4 This chapter documents the statistical procedures that PSPP supports so
8 * DESCRIPTIVES:: Descriptive statistics.
9 * FREQUENCIES:: Frequency tables.
10 * EXAMINE:: Testing data for normality.
11 * CORRELATIONS:: Correlation tables.
12 * CROSSTABS:: Crosstabulation tables.
13 * FACTOR:: Factor analysis and Principal Components analysis
14 * NPAR TESTS:: Nonparametric tests.
15 * T-TEST:: Test hypotheses about means.
16 * ONEWAY:: One way analysis of variance.
17 * RANK:: Compute rank scores.
18 * REGRESSION:: Linear regression.
19 * RELIABILITY:: Reliability analysis.
20 * ROC:: Receiver Operating Characteristic.
30 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
31 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
33 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
34 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
35 SESKEWNESS,SEKURTOSIS@}
36 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
37 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
41 The @cmd{DESCRIPTIVES} procedure reads the active file and outputs
43 statistics requested by the user. In addition, it can optionally
46 The VARIABLES subcommand, which is required, specifies the list of
47 variables to be analyzed. Keyword VARIABLES is optional.
49 All other subcommands are optional:
51 The MISSING subcommand determines the handling of missing variables. If
52 INCLUDE is set, then user-missing values are included in the
53 calculations. If NOINCLUDE is set, which is the default, user-missing
54 values are excluded. If VARIABLE is set, then missing values are
55 excluded on a variable by variable basis; if LISTWISE is set, then
56 the entire case is excluded whenever any value in that case has a
57 system-missing or, if INCLUDE is set, user-missing value.
59 The FORMAT subcommand affects the output format. Currently the
60 LABELS/NOLABELS and NOINDEX/INDEX settings are not used. When SERIAL is
61 set, both valid and missing number of cases are listed in the output;
62 when NOSERIAL is set, only valid cases are listed.
64 The SAVE subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
65 the specified variables. The Z scores are saved to new variables.
66 Variable names are generated by trying first the original variable name
67 with Z prepended and truncated to a maximum of 8 characters, then the
68 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
69 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
70 variable names can be specified explicitly on VARIABLES in the variable
71 list by enclosing them in parentheses after each variable.
73 The STATISTICS subcommand specifies the statistics to be displayed:
77 All of the statistics below.
81 Standard error of the mean.
87 Kurtosis and standard error of the kurtosis.
89 Skewness and standard error of the skewness.
99 Mean, standard deviation of the mean, minimum, maximum.
101 Standard error of the kurtosis.
103 Standard error of the skewness.
106 The SORT subcommand specifies how the statistics should be sorted. Most
107 of the possible values should be self-explanatory. NAME causes the
108 statistics to be sorted by name. By default, the statistics are listed
109 in the order that they are specified on the VARIABLES subcommand. The A
110 and D settings request an ascending or descending sort order,
120 /FORMAT=@{TABLE,NOTABLE,LIMIT(limit)@}
121 @{AVALUE,DVALUE,AFREQ,DFREQ@}
122 /MISSING=@{EXCLUDE,INCLUDE@}
123 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
124 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
125 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
127 /PERCENTILES=percent@dots{}
128 /HISTOGRAM=[MINIMUM(x_min)] [MAXIMUM(x_max)]
129 [@{FREQ[(y_max)],PERCENT[(y_max)]@}] [@{NONORMAL,NORMAL@}]
130 /PIECHART=[MINIMUM(x_min)] [MAXIMUM(x_max)]
131 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
133 (These options are not currently implemented.)
139 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
141 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
142 (including median and mode) and percentiles,
143 @cmd{FREQUENCIES} can also output
144 histograms and pie charts.
146 The VARIABLES subcommand is the only required subcommand. Specify the
147 variables to be analyzed.
149 The FORMAT subcommand controls the output format. It has several
154 TABLE, the default, causes a frequency table to be output for every
155 variable specified. NOTABLE prevents them from being output. LIMIT
156 with a numeric argument causes them to be output except when there are
157 more than the specified number of values in the table.
160 Normally frequency tables are sorted in ascending order by value. This
161 is AVALUE. DVALUE tables are sorted in descending order by value.
162 AFREQ and DFREQ tables are sorted in ascending and descending order,
163 respectively, by frequency count.
166 The MISSING subcommand controls the handling of user-missing values.
167 When EXCLUDE, the default, is set, user-missing values are not included
168 in frequency tables or statistics. When INCLUDE is set, user-missing
169 are included. System-missing values are never included in statistics,
170 but are listed in frequency tables.
