxref{EXAMINE}. The
549 following example produces a histogram plot for the variable @var{weight}.
553 /HISTOGRAM = @var{weight}.
557 @subsection Bar Chart
560 The subcommand @subcmd{BAR} produces a bar chart.
561 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.
562 Following the summary or count function, the keyword @subcmd{BY} should be specified and then a catagorical variable, @var{var2}.
563 The values of the variable @var{var2} determine the labels of the bars to be plotted.
564 Optionally a second categorical variable @var{var3} may be specified in which case a clustered (grouped) bar chart is produced.
566 Valid count functions are
569 The weighted counts of the cases in each category.
571 The weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
573 The cumulative weighted counts of the cases in each category.
575 The cumulative weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
578 The summary function is applied to @var{var1} across all cases in each category.
579 The recognised summary functions are:
591 The following examples assume a dataset which is the results of a survey.
592 Each respondent has indicated annual income, their sex and city of residence.
593 One could create a bar chart showing how the mean income varies between of residents of different cities, thus:
595 GRAPH /BAR = MEAN(@var{income}) BY @var{city}.
598 This can be extended to also indicate how income in each city differs between the sexes.
600 GRAPH /BAR = MEAN(@var{income}) BY @var{city} BY @var{sex}.
603 One might also want to see how many respondents there are from each city. This can be achieved as follows:
605 GRAPH /BAR = COUNT BY @var{city}.
608 Bar charts can also be produced using the @ref{FREQUENCIES} and @ref{CROSSTABS} commands.
611 @section CORRELATIONS
616 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
621 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
622 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
625 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
626 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
627 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
631 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
632 for a set of variables. The significance of the coefficients are also given.
634 At least one @subcmd{VARIABLES} subcommand is required. If you specify the @subcmd{WITH}
635 keyword, then a non-square correlation table is produced.
636 The variables preceding @subcmd{WITH}, are used as the rows of the table,
637 and the variables following @subcmd{WITH} are used as the columns of the table.
638 If no @subcmd{WITH} subcommand is specified, then @cmd{CORRELATIONS} produces a
639 square, symmetrical table using all variables.
641 The @cmd{MISSING} subcommand determines the handling of missing variables.
642 If @subcmd{INCLUDE} is set, then user-missing values are included in the
643 calculations, but system-missing values are not.
644 If @subcmd{EXCLUDE} is set, which is the default, user-missing
645 values are excluded as well as system-missing values.
647 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
648 whenever any variable specified in any @cmd{/VARIABLES} subcommand
649 contains a missing value.
650 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
651 values for the particular coefficient are missing.
652 The default is @subcmd{PAIRWISE}.
654 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
655 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
656 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
657 The default is @subcmd{TWOTAIL}.
659 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
660 0.05 are highlighted.
661 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
664 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
665 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
666 estimator of the standard deviation are displayed.
667 These statistics are displayed in a separated table, for all the variables listed
668 in any @subcmd{/VARIABLES} subcommand.
669 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
670 be displayed for each pair of variables.
671 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
679 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
680 /MISSING=@{TABLE,INCLUDE,REPORT@}
681 /FORMAT=@{TABLES,NOTABLES@}
683 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
684 ASRESIDUAL,ALL,NONE@}
685 /COUNT=@{ASIS,CASE,CELL@}
687 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
688 KAPPA,ETA,CORR,ALL,NONE@}
692 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
695 The @cmd{CROSSTABS} procedure displays crosstabulation
696 tables requested by the user. It can calculate several statistics for
697 each cell in the crosstabulation tables. In addition, a number of
698 statistics can be calculated for each table itself.
700 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
701 number of dimensions is permitted, and any number of variables per
702 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
703 times as needed. This is the only required subcommand in @dfn{general
706 Occasionally, one may want to invoke a special mode called @dfn{integer
707 mode}. Normally, in general mode, @pspp{} automatically determines
708 what values occur in the data. In integer mode, the user specifies the
709 range of values that the data assumes. To invoke this mode, specify the
710 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
711 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
712 the range are truncated to the nearest integer, then assigned to that
713 value. If values occur outside this range, they are discarded. When it
714 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
717 In general mode, numeric and string variables may be specified on
718 TABLES. In integer mode, only numeric variables are allowed.
720 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
721 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
722 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
723 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
724 integer mode, user-missing values are included in tables but marked with
725 a footnote and excluded from statistical calculations.
727 The @subcmd{FORMAT} subcommand controls the characteristics of the
728 crosstabulation tables to be displayed. It has a number of possible
733 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
734 @subcmd{NOTABLES}, which is equivalent to @code{CELLS=NONE}, suppresses them.
737 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
738 @subcmd{DVALUE} asserts a descending sort order.
741 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
742 crosstabulation table. The possible settings are:
758 Standardized residual.
760 Adjusted standardized residual.
764 Suppress cells entirely.
767 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
768 @subcmd{COLUMN}, and @subcmd{TOTAL}.
769 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
772 By default, crosstabulation and statistics use raw case weights,
773 without rounding. Use the @subcmd{/COUNT} subcommand to perform
774 rounding: CASE rounds the weights of individual weights as cases are
775 read, CELL rounds the weights of cells within each crosstabulation
776 table after it has been constructed, and ASIS explicitly specifies the
777 default non-rounding behavior. When rounding is requested, ROUND, the
778 default, rounds to the nearest integer and TRUNCATE rounds toward
781 The @subcmd{STATISTICS} subcommand selects statistics for computation:
787 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
788 correction, linear-by-linear association.
792 Contingency coefficient.
796 Uncertainty coefficient.
812 Spearman correlation, Pearson's r.
819 Selected statistics are only calculated when appropriate for the
820 statistic. Certain statistics require tables of a particular size, and
821 some statistics are calculated only in integer mode.
823 @samp{/STATISTICS} without any settings selects CHISQ. If the
824 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
827 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
828 variables on each table.
829 If a table has more than two variables, the counts for the third and subsequent levels
830 are aggregated and the chart is produced as if there were only two variables.
833 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
834 following limitations:
838 Significance of some symmetric and directional measures is not calculated.
840 Asymptotic standard error is not calculated for
841 Goodman and Kruskal's tau or symmetric Somers' d.
843 Approximate T is not calculated for symmetric uncertainty coefficient.
846 Fixes for any of these deficiencies would be welcomed.
848 @subsection Crosstabs Example
850 @cindex chi-square test of independence
852 A researcher wishes to know if, in an industry, a person's sex is related to
853 the person's occupation. To investigate this, she has determined that the
854 @file{personnel.sav} is a representative, randomly selected sample of persons.
855 The researcher's null hypothesis is that a person's sex has no relation to a
856 person's occupation. She uses a chi-squared test of independence to investigate
859 @float Example, crosstabs:ex
860 @psppsyntax {crosstabs.sps}
861 @caption {Running crosstabs on the @exvar{sex} and @exvar{occupation} variables}
864 The syntax in @ref{crosstabs:ex} conducts a chi-squared test of independence.
865 The line @code{/tables = occupation by sex} indicates that @exvar{occupation}
866 and @exvar{sex} are the variables to be tabulated. To do this using the @gui{}
867 you must place these variable names respectively in the @samp{Row} and
868 @samp{Column} fields as shown in @ref{crosstabs:scr}.
870 @float Screenshot, crosstabs:scr
871 @psppimage {crosstabs}
872 @caption {The Crosstabs dialog box with the @exvar{sex} and @exvar{occupation} variables selected}
875 Similarly, the @samp{Cells} button shows a dialog box to select the @code{count}
876 and @code{expected} options. All other cell options can be deselected for this
879 You would use the @samp{Format} and @samp{Statistics} buttons to select options
880 for the @subcmd{FORMAT} and @subcmd{STATISTICS} subcommands. In this example,
881 the @samp{Statistics} requires only the @samp{Chisq} option to be checked. All
882 other options should be unchecked. No special settings are required from the
883 @samp{Format} dialog.
885 As shown in @ref{crosstabs:res} @cmd{CROSSTABS} generates a contingency table
886 containing the observed count and the expected count of each sex and each
887 occupation. The expected count is the count which would be observed if the
888 null hypothesis were true.
890 The significance of the Pearson Chi-Square value is very much larger than the
891 normally accepted value of 0.05 and so one cannot reject the null hypothesis.
892 Thus the researcher must conclude that a person's sex has no relation to the
895 @float Results, crosstabs:res
896 @psppoutput {crosstabs}
897 @caption {The results of a test of independence between @exvar{sex} and @exvar{occupation}}
904 @cindex custom tables
905 @cindex tables, custom
907 @code{CTABLES} has the following overall syntax. At least one
908 @code{TABLE} subcommand is required:
912 @dots{}@i{global subcommands}@dots{}
913 [@t{/TABLE} @i{axis} [@t{BY} @i{axis} [@t{BY} @i{axis}]]
914 @dots{}@i{per-table subcommands}@dots{}]@dots{}
918 where each @i{axis} may be empty or take one of the following forms:
922 @i{variable} @t{[}@{@t{C} @math{|} @t{S}@}@t{]}
926 @i{axis} @t{[}@i{summary} [@i{string}] [@i{format}]@t{]}
929 The following subcommands precede the first @code{TABLE} subcommand
930 and apply to all of the output tables. All of these subcommands are
935 [@t{MINCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
936 [@t{MAXCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
937 [@t{UNITS=}@{@t{POINTS} @math{|} @t{INCHES} @math{|} @t{CM}@}]
938 [@t{EMPTY=}@{@t{ZERO} @math{|} @t{BLANK} @math{|} @i{string}@}]
939 [@t{MISSING=}@i{string}]
941 @t{VARIABLES=}@i{variables}
942 @t{DISPLAY}=@{@t{DEFAULT} @math{|} @t{NAME} @math{|} @t{LABEL} @math{|} @t{BOTH} @math{|} @t{NONE}@}
943 @ignore @c not yet implemented
944 @t{/MRSETS COUNTDUPLICATES=}@{@t{YES} @math{|} @t{NO}@}
946 @t{/SMISSING} @{@t{VARIABLE} @math{|} @t{LISTWISE}@}
947 @t{/PCOMPUTE} @t{&}@i{postcompute}@t{=EXPR(}@i{expression}@t{)}
948 @t{/PPROPERTIES} @t{&}@i{postcompute}@dots{}
949 [@t{LABEL=}@i{string}]
950 [@t{FORMAT=}[@i{summary} @i{format}]@dots{}]
951 [@t{HIDESOURCECATS=}@{@t{NO} @math{|} @t{YES}@}
952 @t{/WEIGHT VARIABLE=}@i{variable}
953 @t{/HIDESMALLCOUNTS COUNT=@i{count}}
956 The following subcommands follow @code{TABLE} and apply only to the
957 previous @code{TABLE}. All of these subcommands are optional:
961 [@t{POSITION=}@{@t{COLUMN} @math{|} @t{ROW} @math{|} @t{LAYER}@}]
962 [@t{VISIBLE=}@{@t{YES} @math{|} @t{NO}@}]
963 @t{/CLABELS} @{@t{AUTO} @math{|} @{@t{ROWLABELS}@math{|}@t{COLLABELS}@}@t{=}@{@t{OPPOSITE}@math{|}@t{LAYER}@}@}
964 @t{/CATEGORIES} @t{VARIABLES=}@i{variables}
965 @{@t{[}@i{value}@t{,} @i{value}@dots{}@t{]}
966 @math{|} [@t{ORDER=}@{@t{A} @math{|} @t{D}@}]
967 [@t{KEY=}@{@t{VALUE} @math{|} @t{LABEL} @math{|} @i{summary}@t{(}@i{variable}@t{)}@}]
968 [@t{MISSING=}@{@t{EXCLUDE} @math{|} @t{INCLUDE}@}]@}
969 [@t{TOTAL=}@{@t{NO} @math{|} @t{YES}@} [@t{LABEL=}@i{string}] [@t{POSITION=}@{@t{AFTER} @math{|} @t{BEFORE}@}]]
970 [@t{EMPTY=}@{@t{INCLUDE} @math{|} @t{EXCLUDE}@}]
972 [@t{TITLE=}@i{string}@dots{}]
973 [@t{CAPTION=}@i{string}@dots{}]
974 [@t{CORNER=}@i{string}@dots{}]
975 @ignore @c not yet implemented
976 @t{/CRITERIA CILEVEL=}@i{percentage}
977 @t{/SIGTEST TYPE=CHISQUARE}
978 [@t{ALPHA=}@i{siglevel}]
979 [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
980 [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
981 @t{/COMPARETEST TYPE=}@{@t{PROP} @math{|} @t{MEAN}@}
982 [@t{ALPHA=}@i{value}[@t{,} @i{value}]]
983 [@t{ADJUST=}@{@t{BONFERRONI} @math{|} @t{BH} @math{|} @t{NONE}@}]
984 [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
985 [@t{MEANSVARIANCE=}@{@t{ALLCATS} @math{|} @t{TESTEDCATS}@}]
986 [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
987 [@t{MERGE=}@{@t{NO} @math{|} @t{YES}@}]
988 [@t{STYLE=}@{@t{APA} @math{|} @t{SIMPLE}@}]
989 [@t{SHOWSIG=}@{@t{NO} @math{|} @t{YES}@}]
993 The @code{CTABLES} (aka ``custom tables'') command produces
994 multi-dimensional tables from categorical and scale data. It offers
995 many options for data summarization and formatting.