172 The available STATISTICS are the same as available in @cmd{DESCRIPTIVES}
173 (@pxref{DESCRIPTIVES}), with the addition of MEDIAN, the data's median
174 value, and MODE, the mode. (If there are multiple modes, the smallest
175 value is reported.) By default, the mean, standard deviation of the
176 mean, minimum, and maximum are reported for each variable.
179 PERCENTILES causes the specified percentiles to be reported.
180 The percentiles should be presented at a list of numbers between 0
182 The NTILES subcommand causes the percentiles to be reported at the
183 boundaries of the data set divided into the specified number of ranges.
184 For instance, @code{/NTILES=4} would cause quartiles to be reported.
187 The HISTOGRAM subcommand causes the output to include a histogram for
188 each specified numeric variable. The X axis by default ranges from
189 the minimum to the maximum value observed in the data, but the MINIMUM
190 and MAXIMUM keywords can set an explicit range. Specify NORMAL to
191 superimpose a normal curve on the histogram. Histograms are not
192 created for string variables.
195 The PIECHART adds a pie chart for each variable to the data. Each
196 slice represents one value, with the size of the slice proportional to
197 the value's frequency. By default, all non-missing values are given
198 slices. The MINIMUM and MAXIMUM keywords can be used to limit the
199 displayed slices to a given range of values. The MISSING keyword adds
200 slices for missing values.
202 The FREQ and PERCENT options on HISTOGRAM and PIECHART are accepted
203 but not currently honored.
206 @comment node-name, next, previous, up
210 @cindex Normality, testing for
214 VARIABLES=var_list [BY factor_list ]
215 /STATISTICS=@{DESCRIPTIVES, EXTREME[(n)], ALL, NONE@}
216 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, ALL, NONE@}
218 /COMPARE=@{GROUPS,VARIABLES@}
221 /PERCENTILE=[value_list]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
222 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
223 [@{NOREPORT,REPORT@}]
227 The @cmd{EXAMINE} command is used to test how closely a distribution is to a
228 normal distribution. It also shows you outliers and extreme values.
230 The VARIABLES subcommand specifies the dependent variables and the
231 independent variable to use as factors for the analysis. Variables
232 listed before the first BY keyword are the dependent variables.
233 The dependent variables may optionally be followed by a list of
234 factors which tell PSPP how to break down the analysis for each
235 dependent variable. The format for each factor is
241 The STATISTICS subcommand specifies the analysis to be done.
242 DESCRIPTIVES will produce a table showing some parametric and
243 non-parametrics statistics. EXTREME produces a table showing extreme
244 values of the dependent variable. A number in parentheses determines
245 how many upper and lower extremes to show. The default number is 5.
251 The PLOT subcommand specifies which plots are to be produced if any.
252 Available plots are HISTOGRAM, NPPLOT and BOXPLOT.
254 The COMPARE subcommand is only relevant if producing boxplots, and it is only
255 useful there is more than one dependent variable and at least one factor. If
256 /COMPARE=GROUPS is specified, then one plot per dependent variable is produced,
257 containing boxplots for all the factors.
258 If /COMPARE=VARIABLES is specified, then one plot per factor is produced, each
259 each containing one boxplot per dependent variable.
260 If the /COMPARE subcommand is ommitted, then PSPP uses the default value of
263 The ID subcommand also pertains to boxplots. If given, it must
264 specify a variable name. Outliers and extreme cases plotted in
265 boxplots will be labelled with the case from that variable. Numeric or
266 string variables are permissible. If the ID subcommand is not given,
267 then the casenumber will be used for labelling.
269 The CINTERVAL subcommand specifies the confidence interval to use in
270 calculation of the descriptives command. The default it 95%.
273 The PERCENTILES subcommand specifies which percentiles are to be calculated,
274 and which algorithm to use for calculating them. The default is to
275 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
278 The TOTAL and NOTOTAL subcommands are mutually exclusive. If NOTOTAL
279 is given and factors have been specified in the VARIABLES subcommand,
280 then then statistics for the unfactored dependent variables are
281 produced in addition to the factored variables. If there are no
282 factors specified then TOTAL and NOTOTAL have no effect.
285 If many dependent variable are given, or factors are given for which
286 there are many distinct values, then @cmd{EXAMINE} will produce a very
287 large quantity of output.
290 @section CORRELATIONS
295 /VARIABLES = varlist [ WITH varlist ]
300 /VARIABLES = varlist [ WITH varlist ]
301 /VARIABLES = varlist [ WITH varlist ]
304 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
305 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
306 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
310 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
311 for a set of variables. The significance of the coefficients are also given.
313 At least one VARIABLES subcommand is required. If the WITH keyword is used, then a non-square
314 correlation table will be produced.
315 The variables preceding WITH, will be used as the rows of the table, and the variables following
316 will be the columns of the table.