997 This section's examples use data from the 2008 (USA) National Survey
998 of Drinking and Driving Attitudes and Behaviors, a public domain data
999 set from the (USA) National Highway Traffic Administration and
1000 available at @url{https://data.transportation.gov}. @pspp{} includes
1001 this data set, with a slightly modified dictionary, as
1002 @file{examples/nhtsa.sav}.
1004 @node CTABLES Basics
1007 The only required subcommand is @code{TABLE}, which specifies the
1008 variables to include along each axis:
1010 @t{/TABLE} @i{rows} [@t{BY} @i{columns} [@t{BY} @i{layers}]]
1013 In @code{TABLE}, each of @var{rows}, @var{columns}, and @var{layers}
1014 is either empty or an axis expression that specifies one or more
1015 variables. At least one must specify an axis expression.
1018 * CTABLES Categorical Variable Basics::
1019 * CTABLES Scalar Variable Basics::
1020 * CTABLES Overriding Measurement Level::
1023 @node CTABLES Categorical Variable Basics
1024 @subsubsection Categorical Variables
1026 An axis expression that names a categorical variable divides the data
1027 into cells according to the values of that variable. When all the
1028 variables named on @code{TABLE} are categorical, by default each cell
1029 displays the number of cases that it contains, so specifying a single
1030 variable yields a frequency table:
1033 CTABLES /TABLE=AgeGroup.
1035 @psppoutput {ctables1}
1038 Specifying a row and a column categorical variable yields a
1042 CTABLES /TABLE=AgeGroup BY qns3a.
1044 @psppoutput {ctables2}
1047 The @samp{>} ``nesting'' operator nests multiple variables on a single
1051 CTABLES /TABLE qn105ba BY AgeGroup > qns3a.
1053 @psppoutput {ctables3}
1056 The @samp{+} ``stacking'' operator allows a single output table to
1057 include multiple data analyses. With @samp{+}, @code{CTABLES} divides
1058 the output table into multiple @dfn{sections}, each of which includes
1059 an analysis of the full data set. For example, the following command
1060 separately tabulates age group and driving frequency by gender:
1063 CTABLES /TABLE AgeGroup + qn1 BY qns3a.
1065 @psppoutput {ctables4}
1068 When @samp{+} and @samp{>} are used together, @samp{>} binds more
1069 tightly. Use parentheses to override operator precedence. Thus:
1072 CTABLES /TABLE qn26 + qn27 > qns3a.
1073 CTABLES /TABLE (qn26 + qn27) > qns3a.
1075 @psppoutput {ctables5}
1077 @node CTABLES Scalar Variable Basics
1078 @subsubsection Scalar Variables
1080 For a categorical variable, @code{CTABLES} divides the table into a
1081 cell per category. For a scalar variable, @code{CTABLES} instead
1082 calculates a summary measure, by default the mean, of the values that
1083 fall into a cell. For example, if the only variable specified is a
1084 scalar variable, then the output is a single cell that holds the mean
1088 CTABLES /TABLE qnd1.
1090 @psppoutput {ctables6}
1092 A scalar variable may nest with categorical variables. The following
1093 example shows the mean age of survey respondents across gender and
1097 CTABLES /TABLE qns3a > qnd1 BY region.
1099 @psppoutput {ctables7}
1101 The order of nesting of scalar and categorical variables affects table
1102 labeling, but it does not affect the data displayed in the table. The
1103 following example shows how the output changes when the nesting order
1104 of the scalar and categorical variable are interchanged:
1107 CTABLES /TABLE qnd1 > qns3a BY region.
1109 @psppoutput {ctables8}
1111 Only a single scalar variable may appear in each section; that is, a
1112 scalar variable may not nest inside a scalar variable directly or
1113 indirectly. Scalar variables may only appear on one axis within
1116 @node CTABLES Overriding Measurement Level
1117 @subsubsection Overriding Measurement Level
1119 By default, @code{CTABLES} uses a variable's measurement level to
1120 decide whether to treat it as categorical or scalar. Variables
1121 assigned the nominal or ordinal measurement level are treated as
1122 categorical, and scalar variables are treated as scalar.
1124 Use the @code{VARIABLE LEVEL} command to change a variable's
1125 measurement level (@pxref{VARIABLE LEVEL}). To treat a variable as
1126 categorical or scalar only for one use on @code{CTABLES}, add
1127 @samp{[C]} or @samp{[S]}, respectively, after the variable name. The
1128 following example shows how to analyze the scalar variable @code{qn20}
1132 CTABLES /TABLE qn20 [C] BY qns3a.
1134 @psppoutput {ctables9}
1137 @node CTABLES Multiple Response Sets
1138 @subsubheading Multiple Response Sets
1140 The @code{CTABLES} command does not yet support multiple response
1144 @node CTABLES Data Summarization
1145 @subsection Data Summarization
1147 The @code{CTABLES} command allows the user to control how the data are
1148 summarized with summary specifications, which are enclosed in square
1149 brackets following a variable name on the @code{TABLE} subcommand.
1150 When all the variables are categorical, summary specifications can be
1151 given for the innermost nested variables on any one axis. When a
1152 scalar variable is present, only the scalar variable may have summary
1153 specifications. The following example includes a summary
1154 specification for column and row percentages for categorical
1155 variables, and mean and median for a scalar variable:
1159 /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a
1160 /TABLE=AgeGroup [COLPCT, ROWPCT] BY qns3a.
1162 @psppoutput {ctables10}
1164 A summary specification may override the default label and format by
1165 appending a string or format specification or both (in that order) to
1166 the summary function name. For example:
1169 CTABLES /TABLE=AgeGroup [COLPCT 'Gender %' PCT5.0,
1170 ROWPCT 'Age Group %' PCT5.0]
1173 @psppoutput {ctables11}
1175 Parentheses provide a shorthand to apply summary specifications to
1176 multiple variables. For example, both of these commands:
1179 CTABLES /TABLE=AgeGroup[COLPCT] + qns1[COLPCT] BY qns3a.
1180 CTABLES /TABLE=(AgeGroup + qns1)[COLPCT] BY qns3a.
1184 produce the same output shown below:
1186 @psppoutput {ctables12}
1188 The following section lists the available summary functions.
1191 * CTABLES Summary Functions::
1194 @node CTABLES Summary Functions
1195 @subsubsection Summary Functions
1197 This section lists the summary functions that can be applied to cells
1198 in @code{CTABLES}. Many of these functions have an @var{area} in
1199 their names. The supported areas are:
1203 Areas that correspond to parts of @dfn{sections}, where stacked
1204 variables divide each section from another:
1211 A layer within a section.
1214 A row in one layer within a section.
1217 A column in one layer within a section.
1221 Areas that correspond to parts of @dfn{subtables}, whose contents are
1222 the cells that pair an innermost row variable and an innermost column
1223 variable within a single layer. A section can contain multiple
1224 subtables and a subtable is always within a single section:
1228 A row within a subtable.
1231 A column within a subtable.
1234 All the cells in a subtable.
1239 The following summary functions may be applied to any variable
1240 regardless of whether it is categorical or scalar. The default label
1241 for each function is listed in parentheses:
1244 @item @code{COUNT} (``Count'')
1245 The sum of weights in a cell.
1247 If @code{CATEGORIES} for one or more of the variables in a table
1248 include missing values (@pxref{CTABLES Per-Variable Category
1249 Options}), then some or all of the categories for a cell might be
1250 missing values. @code{COUNT} counts data included in a cell
1251 regardless of whether its categories are missing.
1253 @item @code{@i{area}PCT} or @code{@i{area}PCT.COUNT} (``@i{Area} %'')
1254 A percentage within the specified @var{area}.
1256 @item @code{@i{area}PCT.VALIDN} (``@i{Area} Valid N %'')
1257 A percentage of valid values within the specified @var{area}.
1259 @item @code{@i{area}PCT.TOTALN} (``@i{Area} Total N %'')
1260 A percentage of total values within the specified @var{area}.
1263 The following summary functions apply only to scalar variables or
1264 totals and subtotals for categorical variables. Be cautious about
1265 interpreting the summary value in the latter case, because it is not
1266 necessarily meaningful; however, the mean of a Likert scale, etc.@:
1267 may have a straightforward interpreation.
1270 @item @code{MAXIMUM} (``Maximum'')
1273 @item @code{MEAN} (``Mean'')
1276 @item @code{MEDIAN} (``Median'')
1279 @item @code{MINIMUM} (``Minimum'')
1282 @item @code{MISSING} (``Missing'')
1283 Sum of weights of user- and system-missing values.
1285 @item @code{MODE} (``Mode'')
1286 The highest-frequency value. Ties are broken by taking the smallest mode.
1288 @item @code{@i{area}PCT.SUM} (``@i{Area} Sum %'')
1289 Percentage of the sum of the values across @var{area}.
1291 @item @code{PTILE} @i{n} (``Percentile @i{n}'')
1292 The @var{n}th percentile, where @math{0 @leq{} @var{n} @leq{} 100}.
1294 @item @code{RANGE} (``Range'')
1295 The maximum minus the minimum.
1297 @item @code{SEMEAN} (``Std Error of Mean'')
1298 The standard error of the mean.
1300 @item @code{STDDEV} (``Std Deviation'')
1301 The standard deviation.
1303 @item @code{SUM} (``Sum'')
1306 @item @code{TOTALN} (``Total N'')
1307 The sum of weights in a cell.
1309 For scale data, @code{COUNT} and @code{TOTALN} are the same.
1311 For categorical data, @code{TOTALN} counts missing values in excluded
1312 categories, that is, user-missing values not in an explicit category
1313 list on @code{CATEGORIES} (@pxref{CTABLES Per-Variable Category
1314 Options}), or user-missing values excluded because
1315 @code{MISSING=EXCLUDE} is in effect on @code{CATEGORIES}, or
1316 system-missing values. @code{COUNT} does not count these.
1318 @item @code{VALIDN} (``Valid N'')
1319 The sum of valid count weights in included categories.
1321 @code{VALIDN} does not count missing values regardless of whether they
1322 are in included categories via @code{CATEGORIES}. @code{VALIDN} does
1323 not count valid values that are in excluded categories.
1325 @item @code{VARIANCE} (``Variance'')
1329 If the @code{WEIGHT} subcommand specified an adjustment weight
1330 variable, then the following summary functions use its value instead
1331 of the dictionary weight variable. Otherwise, they are equivalent to
1332 the summary function without the @samp{E}-prefix:
1336 @code{ECOUNT} (``Adjusted Count'')
1339 @code{ETOTALN} (``Adjusted Total N'')
1342 @code{EVALIDN} (``Adjusted Valid N'')
1345 The following summary functions with a @samp{U}-prefix are equivalent
1346 to the same ones without the prefix, except that they use unweighted
1351 @code{UCOUNT} (``Unweighted Count'')
1354 @code{U@i{area}PCT} or @code{U@i{area}PCT.COUNT} (``Unweighted @i{Area} %'')
1357 @code{U@i{area}PCT.VALIDN} (``Unweighted @i{Area} Valid N %'')
1360 @code{U@i{area}PCT.TOTALN} (``Unweighted @i{Area} Total N %'')
1363 @code{UMEAN} (``Unweighted Mean'')
1366 @code{UMEDIAN} (``Unweighted Median'')
1369 @code{UMISSING} (``Unweighted Missing'')
1372 @code{UMODE} (``Unweight Mode'')
1375 @code{U@i{area}PCT.SUM} (``Unweighted @i{Area} Sum %'')
1378 @code{UPTILE} @i{n} (``Unweighted Percentile @i{n}'')
1381 @code{USEMEAN} (``Unweighted Std Error of Mean'')
1384 @code{USTDDEV} (``Unweighted Std Deviation'')
1387 @code{USUM} (``Unweighted Sum'')
1390 @code{UTOTALN} (``Unweighted Total N'')
1393 @code{UVALIDN} (``Unweighted Valid N'')
1396 @code{UVARIANCE} (``Unweighted Variance'')
1399 @node CTABLES Statistics Positions and Labels
1400 @subsection Statistics Positions and Labels
1404 [@t{POSITION=}@{@t{COLUMN} @math{|} @t{ROW} @math{|} @t{LAYER}@}]
1405 [@t{VISIBLE=}@{@t{YES} @math{|} @t{NO}@}]
1408 The @code{SLABELS} subcommand controls the position and visibility of
1409 summary statistics for the @code{TABLE} subcommand that it follows.
1411 @code{POSITION} sets the axis on which summary statistics appear.
1412 With @t{POSITION=COLUMN}, which is the default, each summary statistic
1413 appears in a column. For example:
1416 CTABLES /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a.
1418 @psppoutput {ctables13}
1421 With @t{POSITION=ROW}, each summary statistic appears in a row, as
1425 CTABLES /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a /SLABELS POSITION=ROW.
1427 @psppoutput {ctables14}
1430 @t{POSITION=LAYER} is also available to place each summary statistic in
1433 Labels for summary statistics are shown by default. Use
1434 @t{VISIBLE=NO} to suppress them. Because unlabeled data can cause
1435 confusion, it should only be considered if the meaning of the data is
1436 evident, as in a simple case like this:
1439 CTABLES /TABLE=AgeGroup [TABLEPCT] /SLABELS VISIBLE=NO.
1441 @psppoutput {ctables15}
1443 @node CTABLES Category Label Positions
1444 @subsection Category Label Positions
1447 @t{/CLABELS} @{@t{AUTO} @math{|} @{@t{ROWLABELS}@math{|}@t{COLLABELS}@}@t{=}@{@t{OPPOSITE}@math{|}@t{LAYER}@}@}
1450 The @code{CLABELS} subcommand controls the position of category labels
1451 for the @code{TABLE} subcommand that it follows. By default, or if
1452 @t{AUTO} is specified, category labels for a given variable nest
1453 inside the variable's label on the same axis. For example, the
1454 command below results in age categories nesting within the age group
1455 variable on the rows axis and gender categories within the gender
1456 variable on the columns axis:
1459 CTABLES /TABLE AgeGroup BY qns3a.
1461 @psppoutput {ctables16}
1463 @t{ROWLABELS=OPPOSITE} or @t{COLLABELS=OPPOSITE} move row or column
1464 variable category labels, respectively, to the opposite axis. The
1465 setting affects only the innermost variable on the given axis. For
1469 CTABLES /TABLE AgeGroup BY qns3a /CLABELS ROWLABELS=OPPOSITE.
1470 CTABLES /TABLE AgeGroup BY qns3a /CLABELS COLLABELS=OPPOSITE.
1472 @psppoutput {ctables17}
1474 @t{ROWLABELS=LAYER} or @t{COLLABELS=LAYER} move the innermost row or
1475 column variable category labels, respectively, to the layer axis.
1477 Only one axis's labels may be moved, whether to the opposite axis or
1480 @node CTABLES Per-Variable Category Options
1481 @subsection Per-Variable Category Options
1484 @t{/CATEGORIES} @t{VARIABLES=}@i{variables}
1485 @{@t{[}@i{value}@t{,} @i{value}@dots{}@t{]}
1486 @math{|} [@t{ORDER=}@{@t{A} @math{|} @t{D}@}]
1487 [@t{KEY=}@{@t{VALUE} @math{|} @t{LABEL} @math{|} @i{summary}@t{(}@i{variable}@t{)}@}]
1488 [@t{MISSING=}@{@t{EXCLUDE} @math{|} @t{INCLUDE}@}]@}
1489 [@t{TOTAL=}@{@t{NO} @math{|} @t{YES}@} [@t{LABEL=}@i{string}] [@t{POSITION=}@{@t{AFTER} @math{|} @t{BEFORE}@}]]
1490 [@t{EMPTY=}@{@t{INCLUDE} @math{|} @t{EXCLUDE}@}]
1493 The @code{CATEGORIES} subcommand specifies, for one or more
1494 categorical variables, the categories to include and exclude, the sort
1495 order for included categories, and treatment of missing values. It
1496 also controls the totals and subtotals to display. It may be
1497 specified any number of times, each time for a different set of
1498 variables. @code{CATEGORIES} applies to the table produced by the
1499 @code{TABLE} subcommand that it follows.
1501 @code{CATEGORIES} does not apply to scalar variables.
1503 @t{VARIABLES} is required. List the variables for the subcommand
1506 There are two way to specify the Categories to include and their sort
1510 @item Explicit categories.
1511 @anchor{CTABLES Explicit Category List}
1512 To explicitly specify categories to include, list the categories
1513 within square brackets in the desired sort order. Use spaces or
1514 commas to separate values. Categories not covered by the list are
1515 excluded from analysis.
1517 Each element of the list takes one of the following forms:
1522 A numeric or string category value, for variables that have the
1527 A date or time category value, for variables that have a date or time
1530 @item @i{min} THRU @i{max}
1531 @itemx LO THRU @i{max}
1532 @itemx @i{min} THRU HI
1533 A range of category values, where @var{min} and @var{max} each takes
1534 one of the forms above, in increasing order.
1537 All user-missing values. (To match individual user-missing values,
1538 specify their category values.)
1541 Any non-missing value not covered by any other element of the list
1542 (regardless of where @t{OTHERNM} is placed in the list).
1544 @item &@i{postcompute}
1545 A computed category name (@pxref{CTABLES Computed Categories}).
1548 Additional forms, described later, allow for subtotals.
1549 If multiple elements of the list cover a given category, the last one
1550 in the list is considered to be a match.
1552 @item Implicit categories.
1553 Without an explicit list of categories, @pspp{} sorts
1554 categories automatically.
1556 The @code{KEY} setting specifies the sort key. By default, or with
1557 @code{KEY=VALUE}, categories are sorted by default. Categories may
1558 also be sorted by value label, with @code{KEY=LABEL}, or by the value
1559 of a summary function, e.g.@: @code{KEY=COUNT}. For summary
1560 functions, a variable name may be specified in parentheses, e.g.@:
1561 @code{KEY=MAXIUM(qnd1)}, and this is required for functions that apply
1562 only to scalar variables. The @code{PTILE} function also requires a
1563 percentage argument, e.g.@: @code{KEY=PTILE(qnd1, 90)}. Only summary
1564 functions used in the table may be used, except that @code{COUNT} is
1567 By default, or with @code{ORDER=A}, categories are sorted in ascending
1568 order. Specify @code{ORDER=D} to sort in descending order.
1570 User-missing values are excluded by default, or with
1571 @code{MISSING=EXCLUDE}. Specify @code{MISSING=INCLUDE} to include
1572 user-missing values. The system-missing value is always excluded.
1575 @subsubheading Totals and Subtotals
1577 @code{CATEGORIES} also controls display of totals and subtotals.
1578 Totals are not displayed by default, or with @code{TOTAL=NO}. Specify
1579 @code{TOTAL=YES} to display a total. By default, the total is labeled
1580 ``Total''; use @code{LABEL="@i{label}"} to override it.
1582 Subtotals are also not displayed by default. To add one or more
1583 subtotals, use an explicit category list and insert @code{SUBTOTAL} or
1584 @code{HSUBTOTAL} in the position or positions where the subtotal
1585 should appear. With @code{SUBTOTAL}, the subtotal becomes an extra
1586 row or column or layer; @code{HSUBTOTAL} additionally hides the
1587 categories that make up the subtotal. Either way, the default label
1588 is ``Subtotal'', use @code{SUBTOTAL="@i{label}"} or
1589 @code{HSUBTOTAL="@i{label}"} to specify a custom label.
1591 By default, or with @code{POSITION=AFTER}, totals come after the last
1592 category and subtotals apply to categories that precede them. With
1593 @code{POSITION=BEFORE}, totals come before the first category and
1594 subtotals apply to categories that follow them.
1596 Only categorical variables may have totals and subtotals. Scalar
1597 variables may be ``totaled'' indirectly by enabling totals and
1598 subtotals on a categorical variable within which the scalar variable is
1601 @subsubheading Categories Without Values
1603 Some categories might not be included in the data set being analyzed.
1604 For example, our example data set has no cases in the ``15 or
1605 younger'' age group. By default, or with @code{EMPTY=INCLUDE},
1606 @pspp{} includes these empty categories in output tables. To exclude
1607 them, specify @code{EMPTY=EXCLUDE}.