317 If no WITH subcommand is given, then a square, symmetrical table using all variables is produced.
320 The @cmd{MISSING} subcommand determines the handling of missing variables.
321 If INCLUDE is set, then user-missing values are included in the
322 calculations, but system-missing values are not.
323 If EXCLUDE is set, which is the default, user-missing
324 values are excluded as well as system-missing values.
327 If LISTWISE is set, then the entire case is excluded from analysis
328 whenever any variable specified in any @cmd{/VARIABLES} subcommand
329 contains a missing value.
330 If PAIRWISE is set, then a case is considered missing only if either of the
331 values for the particular coefficient are missing.
332 The default is PAIRWISE.
334 The PRINT subcommand is used to control how the reported significance values are printed.
335 If the TWOTAIL option is used, then a two-tailed test of significance is
336 printed. If the ONETAIL option is given, then a one-tailed test is used.
337 The default is TWOTAIL.
339 If the NOSIG option is specified, then correlation coefficients with significance less than
340 0.05 are highlighted.
341 If SIG is specified, then no highlighting is performed. This is the default.
344 The STATISTICS subcommand requests additional statistics to be displayed. The keyword
345 DESCRIPTIVES requests that the mean, number of non-missing cases, and the non-biased
346 estimator of the standard deviation are displayed.
347 These statistics will be displayed in a separated table, for all the variables listed
348 in any /VARIABLES subcommand.
349 The XPROD keyword requests cross-product deviations and covariance estimators to
350 be displayed for each pair of variables.
351 The keyword ALL is the union of DESCRIPTIVES and XPROD.
359 /TABLES=var_list BY var_list [BY var_list]@dots{}
360 /MISSING=@{TABLE,INCLUDE,REPORT@}
361 /WRITE=@{NONE,CELLS,ALL@}
362 /FORMAT=@{TABLES,NOTABLES@}
363 @{LABELS,NOLABELS,NOVALLABS@}
368 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
369 ASRESIDUAL,ALL,NONE@}
370 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
371 KAPPA,ETA,CORR,ALL,NONE@}
374 /VARIABLES=var_list (low,high)@dots{}
377 The @cmd{CROSSTABS} procedure displays crosstabulation
378 tables requested by the user. It can calculate several statistics for
379 each cell in the crosstabulation tables. In addition, a number of
380 statistics can be calculated for each table itself.
382 The TABLES subcommand is used to specify the tables to be reported. Any
383 number of dimensions is permitted, and any number of variables per
384 dimension is allowed. The TABLES subcommand may be repeated as many
385 times as needed. This is the only required subcommand in @dfn{general
388 Occasionally, one may want to invoke a special mode called @dfn{integer
389 mode}. Normally, in general mode, PSPP automatically determines
390 what values occur in the data. In integer mode, the user specifies the
391 range of values that the data assumes. To invoke this mode, specify the
392 VARIABLES subcommand, giving a range of data values in parentheses for
393 each variable to be used on the TABLES subcommand. Data values inside
394 the range are truncated to the nearest integer, then assigned to that
395 value. If values occur outside this range, they are discarded. When it
396 is present, the VARIABLES subcommand must precede the TABLES
399 In general mode, numeric and string variables may be specified on
400 TABLES. In integer mode, only numeric variables are allowed.
402 The MISSING subcommand determines the handling of user-missing values.
403 When set to TABLE, the default, missing values are dropped on a table by
404 table basis. When set to INCLUDE, user-missing values are included in
405 tables and statistics. When set to REPORT, which is allowed only in
406 integer mode, user-missing values are included in tables but marked with
407 an @samp{M} (for ``missing'') and excluded from statistical
410 Currently the WRITE subcommand is ignored.
412 The FORMAT subcommand controls the characteristics of the
413 crosstabulation tables to be displayed. It has a number of possible
418 TABLES, the default, causes crosstabulation tables to be output.
419 NOTABLES suppresses them.
422 LABELS, the default, allows variable labels and value labels to appear
423 in the output. NOLABELS suppresses them. NOVALLABS displays variable
424 labels but suppresses value labels.
427 PIVOT, the default, causes each TABLES subcommand to be displayed in a
428 pivot table format. NOPIVOT causes the old-style crosstabulation format
432 AVALUE, the default, causes values to be sorted in ascending order.
433 DVALUE asserts a descending sort order.
436 INDEX/NOINDEX is currently ignored.
439 BOX/NOBOX is currently ignored.
442 The CELLS subcommand controls the contents of each cell in the displayed
443 crosstabulation table. The possible settings are:
459 Standardized residual.
461 Adjusted standardized residual.
465 Suppress cells entirely.
468 @samp{/CELLS} without any settings specified requests COUNT, ROW,
469 COLUMN, and TOTAL. If CELLS is not specified at all then only COUNT
472 The STATISTICS subcommand selects statistics for computation:
479 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
480 correction, linear-by-linear association.