1609 For implicit categories, empty categories potentially include all the
1610 values with labels for a given variable; for explicit categories, they
1611 include all the values listed individually and all labeled values
1612 covered by ranges or @code{MISSING} or @code{OTHERNM}.
1614 @node CTABLES Titles
1619 [@t{TITLE=}@i{string}@dots{}]
1620 [@t{CAPTION=}@i{string}@dots{}]
1621 [@t{CORNER=}@i{string}@dots{}]
1624 The @code{TITLES} subcommand sets the title, caption, and corner text
1625 for the table output for the previous @code{TABLE} subcommand. The
1626 title appears above the table, the caption below the table, and the
1627 corner text appears in the table's upper left corner. By default, the
1628 title is ``Custom Tables'' and the caption and corner text are empty.
1630 @node CTABLES Table Formatting
1631 @subsection Table Formatting
1635 [@t{MINCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
1636 [@t{MAXCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
1637 [@t{UNITS=}@{@t{POINTS} @math{|} @t{INCHES} @math{|} @t{CM}@}]
1638 [@t{EMPTY=}@{@t{ZERO} @math{|} @t{BLANK} @math{|} @i{string}@}]
1639 [@t{MISSING=}@i{string}]
1642 The @code{FORMAT} subcommand, which must precede the first
1643 @code{TABLE} subcommand, controls formatting for all the output
1644 tables. @code{FORMAT} and all of its settings are optional.
1646 Use @code{MINCOLWIDTH} and @code{MAXCOLWIDTH} to control the minimum
1647 or maximum width of columns in output tables. By default, or with
1648 @code{DEFAULT}, column width varies based on content. Otherwise,
1649 specify a number for either or both of these settings. If both are
1650 specified, @code{MAXCOLWIDTH} must be bigger than @code{MINCOLWIDTH}.
1651 The default unit, or with @code{UNITS=POINTS}, is points (1/72 inch),
1652 but specify @code{UNITS=INCHES} to use inches or @code{UNITS=CM} for
1655 By default, or with @code{EMPTY=ZERO}, zero values are displayed in
1656 their usual format. Use @code{EMPTY=BLANK} to use an empty cell
1657 instead, or @code{EMPTY="@i{string}"} to use the specified string.
1659 By default, missing values are displayed as @samp{.}, the same as in
1660 other tables. Specify @code{MISSING="@i{string}"} to instead use a
1663 @node CTABLES Display of Variable Labels
1664 @subsection Display of Variable Labels
1668 @t{VARIABLES=}@i{variables}
1669 @t{DISPLAY}=@{@t{DEFAULT} @math{|} @t{NAME} @math{|} @t{LABEL} @math{|} @t{BOTH} @math{|} @t{NONE}@}
1672 The @code{VLABELS} subcommand, which must precede the first
1673 @code{TABLE} subcommand, controls display of variable labels in all
1674 the output tables. @code{VLABELS} is optional. It may appear
1675 multiple times to adjust settings for different variables.
1677 @code{VARIABLES} and @code{DISPLAY} are required. The value of
1678 @code{DISPLAY} controls how variable labels are displayed for the
1679 variables listed on @code{VARIABLES}. The supported values are:
1683 Uses the setting from @ref{SET TVARS}.
1686 Show only a variable name.
1689 Show only a variable label.
1692 Show variable name and label.
1698 @node CTABLES Missing Value Treatment
1699 @subsection Missing Value Treatment
1702 @t{/SMISSING} @{@t{VARIABLE} @math{|} @t{LISTWISE}@}
1705 The @code{SMISSING} subcommand, which must precede the first
1706 @code{TABLE} subcommand, controls treatment of missing values for
1707 scalar variables in producing all the output tables. @code{SMISSING}
1710 With @code{SMISSING=VARIABLE}, which is the default, missing values
1711 are excluded on a variable-by-variable basis. With
1712 @code{SMISSING=LISTWISE}, when stacked scalar variables are nested
1713 together with a categorical variable, a missing value for any of the
1714 scalar variables causes the case to be excluded for all of them.
1716 As an example, consider the following dataset, in which @samp{x} is a
1717 categorical variable and @samp{y} and @samp{z} are scale:
1719 @psppoutput{ctables18}
1722 With the default missing-value treatment, @samp{x}'s mean is 20, based
1723 on the values 10, 20, and 30, and @samp{y}'s mean is 50, based on 40,
1727 CTABLES /TABLE (y + z) > x.
1729 @psppoutput{ctables19}
1732 By adding @code{SMISSING=LISTWISE}, only cases where @samp{y} and
1733 @samp{z} are both non-missing are considered, so @samp{x}'s mean
1734 becomes 15, as the average of 10 and 20, and @samp{y}'s mean becomes
1735 55, the average of 50 and 60:
1738 CTABLES /SMISSING LISTWISE /TABLE (y + z) > x.
1740 @psppoutput{ctables20}
1743 Even with @code{SMISSING=LISTWISE}, if @samp{y} and @samp{z} are
1744 separately nested with @samp{x}, instead of using a single @samp{>}
1745 operator, missing values revert to being considered on a
1746 variable-by-variable basis:
1749 CTABLES /SMISSING LISTWISE /TABLE (y > x) + (z > x).
1751 @psppoutput{ctables21}
1753 @node CTABLES Computed Categories
1754 @subsection Computed Categories
1757 @t{/PCOMPUTE} @t{&}@i{postcompute}@t{=EXPR(}@i{expression}@t{)}
1760 @dfn{Computed categories}, also called @dfn{postcomputes}, are
1761 categories created using arithmetic on categories obtained from the
1762 data. The @code{PCOMPUTE} subcommand defines computed categories,
1763 which can then be used in two places: on @code{CATEGORIES} within an
1764 explicit category list (@pxref{CTABLES Explicit Category List}), and on
1765 the @code{PPROPERTIES} subcommand to define further properties for a
1768 @code{PCOMPUTE} must precede the first @code{TABLE} command. It is
1769 optional and it may be used any number of times to define multiple
1772 Each @code{PCOMPUTE} defines one postcompute. Its syntax consists of
1773 a name to identify the postcompute as a @pspp{} identifier prefixed by
1774 @samp{&}, followed by @samp{=} and a postcompute expression enclosed
1775 in @code{EXPR(@dots{})}. A postcompute expression consists of:
1778 @item [@i{category}]
1779 This form evaluates to the summary statistic for @i{category}, e.g.@:
1780 @code{[1]} evaluates to the value of the summary statistic associated
1781 with category 1. The @i{category} may be a number, a quoted string,
1782 or a quoted time or date value, and all of the categories for a given
1783 postcompute must have the same form.
1785 @item [@i{min} THRU @i{max}]
1786 @itemx [LO THRU @i{max}]
1787 @itemx [@i{min} THRU HI]
1790 These forms evaluate to the summary statistics for categories matching
1791 the given syntax, as described in previous sections (@pxref{CTABLES
1792 Explicit Category List}). If more than one category matches, their
1796 The summary statistic for the subtotal category. This form is allowed
1797 only for variables with exactly one subtotal.
1799 @item SUBTOTAL[@i{index}]
1800 The summary statistic for subtotal category @i{index}, where 1 is the
1801 first subtotal, 2 is the second, and so on. This form may be used for
1802 any number of subtotals.
1805 The summary statistic for the total.
1808 @itemx @i{a} - @i{b}
1809 @itemx @i{a} * @i{b}
1810 @itemx @i{a} / @i{b}
1811 @itemx @i{a} ** @i{b}
1812 These forms perform arithmetic on the values of postcompute
1813 expressions @i{a} and @i{b}. The usual operator precedence rules
1817 Numeric constants may be used in postcompute expressions.
1820 Parentheses override operator precedence.
1823 A postcompute is not associated with any particular variable.
1824 Instead, it may be referenced within @code{CATEGORIES} for any
1825 suitable variable (e.g.@: only a string variable is suitable for a
1826 postcompute expression that refers to a string category, only a
1827 variable with subtotals for an expression that refers to subtotals,
1830 Normally a named postcompute is defined only once, but if a later
1831 @code{PCOMPUTE} redefines a postcompute with the same name as an
1832 earlier one, the later one take precedence.
1834 @node CTABLES Computed Category Properties
1835 @subsection Computed Category Properties
1838 @t{/PPROPERTIES} @t{&}@i{postcompute}@dots{}
1839 [@t{LABEL=}@i{string}]
1840 [@t{FORMAT=}[@i{summary} @i{format}]@dots{}]
1841 [@t{HIDESOURCECATS=}@{@t{NO} @math{|} @t{YES}@}
1844 The @code{PPROPERTIES} subcommand, which must appear before
1845 @code{TABLE}, sets properties for one or more postcomputes defined on
1846 prior @code{PCOMPUTE} subcommands. The subcommand syntax begins with
1847 the list of postcomputes, each prefixed with @samp{&} as specified on
1850 All of the settings on @code{PPROPERTIES} are optional. Use
1851 @code{LABEL} to set the label shown for the postcomputes in table
1852 output. The default label for a postcompute is the expression used to
1855 The @code{FORMAT} setting sets summary statistics and display formats
1856 for the postcomputes.
1858 By default, or with @code{HIDESOURCECATS=NO}, categories referred to
1859 by computed categories are displayed like other categories. Use
1860 @code{HIDESOURCECATS=YES} to hide them.
1862 @node CTABLES Base Weight
1863 @subsection Base Weight
1866 @t{/WEIGHT VARIABLE=}@i{variable}
1869 The @code{WEIGHT} subcommand is optional and must appear before
1870 @code{TABLE}. If it appears, it must name a numeric variable, known
1871 as the @dfn{effective base weight} or @dfn{adjustment weight}. The
1872 effective base weight variable is used for the @code{ECOUNT},
1873 @code{ETOTALN}, and @code{EVALIDN} summary functions.
1875 Cases with zero, missing, or negative effective base weight are
1876 excluded from all analysis.
1878 Weights obtained from the @pspp{} dictionary are rounded to the
1879 nearest integer. Effective base weights are not rounded.
1881 @node CTABLES Hiding Small Counts
1882 @subsection Hiding Small Counts
1885 @t{/HIDESMALLCOUNTS COUNT=@i{count}}
1888 The @code{HIDESMALLCOUNTS} subcommand is optional. If it specified,
1889 then count values in output tables less than the value of @i{count}
1890 are shown as @code{<@i{count}} instead of their true values. The
1891 value of @i{count} must be an integer and must be at least 2. Case
1892 weights are considered for deciding whether to hide a count.
1898 @cindex factor analysis
1899 @cindex principal components analysis
1900 @cindex principal axis factoring
1901 @cindex data reduction
1905 VARIABLES=@var{var_list},
1906 MATRIX IN (@{CORR,COV@}=@{*,@var{file_spec}@})
1909 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
1911 [ /ANALYSIS=@var{var_list} ]
1913 [ /EXTRACTION=@{PC, PAF@}]
1915 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
1917 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [AIC] [SIG] [ALL] [DEFAULT] ]
1921 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
1923 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
1925 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
1928 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
1929 common factors in the data or for data reduction purposes.
1931 The @subcmd{VARIABLES} subcommand is required (unless the @subcmd{MATRIX IN}
1932 subcommand is used).
1933 It lists the variables which are to partake in the analysis. (The @subcmd{ANALYSIS}
1934 subcommand may optionally further limit the variables that
1935 participate; it is useful primarily in conjunction with @subcmd{MATRIX IN}.)
1937 If @subcmd{MATRIX IN} instead of @subcmd{VARIABLES} is specified, then the analysis
1938 is performed on a pre-prepared correlation or covariance matrix file instead of on
1939 individual data cases. Typically the matrix file will have been generated by
1940 @cmd{MATRIX DATA} (@pxref{MATRIX DATA}) or provided by a third party.
1941 If specified, @subcmd{MATRIX IN} must be followed by @samp{COV} or @samp{CORR},
1942 then by @samp{=} and @var{file_spec} all in parentheses.
1943 @var{file_spec} may either be an asterisk, which indicates the currently loaded
1944 dataset, or it may be a file name to be loaded. @xref{MATRIX DATA}, for the expected
1947 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors
1948 (components) are extracted from the data.
1949 If @subcmd{PC} is specified, then Principal Components Analysis is used.
1950 If @subcmd{PAF} is specified, then Principal Axis Factoring is
1951 used. By default Principal Components Analysis is used.
1953 The @subcmd{/ROTATION} subcommand is used to specify the method by which the
1954 extracted solution is rotated. Three orthogonal rotation methods are available:
1955 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
1956 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
1957 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
1958 The default value of @var{k} is 5.
1959 If you don't want any rotation to be performed, the word @subcmd{NOROTATE}
1960 prevents the command from performing any rotation on the data.
1962 The @subcmd{/METHOD} subcommand should be used to determine whether the
1963 covariance matrix or the correlation matrix of the data is
1964 to be analysed. By default, the correlation matrix is analysed.
1966 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
1969 @item @subcmd{UNIVARIATE}
1970 A table of mean values, standard deviations and total weights are printed.
1971 @item @subcmd{INITIAL}
1972 Initial communalities and eigenvalues are printed.
1973 @item @subcmd{EXTRACTION}
1974 Extracted communalities and eigenvalues are printed.
1975 @item @subcmd{ROTATION}
1976 Rotated communalities and eigenvalues are printed.
1977 @item @subcmd{CORRELATION}
1978 The correlation matrix is printed.
1979 @item @subcmd{COVARIANCE}
1980 The covariance matrix is printed.
1982 The determinant of the correlation or covariance matrix is printed.
1984 The anti-image covariance and anti-image correlation matrices are printed.
1986 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
1988 The significance of the elements of correlation matrix is printed.
1990 All of the above are printed.
1991 @item @subcmd{DEFAULT}
1992 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
1995 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues is
1996 printed. This can be useful for visualizing the factors and deciding
1997 which factors (components) should be retained.
1999 The @subcmd{/FORMAT} subcommand determined how data are to be
2000 displayed in loading matrices. If @subcmd{SORT} is specified, then
2001 the variables are sorted in descending order of significance. If
2002 @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute
2003 value is less than @var{n} are not printed. If the keyword
2004 @subcmd{DEFAULT} is specified, or if no @subcmd{/FORMAT} subcommand is
2005 specified, then no sorting is performed, and all coefficients are printed.
2007 You can use the @subcmd{/CRITERIA} subcommand to specify how the number of
2008 extracted factors (components) are chosen. If @subcmd{FACTORS(@var{n})} is
2009 specified, where @var{n} is an integer, then @var{n} factors are
2010 extracted. Otherwise, the @subcmd{MINEIGEN} setting is used.
2011 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues
2012 are greater than or equal to @var{l} are extracted. The default value
2013 of @var{l} is 1. The @subcmd{ECONVERGE} setting has effect only when
2014 using iterative algorithms for factor extraction (such as Principal Axis
2015 Factoring). @subcmd{ECONVERGE(@var{delta})} specifies that
2016 iteration should cease when the maximum absolute value of the
2017 communality estimate between one iteration and the previous is less
2018 than @var{delta}. The default value of @var{delta} is 0.001.
2020 The @subcmd{ITERATE(@var{m})} may appear any number of times and is
2021 used for two different purposes. It is used to set the maximum number
2022 of iterations (@var{m}) for convergence and also to set the maximum
2023 number of iterations for rotation.
2024 Whether it affects convergence or rotation depends upon which
2025 subcommand follows the @subcmd{ITERATE} subcommand.
2026 If @subcmd{EXTRACTION} follows, it affects convergence.
2027 If @subcmd{ROTATION} follows, it affects rotation.
2028 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a
2029 @subcmd{ITERATE} subcommand, then the entire subcommand is ignored.
2030 The default value of @var{m} is 25.
2032 The @cmd{MISSING} subcommand determines the handling of missing
2033 variables. If @subcmd{INCLUDE} is set, then user-missing values are
2034 included in the calculations, but system-missing values are not.
2035 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2036 values are excluded as well as system-missing values. This is the
2037 default. If @subcmd{LISTWISE} is set, then the entire case is excluded
2038 from analysis whenever any variable specified in the @cmd{VARIABLES}
2039 subcommand contains a missing value.
2041 If @subcmd{PAIRWISE} is set, then a case is considered missing only if
2042 either of the values for the particular coefficient are missing.
2043 The default is @subcmd{LISTWISE}.
2049 @cindex univariate analysis of variance
2050 @cindex fixed effects
2051 @cindex factorial anova
2052 @cindex analysis of variance
2057 GLM @var{dependent_vars} BY @var{fixed_factors}
2058 [/METHOD = SSTYPE(@var{type})]
2059 [/DESIGN = @var{interaction_0} [@var{interaction_1} [... @var{interaction_n}]]]
2060 [/INTERCEPT = @{INCLUDE|EXCLUDE@}]
2061 [/MISSING = @{INCLUDE|EXCLUDE@}]
2064 The @cmd{GLM} procedure can be used for fixed effects factorial Anova.
2066 The @var{dependent_vars} are the variables to be analysed.
2067 You may analyse several variables in the same command in which case they should all
2068 appear before the @code{BY} keyword.
2070 The @var{fixed_factors} list must be one or more categorical variables. Normally it
2071 does not make sense to enter a scalar variable in the @var{fixed_factors} and doing
2072 so may cause @pspp{} to do a lot of unnecessary processing.
2074 The @subcmd{METHOD} subcommand is used to change the method for producing the sums of
2075 squares. Available values of @var{type} are 1, 2 and 3. The default is type 3.
2077 You may specify a custom design using the @subcmd{DESIGN} subcommand.
2078 The design comprises a list of interactions where each interaction is a
2079 list of variables separated by a @samp{*}. For example the command
2081 GLM subject BY sex age_group race
2082 /DESIGN = age_group sex group age_group*sex age_group*race
2084 @noindent specifies the model @math{subject = age_group + sex + race + age_group*sex + age_group*race}.
2085 If no @subcmd{DESIGN} subcommand is specified, then the default is all possible combinations
2086 of the fixed factors. That is to say
2088 GLM subject BY sex age_group race
2091 @math{subject = age_group + sex + race + age_group*sex + age_group*race + sex*race + age_group*sex*race}.
2094 The @subcmd{MISSING} subcommand determines the handling of missing
2096 If @subcmd{INCLUDE} is set then, for the purposes of GLM analysis,
2097 only system-missing values are considered
2098 to be missing; user-missing values are not regarded as missing.
2099 If @subcmd{EXCLUDE} is set, which is the default, then user-missing
2100 values are considered to be missing as well as system-missing values.
2101 A case for which any dependent variable or any factor
2102 variable has a missing value is excluded from the analysis.
2104 @node LOGISTIC REGRESSION
2105 @section LOGISTIC REGRESSION
2107 @vindex LOGISTIC REGRESSION
2108 @cindex logistic regression
2109 @cindex bivariate logistic regression
2112 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
2114 [/CATEGORICAL = @var{categorical_predictors}]
2116 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
2118 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
2120 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
2121 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
2122 [CUT(@var{cut_point})]]
2124 [/MISSING = @{INCLUDE|EXCLUDE@}]
2127 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
2128 variable in terms of one or more predictor variables.
2130 The minimum command is
2132 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
2134 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
2135 are the predictor variables whose coefficients the procedure estimates.
2137 By default, a constant term is included in the model.
2138 Hence, the full model is
2141 = b_0 + b_1 {\bf x_1}
2147 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
2148 Simple variables as well as interactions between variables may be listed here.
2150 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
2151 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
2153 An iterative Newton-Raphson procedure is used to fit the model.
2154 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
2155 and other parameters.
2156 The value of @var{cut_point} is used in the classification table. It is the
2157 threshold above which predicted values are considered to be 1. Values
2158 of @var{cut_point} must lie in the range [0,1].
2159 During iterations, if any one of the stopping criteria are satisfied, the procedure is
2160 considered complete.
2161 The stopping criteria are:
2163 @item The number of iterations exceeds @var{max_iterations}.
2164 The default value of @var{max_iterations} is 20.
2165 @item The change in the all coefficient estimates are less than @var{min_delta}.
2166 The default value of @var{min_delta} is 0.001.
2167 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
2168 The default value of @var{min_delta} is zero.
2169 This means that this criterion is disabled.
2170 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
2171 In other words, the probabilities are close to zero or one.
2172 The default value of @var{min_epsilon} is 0.00000001.
2176 The @subcmd{PRINT} subcommand controls the display of optional statistics.
2177 Currently there is one such option, @subcmd{CI}, which indicates that the
2178 confidence interval of the odds ratio should be displayed as well as its value.
2179 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
2180 confidence level of the desired confidence interval.
2182 The @subcmd{MISSING} subcommand determines the handling of missing
2184 If @subcmd{INCLUDE} is set, then user-missing values are included in the
2185 calculations, but system-missing values are not.
2186 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2187 values are excluded as well as system-missing values.
2188 This is the default.
2199 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
2201 [ /@{@var{var_list}@}
2202 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
2204 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
2205 [VARIANCE] [KURT] [SEKURT]
2206 [SKEW] [SESKEW] [FIRST] [LAST]
2207 [HARMONIC] [GEOMETRIC]
2212 [/MISSING = [INCLUDE] [DEPENDENT]]
2215 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
2216 statistics, either for the dataset as a whole or for categories of data.
2218 The simplest form of the command is
2222 @noindent which calculates the mean, count and standard deviation for @var{v}.
2223 If you specify a grouping variable, for example
2225 MEANS @var{v} BY @var{g}.
2227 @noindent then the means, counts and standard deviations for @var{v} after having
2228 been grouped by @var{g} are calculated.
2229 Instead of the mean, count and standard deviation, you could specify the statistics
2230 in which you are interested:
2232 MEANS @var{x} @var{y} BY @var{g}
2233 /CELLS = HARMONIC SUM MIN.