484 Contingency coefficient.
488 Uncertainty coefficient.
504 Spearman correlation, Pearson's r.
511 Selected statistics are only calculated when appropriate for the
512 statistic. Certain statistics require tables of a particular size, and
513 some statistics are calculated only in integer mode.
515 @samp{/STATISTICS} without any settings selects CHISQ. If the
516 STATISTICS subcommand is not given, no statistics are calculated.
518 @strong{Please note:} Currently the implementation of CROSSTABS has the
523 Pearson's R (but not Spearman) is off a little.
525 T values for Spearman's R and Pearson's R are wrong.
527 Significance of symmetric and directional measures is not calculated.
529 Asymmetric ASEs and T values for lambda are wrong.
531 ASE of Goodman and Kruskal's tau is not calculated.
533 ASE of symmetric somers' d is wrong.
535 Approximate T of uncertainty coefficient is wrong.
538 Fixes for any of these deficiencies would be welcomed.
544 @cindex factor analysis
545 @cindex principal components analysis
546 @cindex principal axis factoring
547 @cindex data reduction
550 FACTOR VARIABLES=var_list
552 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
554 [ /EXTRACTION=@{PC, PAF@}]
556 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
558 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [SIG] [ALL] [DEFAULT] ]
562 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
564 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
566 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
569 The FACTOR command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
570 common factors in the data or for data reduction purposes.
572 The VARIABLES subcommand is required. It lists the variables which are to partake in the analysis.
574 The /EXTRACTION subcommand is used to specify the way in which factors (components) are extracted from the data.
575 If PC is specified, then Principal Components Analysis is used. If PAF is specified, then Principal Axis Factoring is
576 used. By default Principal Components Analysis will be used.
578 The /ROTATION subcommand is used to specify the method by which the extracted solution will be rotated.
579 Three methods are available: VARIMAX (which is the default), EQUAMAX, and QUARTIMAX.
580 If don't want any rotation to be performed, the word NOROTATE will prevent the command from performing any
581 rotation on the data. Oblique rotations are not supported.
583 The /METHOD subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
584 to be analysed. By default, the correlation matrix is analysed.
586 The /PRINT subcommand may be used to select which features of the analysis are reported:
590 A table of mean values, standard deviations and total weights are printed.
592 Initial communalities and eigenvalues are printed.
594 Extracted communalities and eigenvalues are printed.
596 Rotated communalities and eigenvalues are printed.
598 The correlation matrix is printed.
600 The covariance matrix is printed.
602 The determinant of the correlation or covariance matrix is printed.
604 The significance of the elements of correlation matrix is printed.
606 All of the above are printed.
608 Identical to INITIAL and EXTRACTION.
611 If /PLOT=EIGEN is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualising
612 which factors (components) should be retained.
614 The /FORMAT subcommand determined how data are to be displayed in loading matrices. If SORT is specified, then the variables
615 are sorted in descending order of significance. If BLANK(@var{n}) is specified, then coefficients whose absolute value is less
616 than @var{n} will not be printed. If the keyword DEFAULT is given, or if no /FORMAT subcommand is given, then no sorting is
617 performed, and all coefficients will be printed.
619 The /CRITERIA subcommand is used to specify how the number of extracted factors (components) are chosen. If FACTORS(@var{n}) is
620 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the MINEIGEN setting will
621 be used. MINEIGEN(@var{l}) requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
622 The default value of @var{l} is 1. The ECONVERGE and ITERATE settings have effect only when iterative algorithms for factor
623 extraction (such as Principal Axis Factoring) are used. ECONVERGE(@var{delta}) specifies that iteration should cease when
624 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
625 default value of @var{delta} is 0.001.
626 The ITERATE(@var{m}) setting sets the maximum number of iterations to @var{m}. The default value of @var{m} is 25.
628 The @cmd{MISSING} subcommand determines the handling of missing variables.
629 If INCLUDE is set, then user-missing values are included in the
630 calculations, but system-missing values are not.
631 If EXCLUDE is set, which is the default, user-missing
632 values are excluded as well as system-missing values.
634 If LISTWISE is set, then the entire case is excluded from analysis
635 whenever any variable specified in the @cmd{VARIABLES} subcommand
636 contains a missing value.
637 If PAIRWISE is set, then a case is considered missing only if either of the
638 values for the particular coefficient are missing.