2235 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
2238 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
2242 @cindex arithmetic mean
2243 The arithmetic mean.
2244 @item @subcmd{COUNT}
2245 The count of the values.
2246 @item @subcmd{STDDEV}
2247 The standard deviation.
2248 @item @subcmd{SEMEAN}
2249 The standard error of the mean.
2251 The sum of the values.
2256 @item @subcmd{RANGE}
2257 The difference between the maximum and minimum values.
2258 @item @subcmd{VARIANCE}
2260 @item @subcmd{FIRST}
2261 The first value in the category.
2263 The last value in the category.
2266 @item @subcmd{SESKEW}
2267 The standard error of the skewness.
2270 @item @subcmd{SEKURT}
2271 The standard error of the kurtosis.
2272 @item @subcmd{HARMONIC}
2273 @cindex harmonic mean
2275 @item @subcmd{GEOMETRIC}
2276 @cindex geometric mean
2280 In addition, three special keywords are recognized:
2282 @item @subcmd{DEFAULT}
2283 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
2285 All of the above statistics are calculated.
2287 No statistics are calculated (only a summary is shown).
2291 More than one @dfn{table} can be specified in a single command.
2292 Each table is separated by a @samp{/}. For
2296 @var{c} @var{d} @var{e} BY @var{x}
2297 /@var{a} @var{b} BY @var{x} @var{y}
2298 /@var{f} BY @var{y} BY @var{z}.
2300 has three tables (the @samp{TABLE =} is optional).
2301 The first table has three dependent variables @var{c}, @var{d} and @var{e}
2302 and a single categorical variable @var{x}.
2303 The second table has two dependent variables @var{a} and @var{b},
2304 and two categorical variables @var{x} and @var{y}.
2305 The third table has a single dependent variables @var{f}
2306 and a categorical variable formed by the combination of @var{y} and @var{z}.
2309 By default values are omitted from the analysis only if missing values
2310 (either system missing or user missing)
2311 for any of the variables directly involved in their calculation are
2313 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
2314 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
2316 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
2317 variables or in the categorical variables should be taken at their face
2318 value, and not excluded.
2320 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
2321 variables should be taken at their face value, however cases which
2322 have user missing values for the categorical variables should be omitted
2323 from the calculation.
2325 @subsection Example Means
2327 The dataset in @file{repairs.sav} contains the mean time between failures (@exvar{mtbf})
2328 for a sample of artifacts produced by different factories and trialed under
2329 different operating conditions.
2330 Since there are four combinations of categorical variables, by simply looking
2331 at the list of data, it would be hard to how the scores vary for each category.
2332 @ref{means:ex} shows one way of tabulating the @exvar{mtbf} in a way which is
2333 easier to understand.
2335 @float Example, means:ex
2336 @psppsyntax {means.sps}
2337 @caption {Running @cmd{MEANS} on the @exvar{mtbf} score with categories @exvar{factory} and @exvar{environment}}
2340 The results are shown in @ref{means:res}. The figures shown indicate the mean,
2341 standard deviation and number of samples in each category.
2342 These figures however do not indicate whether the results are statistically
2343 significant. For that, you would need to use the procedures @cmd{ONEWAY}, @cmd{GLM} or
2344 @cmd{T-TEST} depending on the hypothesis being tested.
2346 @float Result, means:res
2348 @caption {The @exvar{mtbf} categorised by @exvar{factory} and @exvar{environment}}
2351 Note that there is no limit to the number of variables for which you can calculate
2352 statistics, nor to the number of categorical variables per layer, nor the number
2354 However, running @cmd{MEANS} on a large numbers of variables, or with categorical variables
2355 containing a large number of distinct values may result in an extremely large output, which
2356 will not be easy to interpret.
2357 So you should consider carefully which variables to select for participation in the analysis.
2363 @cindex nonparametric tests
2368 nonparametric test subcommands
2373 [ /STATISTICS=@{DESCRIPTIVES@} ]
2375 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
2377 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
2380 @cmd{NPAR TESTS} performs nonparametric tests.
2381 Non parametric tests make very few assumptions about the distribution of the
2383 One or more tests may be specified by using the corresponding subcommand.
2384 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
2385 produces for each variable that is the subject of any test.
2387 Certain tests may take a long time to execute, if an exact figure is required.
2388 Therefore, by default asymptotic approximations are used unless the
2389 subcommand @subcmd{/METHOD=EXACT} is specified.
2390 Exact tests give more accurate results, but may take an unacceptably long
2391 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
2392 after which the test is abandoned, and a warning message printed.
2393 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
2394 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
2399 * BINOMIAL:: Binomial Test
2400 * CHISQUARE:: Chi-square Test
2401 * COCHRAN:: Cochran Q Test
2402 * FRIEDMAN:: Friedman Test
2403 * KENDALL:: Kendall's W Test
2404 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
2405 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
2406 * MANN-WHITNEY:: Mann Whitney U Test
2407 * MCNEMAR:: McNemar Test
2408 * MEDIAN:: Median Test
2410 * SIGN:: The Sign Test
2411 * WILCOXON:: Wilcoxon Signed Ranks Test
2416 @subsection Binomial test
2418 @cindex binomial test
2421 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
2424 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
2425 variable with that of a binomial distribution.
2426 The variable @var{p} specifies the test proportion of the binomial
2428 The default value of 0.5 is assumed if @var{p} is omitted.
2430 If a single value appears after the variable list, then that value is
2431 used as the threshold to partition the observed values. Values less
2432 than or equal to the threshold value form the first category. Values
2433 greater than the threshold form the second category.
2435 If two values appear after the variable list, then they are used
2436 as the values which a variable must take to be in the respective
2438 Cases for which a variable takes a value equal to neither of the specified
2439 values, take no part in the test for that variable.
2441 If no values appear, then the variable must assume dichotomous
2443 If more than two distinct, non-missing values for a variable
2444 under test are encountered then an error occurs.
2446 If the test proportion is equal to 0.5, then a two tailed test is
2447 reported. For any other test proportion, a one tailed test is
2449 For one tailed tests, if the test proportion is less than
2450 or equal to the observed proportion, then the significance of
2451 observing the observed proportion or more is reported.
2452 If the test proportion is more than the observed proportion, then the
2453 significance of observing the observed proportion or less is reported.
2454 That is to say, the test is always performed in the observed
2457 @pspp{} uses a very precise approximation to the gamma function to
2458 compute the binomial significance. Thus, exact results are reported
2459 even for very large sample sizes.
2463 @subsection Chi-square Test
2465 @cindex chi-square test
2469 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
2473 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
2474 between the expected and observed frequencies of the categories of a variable.
2475 Optionally, a range of values may appear after the variable list.
2476 If a range is given, then non integer values are truncated, and values
2477 outside the specified range are excluded from the analysis.
2479 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
2481 There must be exactly one non-zero expected value, for each observed
2482 category, or the @subcmd{EQUAL} keyword must be specified.
2483 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
2484 consecutive expected categories all taking a frequency of @var{f}.
2485 The frequencies given are proportions, not absolute frequencies. The
2486 sum of the frequencies need not be 1.
2487 If no @subcmd{/EXPECTED} subcommand is given, then equal frequencies
2490 @subsubsection Chi-square Example
2492 A researcher wishes to investigate whether there are an equal number of
2493 persons of each sex in a population. The sample chosen for invesigation
2494 is that from the @file {physiology.sav} dataset. The null hypothesis for
2495 the test is that the population comprises an equal number of males and females.
2496 The analysis is performed as shown in @ref{chisquare:ex}.
2498 @float Example, chisquare:ex
2499 @psppsyntax {chisquare.sps}
2500 @caption {Performing a chi-square test to check for equal distribution of sexes}
2503 There is only one test variable, @i{viz:} @exvar{sex}. The other variables in the dataset
2506 @float Screenshot, chisquare:scr
2507 @psppimage {chisquare}
2508 @caption {Performing a chi-square test using the graphic user interface}
2511 In @ref{chisquare:res} the summary box shows that in the sample, there are more males
2512 than females. However the significance of chi-square result is greater than 0.05
2513 --- the most commonly accepted p-value --- and therefore
2514 there is not enough evidence to reject the null hypothesis and one must conclude
2515 that the evidence does not indicate that there is an imbalance of the sexes
2518 @float Result, chisquare:res
2519 @psppoutput {chisquare}
2520 @caption {The results of running a chi-square test on @exvar{sex}}
2525 @subsection Cochran Q Test
2527 @cindex Cochran Q test
2528 @cindex Q, Cochran Q
2531 [ /COCHRAN = @var{var_list} ]
2534 The Cochran Q test is used to test for differences between three or more groups.
2535 The data for @var{var_list} in all cases must assume exactly two
2536 distinct values (other than missing values).
2538 The value of Q is displayed along with its Asymptotic significance
2539 based on a chi-square distribution.
2542 @subsection Friedman Test
2544 @cindex Friedman test
2547 [ /FRIEDMAN = @var{var_list} ]
2550 The Friedman test is used to test for differences between repeated measures when
2551 there is no indication that the distributions are normally distributed.
2553 A list of variables which contain the measured data must be given. The procedure
2554 prints the sum of ranks for each variable, the test statistic and its significance.
2557 @subsection Kendall's W Test
2559 @cindex Kendall's W test
2560 @cindex coefficient of concordance
2563 [ /KENDALL = @var{var_list} ]
2566 The Kendall test investigates whether an arbitrary number of related samples come from the
2568 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
2569 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
2570 unity indicates complete agreement.
2573 @node KOLMOGOROV-SMIRNOV
2574 @subsection Kolmogorov-Smirnov Test
2575 @vindex KOLMOGOROV-SMIRNOV
2577 @cindex Kolmogorov-Smirnov test
2580 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
2583 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
2584 drawn from a particular distribution. Four distributions are supported, @i{viz:}
2585 Normal, Uniform, Poisson and Exponential.
2587 Ideally you should provide the parameters of the distribution against
2588 which you wish to test the data. For example, with the normal
2589 distribution the mean (@var{mu})and standard deviation (@var{sigma})
2590 should be given; with the uniform distribution, the minimum
2591 (@var{min})and maximum (@var{max}) value should be provided.
2592 However, if the parameters are omitted they are imputed from the
2593 data. Imputing the parameters reduces the power of the test so should
2594 be avoided if possible.
2596 In the following example, two variables @var{score} and @var{age} are
2597 tested to see if they follow a normal distribution with a mean of 3.5
2598 and a standard deviation of 2.0.
2601 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
2603 If the variables need to be tested against different distributions, then a separate
2604 subcommand must be used. For example the following syntax tests @var{score} against
2605 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
2606 is tested against a normal distribution of mean 40 and standard deviation 1.5.
2609 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
2610 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
2613 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
2615 @node KRUSKAL-WALLIS
2616 @subsection Kruskal-Wallis Test
2617 @vindex KRUSKAL-WALLIS
2619 @cindex Kruskal-Wallis test
2622 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
2625 The Kruskal-Wallis test is used to compare data from an
2626 arbitrary number of populations. It does not assume normality.
2627 The data to be compared are specified by @var{var_list}.
2628 The categorical variable determining the groups to which the
2629 data belongs is given by @var{var}. The limits @var{lower} and
2630 @var{upper} specify the valid range of @var{var}.
2631 If @var{upper} is smaller than @var{lower}, the PSPP will assume their values
2632 to be reversed. Any cases for which @var{var} falls outside
2633 [@var{lower}, @var{upper}] are ignored.
2635 The mean rank of each group as well as the chi-squared value and
2636 significance of the test are printed.
2637 The abbreviated subcommand @subcmd{K-W} may be used in place of
2638 @subcmd{KRUSKAL-WALLIS}.
2642 @subsection Mann-Whitney U Test
2643 @vindex MANN-WHITNEY
2645 @cindex Mann-Whitney U test
2646 @cindex U, Mann-Whitney U
2649 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
2652 The Mann-Whitney subcommand is used to test whether two groups of data
2653 come from different populations. The variables to be tested should be
2654 specified in @var{var_list} and the grouping variable, that determines
2655 to which group the test variables belong, in @var{var}.
2656 @var{Var} may be either a string or an alpha variable.
2657 @var{Group1} and @var{group2} specify the
2658 two values of @var{var} which determine the groups of the test data.
2659 Cases for which the @var{var} value is neither @var{group1} or
2660 @var{group2} are ignored.
2662 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the
2663 significance are printed.
2664 You may abbreviated the subcommand @subcmd{MANN-WHITNEY} to
2669 @subsection McNemar Test
2671 @cindex McNemar test
2674 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2677 Use McNemar's test to analyse the significance of the difference between
2678 pairs of correlated proportions.
2680 If the @code{WITH} keyword is omitted, then tests for all
2681 combinations of the listed variables are performed.
2682 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
2683 is also given, then the number of variables preceding @code{WITH}
2684 must be the same as the number following it.
2685 In this case, tests for each respective pair of variables are
2687 If the @code{WITH} keyword is given, but the
2688 @code{(PAIRED)} keyword is omitted, then tests for each combination
2689 of variable preceding @code{WITH} against variable following
2690 @code{WITH} are performed.
2692 The data in each variable must be dichotomous. If there are more
2693 than two distinct variables an error will occur and the test will
2697 @subsection Median Test
2702 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
2705 The median test is used to test whether independent samples come from
2706 populations with a common median.
2707 The median of the populations against which the samples are to be tested
2708 may be given in parentheses immediately after the
2709 @subcmd{/MEDIAN} subcommand. If it is not given, the median is imputed from the
2710 union of all the samples.
2712 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
2713 keyword @code{BY} must come next, and then the grouping variable. Two values
2714 in parentheses should follow. If the first value is greater than the second,
2715 then a 2 sample test is performed using these two values to determine the groups.
2716 If however, the first variable is less than the second, then a @i{k} sample test is
2717 conducted and the group values used are all values encountered which lie in the
2718 range [@var{value1},@var{value2}].
2722 @subsection Runs Test
2727 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
2730 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
2732 It works by examining the number of times a variable's value crosses a given threshold.
2733 The desired threshold must be specified within parentheses.
2734 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
2735 Following the threshold specification comes the list of variables whose values are to be
2738 The subcommand shows the number of runs, the asymptotic significance based on the
2742 @subsection Sign Test
2747 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2750 The @subcmd{/SIGN} subcommand tests for differences between medians of the
2752 The test does not make any assumptions about the
2753 distribution of the data.
2755 If the @code{WITH} keyword is omitted, then tests for all
2756 combinations of the listed variables are performed.
2757 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
2758 is also given, then the number of variables preceding @code{WITH}
2759 must be the same as the number following it.
2760 In this case, tests for each respective pair of variables are
2762 If the @code{WITH} keyword is given, but the
2763 @code{(PAIRED)} keyword is omitted, then tests for each combination
2764 of variable preceding @code{WITH} against variable following
2765 @code{WITH} are performed.
2768 @subsection Wilcoxon Matched Pairs Signed Ranks Test
2770 @cindex wilcoxon matched pairs signed ranks test
2773 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2776 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
2778 The test does not make any assumptions about the variances of the samples.
2779 It does however assume that the distribution is symmetrical.
2781 If the @subcmd{WITH} keyword is omitted, then tests for all
2782 combinations of the listed variables are performed.
2783 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
2784 is also given, then the number of variables preceding @subcmd{WITH}
2785 must be the same as the number following it.
2786 In this case, tests for each respective pair of variables are
2788 If the @subcmd{WITH} keyword is given, but the
2789 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
2790 of variable preceding @subcmd{WITH} against variable following
2791 @subcmd{WITH} are performed.
2800 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
2801 /CRITERIA=CI(@var{confidence})
2805 TESTVAL=@var{test_value}
2806 /VARIABLES=@var{var_list}
2809 (Independent Samples mode.)
2810 GROUPS=var(@var{value1} [, @var{value2}])
2811 /VARIABLES=@var{var_list}
2814 (Paired Samples mode.)
2815 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
2820 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
2822 It operates in one of three modes:
2824 @item One Sample mode.
2825 @item Independent Groups mode.
2830 Each of these modes are described in more detail below.
2831 There are two optional subcommands which are common to all modes.
2833 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
2834 in the tests. The default value is 0.95.
2837 The @cmd{MISSING} subcommand determines the handling of missing
2839 If @subcmd{INCLUDE} is set, then user-missing values are included in the
2840 calculations, but system-missing values are not.
2841 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2842 values are excluded as well as system-missing values.
2843 This is the default.
2845 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
2846 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
2847 @subcmd{/GROUPS} subcommands contains a missing value.
2848 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
2849 which they would be needed. This is the default.
2853 * One Sample Mode:: Testing against a hypothesized mean
2854 * Independent Samples Mode:: Testing two independent groups for equal mean
2855 * Paired Samples Mode:: Testing two interdependent groups for equal mean
2858 @node One Sample Mode
2859 @subsection One Sample Mode
2861 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
2862 This mode is used to test a population mean against a hypothesized
2864 The value given to the @subcmd{TESTVAL} subcommand is the value against
2865 which you wish to test.
2866 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
2867 tell @pspp{} which variables you wish to test.
2869 @subsubsection Example - One Sample T-test
2871 A researcher wishes to know whether the weight of persons in a population
2872 is different from the national average.
2873 The samples are drawn from the population under investigation and recorded
2874 in the file @file{physiology.sav}.
2875 From the Department of Health, she
2876 knows that the national average weight of healthy adults is 76.8kg.
2877 Accordingly the @subcmd{TESTVAL} is set to 76.8.
2878 The null hypothesis therefore is that the mean average weight of the
2879 population from which the sample was drawn is 76.8kg.
2881 As previously noted (@pxref{Identifying incorrect data}), one
2882 sample in the dataset contains a weight value
2883 which is clearly incorrect. So this is excluded from the analysis
2884 using the @cmd{SELECT} command.
2886 @float Example, one-sample-t:ex
2887 @psppsyntax {one-sample-t.sps}
2888 @caption {Running a one sample T-Test after excluding all non-positive values}
2891 @float Screenshot, one-sample-t:scr
2892 @psppimage {one-sample-t}
2893 @caption {Using the One Sample T-Test dialog box to test @exvar{weight} for a mean of 76.8kg}
2897 @ref{one-sample-t:res} shows that the mean of our sample differs from the test value
2898 by -1.40kg. However the significance is very high (0.610). So one cannot
2899 reject the null hypothesis, and must conclude there is not enough evidence
2900 to suggest that the mean weight of the persons in our population is different
2903 @float Results, one-sample-t:res
2904 @psppoutput {one-sample-t}
2905 @caption {The results of a one sample T-test of @exvar{weight} using a test value of 76.8kg}
2908 @node Independent Samples Mode
2909 @subsection Independent Samples Mode
2911 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
2913 This mode is used to test whether two groups of values have the
2914 same population mean.
2915 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
2916 tell @pspp{} the dependent variables you wish to test.
2918 The variable given in the @subcmd{GROUPS} subcommand is the independent
2919 variable which determines to which group the samples belong.
2920 The values in parentheses are the specific values of the independent
2921 variable for each group.
2922 If the parentheses are omitted and no values are given, the default values
2923 of 1.0 and 2.0 are assumed.
2925 If the independent variable is numeric,
2926 it is acceptable to specify only one value inside the parentheses.
2927 If you do this, cases where the independent variable is
2928 greater than or equal to this value belong to the first group, and cases
2929 less than this value belong to the second group.
2930 When using this form of the @subcmd{GROUPS} subcommand, missing values in
2931 the independent variable are excluded on a listwise basis, regardless
2932 of whether @subcmd{/MISSING=LISTWISE} was specified.
2934 @subsubsection Example - Independent Samples T-test
2936 A researcher wishes to know whether within a population, adult males
2937 are taller than adult females.
2938 The samples are drawn from the population under investigation and recorded
2939 in the file @file{physiology.sav}.
2941 As previously noted (@pxref{Identifying incorrect data}), one
2942 sample in the dataset contains a height value
2943 which is clearly incorrect. So this is excluded from the analysis
2944 using the @cmd{SELECT} command.
2947 @float Example, indepdendent-samples-t:ex
2948 @psppsyntax {independent-samples-t.sps}
2949 @caption {Running a independent samples T-Test after excluding all observations less than 200kg}
2953 The null hypothesis is that both males and females are on average
2956 @float Screenshot, independent-samples-t:scr
2957 @psppimage {independent-samples-t}
2958 @caption {Using the Independent Sample T-test dialog, to test for differences of @exvar{height} between values of @exvar{sex}}
2962 In this case, the grouping variable is @exvar{sex}, so this is entered
2963 as the variable for the @subcmd{GROUP} subcommand. The group values are 0 (male) and
2966 If you are running the proceedure using syntax, then you need to enter
2967 the values corresponding to each group within parentheses.
2968 If you are using the graphic user interface, then you have to open
2969 the ``Define Groups'' dialog box and enter the values corresponding
2970 to each group as shown in @ref{define-groups-t:scr}. If, as in this case, the dataset has defined value
2971 labels for the group variable, then you can enter them by label
2974 @float Screenshot, define-groups-t:scr
2975 @psppimage {define-groups-t}
2976 @caption {Setting the values of the grouping variable for an Independent Samples T-test}
2979 From @ref{independent-samples-t:res}, one can clearly see that the @emph{sample} mean height
2980 is greater for males than for females. However in order to see if this
2981 is a significant result, one must consult the T-Test table.
2983 The T-Test table contains two rows; one for use if the variance of the samples
2984 in each group may be safely assumed to be equal, and the second row
2985 if the variances in each group may not be safely assumed to be equal.
2987 In this case however, both rows show a 2-tailed significance less than 0.001 and
2988 one must therefore reject the null hypothesis and conclude that within
2989 the population the mean height of males and of females are unequal.
2991 @float Result, independent-samples-t:res
2992 @psppoutput {independent-samples-t}
2993 @caption {The results of an independent samples T-test of @exvar{height} by @exvar{sex}}
2996 @node Paired Samples Mode
2997 @subsection Paired Samples Mode
2999 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
3000 Use this mode when repeated measures have been taken from the same
3002 If the @subcmd{WITH} keyword is omitted, then tables for all
3003 combinations of variables given in the @cmd{PAIRS} subcommand are
3005 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
3006 is also given, then the number of variables preceding @subcmd{WITH}
3007 must be the same as the number following it.
3008 In this case, tables for each respective pair of variables are
3010 In the event that the @subcmd{WITH} keyword is given, but the
3011 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
3012 of variable preceding @subcmd{WITH} against variable following
3013 @subcmd{WITH} are generated.