639 The default is LISTWISE.
646 @cindex nonparametric tests
651 nonparametric test subcommands
656 [ /STATISTICS=@{DESCRIPTIVES@} ]
658 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
660 [ /METHOD=EXACT [ TIMER [(n)] ] ]
663 NPAR TESTS performs nonparametric tests.
664 Non parametric tests make very few assumptions about the distribution of the
666 One or more tests may be specified by using the corresponding subcommand.
667 If the /STATISTICS subcommand is also specified, then summary statistics are
668 produces for each variable that is the subject of any test.
670 Certain tests may take a long time to execute, if an exact figure is required.
671 Therefore, by default asymptotic approximations are used unless the
672 subcommand /METHOD=EXACT is specified.
673 Exact tests give more accurate results, but may take an unacceptably long
674 time to perform. If the TIMER keyword is used, it sets a maximum time,
675 after which the test will be abandoned, and a warning message printed.
676 The time, in minutes, should be specified in parentheses after the TIMER keyword.
677 If the TIMER keyword is given without this figure, then a default value of 5 minutes
682 * BINOMIAL:: Binomial Test
683 * CHISQUARE:: Chisquare Test
684 * FRIEDMAN:: Friedman Test
685 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
687 * SIGN:: The Sign Test
688 * WILCOXON:: Wilcoxon Signed Ranks Test
693 @subsection Binomial test
695 @cindex binomial test
698 [ /BINOMIAL[(p)]=var_list[(value1[, value2)] ] ]
701 The /BINOMIAL subcommand compares the observed distribution of a dichotomous
702 variable with that of a binomial distribution.
703 The variable @var{p} specifies the test proportion of the binomial
705 The default value of 0.5 is assumed if @var{p} is omitted.
707 If a single value appears after the variable list, then that value is
708 used as the threshold to partition the observed values. Values less
709 than or equal to the threshold value form the first category. Values
710 greater than the threshold form the second category.
712 If two values appear after the variable list, then they will be used
713 as the values which a variable must take to be in the respective
715 Cases for which a variable takes a value equal to neither of the specified
716 values, take no part in the test for that variable.
718 If no values appear, then the variable must assume dichotomous
720 If more than two distinct, non-missing values for a variable
721 under test are encountered then an error occurs.
723 If the test proportion is equal to 0.5, then a two tailed test is
724 reported. For any other test proportion, a one tailed test is
726 For one tailed tests, if the test proportion is less than
727 or equal to the observed proportion, then the significance of
728 observing the observed proportion or more is reported.
729 If the test proportion is more than the observed proportion, then the
730 significance of observing the observed proportion or less is reported.
731 That is to say, the test is always performed in the observed
734 PSPP uses a very precise approximation to the gamma function to
735 compute the binomial significance. Thus, exact results are reported
736 even for very large sample sizes.
741 @subsection Chisquare Test
743 @cindex chisquare test
747 [ /CHISQUARE=var_list[(lo,hi)] [/EXPECTED=@{EQUAL|f1, f2 @dots{} fn@}] ]
751 The /CHISQUARE subcommand produces a chi-square statistic for the differences
752 between the expected and observed frequencies of the categories of a variable.
753 Optionally, a range of values may appear after the variable list.
754 If a range is given, then non integer values are truncated, and values
755 outside the specified range are excluded from the analysis.
757 The /EXPECTED subcommand specifies the expected values of each
759 There must be exactly one non-zero expected value, for each observed
760 category, or the EQUAL keywork must be specified.
761 You may use the notation @var{n}*@var{f} to specify @var{n}
762 consecutive expected categories all taking a frequency of @var{f}.
763 The frequencies given are proportions, not absolute frequencies. The
764 sum of the frequencies need not be 1.
765 If no /EXPECTED subcommand is given, then then equal frequencies
770 @subsection Friedman Test
772 @cindex Friedman test
775 [ /FRIEDMAN = varlist ]
778 The Friedman test is used to test for differences between repeated measures when there is no indication that the distributions are normally distributed.
780 A list of variables which contain the measured data must be given. The procedure prints the sum of ranks for each variable, the test statistic and its significance.
783 @subsection Kruskal-Wallis Test
784 @vindex KRUSKAL-WALLIS
786 @cindex Kruskal-Wallis test
789 [ /KRUSKAL-WALLIS = varlist BY var (lower, upper) ]
792 The Kruskal-Wallis test is used to compare data from an
793 arbitrary number of populations. It does not assume normality.
794 The data to be compared are specified by @var{varlist}.
795 The categorical variable determining the groups to which the
796 data belongs is given by @var{var}. The limits @var{lower} and
797 @var{upper} specify the valid range of @var{var}. Any cases for
798 which @var{var} falls outside [@var{lower}, @var{upper}] will be
801 The mean rank of each group as well as the chi-squared value and significance
802 of the test will be printed.