3020 @cindex analysis of variance
3025 [/VARIABLES = ] @var{var_list} BY @var{var}
3026 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
3027 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
3028 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
3029 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
3032 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
3033 variables factored by a single independent variable.
3034 It is used to compare the means of a population
3035 divided into more than two groups.
3037 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
3039 The list of variables must be followed by the @subcmd{BY} keyword and
3040 the name of the independent (or factor) variable.
3042 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
3043 ancillary information. The options accepted are:
3046 Displays descriptive statistics about the groups factored by the independent
3049 Displays the Levene test of Homogeneity of Variance for the
3050 variables and their groups.
3053 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
3054 differences between the groups.
3055 The subcommand must be followed by a list of numerals which are the
3056 coefficients of the groups to be tested.
3057 The number of coefficients must correspond to the number of distinct
3058 groups (or values of the independent variable).
3059 If the total sum of the coefficients are not zero, then @pspp{} will
3060 display a warning, but will proceed with the analysis.
3061 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
3062 to specify different contrast tests.
3063 The @subcmd{MISSING} subcommand defines how missing values are handled.
3064 If @subcmd{LISTWISE} is specified then cases which have missing values for
3065 the independent variable or any dependent variable are ignored.
3066 If @subcmd{ANALYSIS} is specified, then cases are ignored if the independent
3067 variable is missing or if the dependent variable currently being
3068 analysed is missing. The default is @subcmd{ANALYSIS}.
3069 A setting of @subcmd{EXCLUDE} means that variables whose values are
3070 user-missing are to be excluded from the analysis. A setting of
3071 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
3073 Using the @code{POSTHOC} subcommand you can perform multiple
3074 pairwise comparisons on the data. The following comparison methods
3078 Least Significant Difference.
3079 @item @subcmd{TUKEY}
3080 Tukey Honestly Significant Difference.
3081 @item @subcmd{BONFERRONI}
3083 @item @subcmd{SCHEFFE}
3085 @item @subcmd{SIDAK}
3088 The Games-Howell test.
3092 Use the optional syntax @code{ALPHA(@var{value})} to indicate that
3093 @cmd{ONEWAY} should perform the posthoc tests at a confidence level of
3094 @var{value}. If @code{ALPHA(@var{value})} is not specified, then the
3095 confidence level used is 0.05.
3098 @section QUICK CLUSTER
3099 @vindex QUICK CLUSTER
3101 @cindex K-means clustering
3105 QUICK CLUSTER @var{var_list}
3106 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
3107 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
3108 [/PRINT=@{INITIAL@} @{CLUSTER@}]
3109 [/SAVE[=[CLUSTER[(@var{membership_var})]] [DISTANCE[(@var{distance_var})]]]
3112 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
3113 dataset. This is useful when you wish to allocate cases into clusters
3114 of similar values and you already know the number of clusters.
3116 The minimum specification is @samp{QUICK CLUSTER} followed by the names
3117 of the variables which contain the cluster data. Normally you will also
3118 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
3119 number of clusters. If this is not specified, then @var{k} defaults to 2.
3121 If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
3122 the initial clusters is used. This will provide for faster execution but
3123 less well separated initial clusters and hence possibly an inferior final
3127 @cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
3128 The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
3129 During classification, @pspp{} will continue iterating until until @var{max_iter}
3130 iterations have been done or the convergence criterion (see below) is fulfilled.
3131 The default value of @var{max_iter} is 2.
3133 If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
3134 no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
3137 The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
3138 to set the convergence criterion. The value of convergence criterion is @var{epsilon}
3139 times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
3140 the mean cluster distance between one iteration and the next
3141 is less than the convergence criterion. The default value of @var{epsilon} is zero.
3143 The @subcmd{MISSING} subcommand determines the handling of missing variables.
3144 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
3145 value and not as missing values.
3146 If @subcmd{EXCLUDE} is set, which is the default, user-missing
3147 values are excluded as well as system-missing values.
3149 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
3150 whenever any of the clustering variables contains a missing value.
3151 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
3152 clustering variables contain missing values. Otherwise it is clustered
3153 on the basis of the non-missing values.
3154 The default is @subcmd{LISTWISE}.
3156 The @subcmd{PRINT} subcommand requests additional output to be printed.
3157 If @subcmd{INITIAL} is set, then the initial cluster memberships will
3159 If @subcmd{CLUSTER} is set, the cluster memberships of the individual
3160 cases are displayed (potentially generating lengthy output).
3162 You can specify the subcommand @subcmd{SAVE} to ask that each case's cluster membership
3163 and the euclidean distance between the case and its cluster center be saved to
3164 a new variable in the active dataset. To save the cluster membership use the
3165 @subcmd{CLUSTER} keyword and to save the distance use the @subcmd{DISTANCE} keyword.
3166 Each keyword may optionally be followed by a variable name in parentheses to specify
3167 the new variable which is to contain the saved parameter. If no variable name is specified,
3168 then PSPP will create one.
3176 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
3177 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
3178 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
3180 /MISSING=@{EXCLUDE,INCLUDE@}
3182 /RANK [INTO @var{var_list}]
3183 /NTILES(k) [INTO @var{var_list}]
3184 /NORMAL [INTO @var{var_list}]
3185 /PERCENT [INTO @var{var_list}]
3186 /RFRACTION [INTO @var{var_list}]
3187 /PROPORTION [INTO @var{var_list}]
3188 /N [INTO @var{var_list}]
3189 /SAVAGE [INTO @var{var_list}]
3192 The @cmd{RANK} command ranks variables and stores the results into new
3195 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
3196 more variables whose values are to be ranked.
3197 After each variable, @samp{A} or @samp{D} may appear, indicating that
3198 the variable is to be ranked in ascending or descending order.
3199 Ascending is the default.
3200 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
3201 which are to serve as group variables.
3202 In this case, the cases are gathered into groups, and ranks calculated
3205 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
3206 default is to take the mean value of all the tied cases.
3208 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
3209 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
3210 functions are requested.
3212 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
3213 variables created should appear in the output.
3215 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
3216 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
3217 If none are given, then the default is RANK.
3218 The @subcmd{NTILES} subcommand must take an integer specifying the number of
3219 partitions into which values should be ranked.
3220 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
3221 variables which are the variables to be created and receive the rank
3222 scores. There may be as many variables specified as there are
3223 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
3224 then the variable names are automatically created.
3226 The @subcmd{MISSING} subcommand determines how user missing values are to be
3227 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
3228 user-missing are to be excluded from the rank scores. A setting of
3229 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
3231 @include regression.texi
3235 @section RELIABILITY
3240 /VARIABLES=@var{var_list}
3241 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
3242 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
3243 /SUMMARY=@{TOTAL,ALL@}
3244 /MISSING=@{EXCLUDE,INCLUDE@}
3247 @cindex Cronbach's Alpha
3248 The @cmd{RELIABILITY} command performs reliability analysis on the data.
3250 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
3251 upon which analysis is to be performed.
3253 The @subcmd{SCALE} subcommand determines the variables for which
3254 reliability is to be calculated. If @subcmd{SCALE} is omitted, then analysis for
3255 all variables named in the @subcmd{VARIABLES} subcommand are used.
3256 Optionally, the @var{name} parameter may be specified to set a string name
3259 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
3260 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
3261 then the variables are divided into 2 subsets. An optional parameter
3262 @var{n} may be given, to specify how many variables to be in the first subset.
3263 If @var{n} is omitted, then it defaults to one half of the variables in the
3264 scale, or one half minus one if there are an odd number of variables.
3265 The default model is @subcmd{ALPHA}.
3267 By default, any cases with user missing, or system missing values for
3268 any variables given in the @subcmd{VARIABLES} subcommand are omitted
3269 from the analysis. The @subcmd{MISSING} subcommand determines whether
3270 user missing values are included or excluded in the analysis.
3272 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
3273 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
3274 analysis tested against the totals.
3276 @subsection Example - Reliability
3278 Before analysing the results of a survey -- particularly for a multiple choice survey --
3279 it is desireable to know whether the respondents have considered their answers
3280 or simply provided random answers.
3282 In the following example the survey results from the file @file{hotel.sav} are used.
3283 All five survey questions are included in the reliability analysis.
3284 However, before running the analysis, the data must be preprocessed.
3285 An examination of the survey questions reveals that two questions, @i{viz:} v3 and v5
3286 are negatively worded, whereas the others are positively worded.
3287 All questions must be based upon the same scale for the analysis to be meaningful.
3288 One could use the @cmd{RECODE} command (@pxref{RECODE}), however a simpler way is
3289 to use @cmd{COMPUTE} (@pxref{COMPUTE}) and this is what is done in @ref{reliability:ex}.
3291 @float Example, reliability:ex
3292 @psppsyntax {reliability.sps}
3293 @caption {Investigating the reliability of survey responses}
3296 In this case, all variables in the data set are used. So we can use the special
3297 keyword @samp{ALL} (@pxref{BNF}).
3299 @float Screenshot, reliability:src
3300 @psppimage {reliability}
3301 @caption {Reliability dialog box with all variables selected}
3304 @ref{reliability:res} shows that Cronbach's Alpha is 0.11 which is a value normally considered too
3305 low to indicate consistency within the data. This is possibly due to the small number of
3306 survey questions. The survey should be redesigned before serious use of the results are
3309 @float Result, reliability:res
3310 @psppoutput {reliability}
3311 @caption {The results of the reliability command on @file{hotel.sav}}
3319 @cindex Receiver Operating Characteristic
3320 @cindex Area under curve
3323 ROC @var{var_list} BY @var{state_var} (@var{state_value})
3324 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
3325 /PRINT = [ SE ] [ COORDINATES ]
3326 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
3327 [ TESTPOS (@{LARGE,SMALL@}) ]
3328 [ CI (@var{confidence}) ]
3329 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
3330 /MISSING=@{EXCLUDE,INCLUDE@}
3334 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
3335 of a dataset, and to estimate the area under the curve.
3336 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
3338 The mandatory @var{var_list} is the list of predictor variables.
3339 The variable @var{state_var} is the variable whose values represent the actual states,
3340 and @var{state_value} is the value of this variable which represents the positive state.
3342 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
3343 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
3344 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
3345 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
3346 By default, the curve is drawn with no reference line.
3348 The optional subcommand @subcmd{PRINT} determines which additional
3349 tables should be printed. Two additional tables are available. The
3350 @subcmd{SE} keyword says that standard error of the area under the
3351 curve should be printed as well as the area itself. In addition, a
3352 p-value for the null hypothesis that the area under the curve equals
3353 0.5 is printed. The @subcmd{COORDINATES} keyword says that a
3354 table of coordinates of the @subcmd{ROC} curve should be printed.
3356 The @subcmd{CRITERIA} subcommand has four optional parameters:
3358 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
3359 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
3360 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
3362 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
3363 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
3365 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
3367 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
3368 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
3369 exponential distribution estimate.
3370 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
3371 equal to the number of negative actual states.
3372 The default is @subcmd{FREE}.
3374 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
3377 The @subcmd{MISSING} subcommand determines whether user missing values are to
3378 be included or excluded in the analysis. The default behaviour is to
3380 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
3381 or if the variable @var{state_var} is missing, then the entire case is
3384 @c LocalWords: subcmd subcommand