803 The abbreviated subcommand K-W may be used in place of KRUSKAL-WALLIS.
807 @subsection Runs Test
812 [ /RUNS (@{MEAN, MEDIAN, MODE, value@}) varlist ]
815 The /RUNS subcommand tests whether a data sequence is randomly ordered.
817 It works by examining the number of times a variable's value crosses a given threshold.
818 The desired threshold must be specified within parentheses.
819 It may either be specified as a number or as one of MEAN, MEDIAN or MODE.
820 Following the threshold specification comes the list of variables whose values are to be
823 The subcommand shows the number of runs, the asymptotic significance based on the
827 @subsection Sign Test
832 [ /SIGN varlist [ WITH varlist [ (PAIRED) ]]]
835 The /SIGN subcommand tests for differences between medians of the
837 The test does not make any assumptions about the
838 distribution of the data.
840 If the @code{WITH} keyword is omitted, then tests for all
841 combinations of the listed variables are performed.
842 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
843 is also given, then the number of variables preceding @code{WITH}
844 must be the same as the number following it.
845 In this case, tests for each respective pair of variables are
847 If the @code{WITH} keyword is given, but the
848 @code{(PAIRED)} keyword is omitted, then tests for each combination
849 of variable preceding @code{WITH} against variable following
850 @code{WITH} are performed.
853 @subsection Wilcoxon Matched Pairs Signed Ranks Test
854 @comment node-name, next, previous, up
856 @cindex wilcoxon matched pairs signed ranks test
859 [ /WILCOXON varlist [ WITH varlist [ (PAIRED) ]]]
862 The /WILCOXON subcommand tests for differences between medians of the
864 The test does not make any assumptions about the variances of the samples.
865 It does however assume that the distribution is symetrical.
867 If the @code{WITH} keyword is omitted, then tests for all
868 combinations of the listed variables are performed.
869 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
870 is also given, then the number of variables preceding @code{WITH}
871 must be the same as the number following it.
872 In this case, tests for each respective pair of variables are
874 If the @code{WITH} keyword is given, but the
875 @code{(PAIRED)} keyword is omitted, then tests for each combination
876 of variable preceding @code{WITH} against variable following
877 @code{WITH} are performed.
880 @comment node-name, next, previous, up
887 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
888 /CRITERIA=CIN(confidence)
896 (Independent Samples mode.)
897 GROUPS=var(value1 [, value2])
901 (Paired Samples mode.)
902 PAIRS=var_list [WITH var_list [(PAIRED)] ]
907 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
909 It operates in one of three modes:
911 @item One Sample mode.
912 @item Independent Groups mode.
917 Each of these modes are described in more detail below.
918 There are two optional subcommands which are common to all modes.
920 The @cmd{/CRITERIA} subcommand tells PSPP the confidence interval used
921 in the tests. The default value is 0.95.
924 The @cmd{MISSING} subcommand determines the handling of missing
926 If INCLUDE is set, then user-missing values are included in the
927 calculations, but system-missing values are not.
928 If EXCLUDE is set, which is the default, user-missing
929 values are excluded as well as system-missing values.
932 If LISTWISE is set, then the entire case is excluded from analysis
933 whenever any variable specified in the @cmd{/VARIABLES}, @cmd{/PAIRS} or
934 @cmd{/GROUPS} subcommands contains a missing value.
935 If ANALYSIS is set, then missing values are excluded only in the analysis for
936 which they would be needed. This is the default.
940 * One Sample Mode:: Testing against a hypothesised mean
941 * Independent Samples Mode:: Testing two independent groups for equal mean
942 * Paired Samples Mode:: Testing two interdependent groups for equal mean
945 @node One Sample Mode
946 @subsection One Sample Mode
948 The @cmd{TESTVAL} subcommand invokes the One Sample mode.
949 This mode is used to test a population mean against a hypothesised
951 The value given to the @cmd{TESTVAL} subcommand is the value against
952 which you wish to test.
953 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
954 tell PSPP which variables you wish to test.
956 @node Independent Samples Mode
957 @comment node-name, next, previous, up
958 @subsection Independent Samples Mode
960 The @cmd{GROUPS} subcommand invokes Independent Samples mode or
962 This mode is used to test whether two groups of values have the
963 same population mean.
964 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
965 tell PSPP the dependent variables you wish to test.
967 The variable given in the @cmd{GROUPS} subcommand is the independent
968 variable which determines to which group the samples belong.
969 The values in parentheses are the specific values of the independent
970 variable for each group.
971 If the parentheses are omitted and no values are given, the default values
972 of 1.0 and 2.0 are assumed.
974 If the independent variable is numeric,
975 it is acceptable to specify only one value inside the parentheses.
976 If you do this, cases where the independent variable is
977 greater than or equal to this value belong to the first group, and cases
978 less than this value belong to the second group.
979 When using this form of the @cmd{GROUPS} subcommand, missing values in
980 the independent variable are excluded on a listwise basis, regardless
981 of whether @cmd{/MISSING=LISTWISE} was specified.
984 @node Paired Samples Mode
985 @comment node-name, next, previous, up
986 @subsection Paired Samples Mode
988 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
989 Use this mode when repeated measures have been taken from the same
991 If the @code{WITH} keyword is omitted, then tables for all
992 combinations of variables given in the @cmd{PAIRS} subcommand are
994 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
995 is also given, then the number of variables preceding @code{WITH}
996 must be the same as the number following it.
997 In this case, tables for each respective pair of variables are
999 In the event that the @code{WITH} keyword is given, but the
1000 @code{(PAIRED)} keyword is omitted, then tables for each combination
1001 of variable preceding @code{WITH} against variable following
1002 @code{WITH} are generated.
1006 @comment node-name, next, previous, up
1010 @cindex analysis of variance
1015 [/VARIABLES = ] var_list BY var
1016 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1017 /CONTRAST= value1 [, value2] ... [,valueN]
1018 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1022 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1023 variables factored by a single independent variable.
1024 It is used to compare the means of a population
1025 divided into more than two groups.
1027 The dependent variables to be analysed should be given in the @code{VARIABLES}
1029 The list of variables must be followed by the @code{BY} keyword and
1030 the name of the independent (or factor) variable.
1032 You can use the @code{STATISTICS} subcommand to tell PSPP to display
1033 ancilliary information. The options accepted are:
1036 Displays descriptive statistics about the groups factored by the independent
1039 Displays the Levene test of Homogeneity of Variance for the
1040 variables and their groups.
1043 The @code{CONTRAST} subcommand is used when you anticipate certain
1044 differences between the groups.
1045 The subcommand must be followed by a list of numerals which are the
1046 coefficients of the groups to be tested.
1047 The number of coefficients must correspond to the number of distinct
1048 groups (or values of the independent variable).
1049 If the total sum of the coefficients are not zero, then PSPP will
1050 display a warning, but will proceed with the analysis.
1051 The @code{CONTRAST} subcommand may be given up to 10 times in order
1052 to specify different contrast tests.
1053 The @code{MISSING} subcommand defines how missing values are handled.
1054 If LISTWISE is specified then cases which have missing values for
1055 the independent variable or any dependent variable will be ignored.
1056 If ANALYSIS is specified, then cases will be ignored if the independent
1057 variable is missing or if the dependent variable currently being
1058 analysed is missing. The default is ANALYSIS.
1059 A setting of EXCLUDE means that variables whose values are
1060 user-missing are to be excluded from the analysis. A setting of
1061 INCLUDE means they are to be included. The default is EXCLUDE.
1065 @comment node-name, next, previous, up
1071 [VARIABLES=] var_list [@{A,D@}] [BY var_list]
1072 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1073 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1075 /MISSING=@{EXCLUDE,INCLUDE@}
1077 /RANK [INTO var_list]
1078 /NTILES(k) [INTO var_list]
1079 /NORMAL [INTO var_list]
1080 /PERCENT [INTO var_list]
1081 /RFRACTION [INTO var_list]
1082 /PROPORTION [INTO var_list]
1084 /SAVAGE [INTO var_list]
1087 The @cmd{RANK} command ranks variables and stores the results into new
1090 The VARIABLES subcommand, which is mandatory, specifies one or
1091 more variables whose values are to be ranked.
1092 After each variable, @samp{A} or @samp{D} may appear, indicating that
1093 the variable is to be ranked in ascending or descending order.
1094 Ascending is the default.
1095 If a BY keyword appears, it should be followed by a list of variables
1096 which are to serve as group variables.
1097 In this case, the cases are gathered into groups, and ranks calculated
1100 The TIES subcommand specifies how tied values are to be treated. The
1101 default is to take the mean value of all the tied cases.
1103 The FRACTION subcommand specifies how proportional ranks are to be
1104 calculated. This only has any effect if NORMAL or PROPORTIONAL rank
1105 functions are requested.
1107 The PRINT subcommand may be used to specify that a summary of the rank
1108 variables created should appear in the output.
1110 The function subcommands are RANK, NTILES, NORMAL, PERCENT, RFRACTION,
1111 PROPORTION and SAVAGE. Any number of function subcommands may appear.
1112 If none are given, then the default is RANK.
1113 The NTILES subcommand must take an integer specifying the number of
1114 partitions into which values should be ranked.
1115 Each subcommand may be followed by the INTO keyword and a list of
1116 variables which are the variables to be created and receive the rank
1117 scores. There may be as many variables specified as there are
1118 variables named on the VARIABLES subcommand. If fewer are specified,
1119 then the variable names are automatically created.
1121 The MISSING subcommand determines how user missing values are to be
1122 treated. A setting of EXCLUDE means that variables whose values are
1123 user-missing are to be excluded from the rank scores. A setting of
1124 INCLUDE means they are to be included. The default is EXCLUDE.
1126 @include regression.texi
1130 @section RELIABILITY
1136 /SCALE (@var{name}) = @{var_list, ALL@}
1137 /MODEL=@{ALPHA, SPLIT[(N)]@}
1138 /SUMMARY=@{TOTAL,ALL@}
1139 /MISSING=@{EXCLUDE,INCLUDE@}
1142 @cindex Cronbach's Alpha
1143 The @cmd{RELIABILTY} command performs reliablity analysis on the data.
1145 The VARIABLES subcommand is required. It determines the set of variables
1146 upon which analysis is to be performed.
1148 The SCALE subcommand determines which variables reliability is to be
1149 calculated for. If it is omitted, then analysis for all variables named
1150 in the VARIABLES subcommand will be used.
1151 Optionally, the @var{name} parameter may be specified to set a string name
1154 The MODEL subcommand determines the type of analysis. If ALPHA is specified,
1155 then Cronbach's Alpha is calculated for the scale. If the model is SPLIT,
1156 then the variables are divided into 2 subsets. An optional parameter
1157 @var{N} may be given, to specify how many variables to be in the first subset.
1158 If @var{N} is omitted, then it defaults to one half of the variables in the
1159 scale, or one half minus one if there are an odd number of variables.
1160 The default model is ALPHA.
1162 By default, any cases with user missing, or system missing values for
1164 in the VARIABLES subcommand will be omitted from analysis.
1165 The MISSING subcommand determines whether user missing values are to
1166 be included or excluded in the analysis.
1168 The SUMMARY subcommand determines the type of summary analysis to be performed.
1169 Currently there is only one type: SUMMARY=TOTAL, which displays per-item
1170 analysis tested against the totals.
1178 @cindex Receiver Operating Characterstic
1179 @cindex Area under curve
1182 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1183 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1184 /PRINT = [ SE ] [ COORDINATES ]
1185 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1186 [ TESTPOS (@{LARGE,SMALL@}) ]
1187 [ CI (@var{confidence}) ]
1188 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1189 /MISSING=@{EXCLUDE,INCLUDE@}
1193 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1194 of a dataset, and to estimate the area under the curve.
1195 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1197 The mandatory @var{var_list} is the list of predictor variables.
1198 The variable @var{state_var} is the variable whose values represent the actual states,
1199 and @var{state_value} is the value of this variable which represents the positive state.
1201 The optional subcommand PLOT is used to determine if and how the ROC curve is drawn.
1202 The keyword CURVE means that the ROC curve should be drawn, and the optional keyword REFERENCE,
1203 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1204 If the keyword NONE is given, then no ROC curve is drawn.
1205 By default, the curve is drawn with no reference line.
1207 The optional subcommand PRINT determines which additional tables should be printed.
1208 Two additional tables are available.
1209 The SE keyword says that standard error of the area under the curve should be printed as well as
1211 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1213 The COORDINATES keyword says that a table of coordinates of the ROC curve should be printed.
1215 The CRITERIA subcommand has four optional parameters:
1217 @item The TESTPOS parameter may be LARGE or SMALL.
1218 LARGE is the default, and says that larger values in the predictor variables are to be
1219 considered positive. SMALL indicates that smaller values should be considered positive.
1221 @item The CI parameter specifies the confidence interval that should be printed.
1222 It has no effect if the SE keyword in the PRINT subcommand has not been given.
1224 @item The DISTRIBUTION parameter determines the method to be used when estimating the area
1226 There are two possibilities, @i{viz}: FREE and NEGEXPO.
1227 The FREE method uses a non-parametric estimate, and the NEGEXPO method a bi-negative
1228 exponential distribution estimate.
1229 The NEGEXPO method should only be used when the number of positive actual states is
1230 equal to the number of negative actual states.
1231 The default is FREE.
1233 @item The CUTOFF parameter is for compatibility and is ignored.
1236 The MISSING subcommand determines whether user missing values are to
1237 be included or excluded in the analysis. The default behaviour is to
1239 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1240 or if the variable @var{state_var} is missing, then the entire case will be