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 * QUICK CLUSTER:: K-Means clustering.
18 * RANK:: Compute rank scores.
19 * REGRESSION:: Linear regression.
20 * RELIABILITY:: Reliability analysis.
21 * ROC:: Receiver Operating Characteristic.
31 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
32 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
34 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
35 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
36 SESKEWNESS,SEKURTOSIS@}
37 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
38 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
42 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
44 statistics requested by the user. In addition, it can optionally
47 The VARIABLES subcommand, which is required, specifies the list of
48 variables to be analyzed. Keyword VARIABLES is optional.
50 All other subcommands are optional:
52 The MISSING subcommand determines the handling of missing variables. If
53 INCLUDE is set, then user-missing values are included in the
54 calculations. If NOINCLUDE is set, which is the default, user-missing
55 values are excluded. If VARIABLE is set, then missing values are
56 excluded on a variable by variable basis; if LISTWISE is set, then
57 the entire case is excluded whenever any value in that case has a
58 system-missing or, if INCLUDE is set, user-missing value.
60 The FORMAT subcommand affects the output format. Currently the
61 LABELS/NOLABELS and NOINDEX/INDEX settings are not used. When SERIAL is
62 set, both valid and missing number of cases are listed in the output;
63 when NOSERIAL is set, only valid cases are listed.
65 The SAVE subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
66 the specified variables. The Z scores are saved to new variables.
67 Variable names are generated by trying first the original variable name
68 with Z prepended and truncated to a maximum of 8 characters, then the
69 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
70 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
71 variable names can be specified explicitly on VARIABLES in the variable
72 list by enclosing them in parentheses after each variable.
74 The STATISTICS subcommand specifies the statistics to be displayed:
78 All of the statistics below.
82 Standard error of the mean.
88 Kurtosis and standard error of the kurtosis.
90 Skewness and standard error of the skewness.
100 Mean, standard deviation of the mean, minimum, maximum.
102 Standard error of the kurtosis.
104 Standard error of the skewness.
107 The SORT subcommand specifies how the statistics should be sorted. Most
108 of the possible values should be self-explanatory. NAME causes the
109 statistics to be sorted by name. By default, the statistics are listed
110 in the order that they are specified on the VARIABLES subcommand. The A
111 and D settings request an ascending or descending sort order,
121 /FORMAT=@{TABLE,NOTABLE,LIMIT(limit)@}
122 @{AVALUE,DVALUE,AFREQ,DFREQ@}
123 /MISSING=@{EXCLUDE,INCLUDE@}
124 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
125 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
126 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
128 /PERCENTILES=percent@dots{}
129 /HISTOGRAM=[MINIMUM(x_min)] [MAXIMUM(x_max)]
130 [@{FREQ[(y_max)],PERCENT[(y_max)]@}] [@{NONORMAL,NORMAL@}]
131 /PIECHART=[MINIMUM(x_min)] [MAXIMUM(x_max)]
132 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
134 (These options are not currently implemented.)
140 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
142 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
143 (including median and mode) and percentiles,
144 @cmd{FREQUENCIES} can also output
145 histograms and pie charts.
147 The VARIABLES subcommand is the only required subcommand. Specify the
148 variables to be analyzed.
150 The FORMAT subcommand controls the output format. It has several
155 TABLE, the default, causes a frequency table to be output for every
156 variable specified. NOTABLE prevents them from being output. LIMIT
157 with a numeric argument causes them to be output except when there are
158 more than the specified number of values in the table.
161 Normally frequency tables are sorted in ascending order by value. This
162 is AVALUE. DVALUE tables are sorted in descending order by value.
163 AFREQ and DFREQ tables are sorted in ascending and descending order,
164 respectively, by frequency count.
167 The MISSING subcommand controls the handling of user-missing values.
168 When EXCLUDE, the default, is set, user-missing values are not included
169 in frequency tables or statistics. When INCLUDE is set, user-missing
170 are included. System-missing values are never included in statistics,
171 but are listed in frequency tables.
173 The available STATISTICS are the same as available in @cmd{DESCRIPTIVES}
174 (@pxref{DESCRIPTIVES}), with the addition of MEDIAN, the data's median
175 value, and MODE, the mode. (If there are multiple modes, the smallest
176 value is reported.) By default, the mean, standard deviation of the
177 mean, minimum, and maximum are reported for each variable.
180 PERCENTILES causes the specified percentiles to be reported.
181 The percentiles should be presented at a list of numbers between 0
183 The NTILES subcommand causes the percentiles to be reported at the
184 boundaries of the data set divided into the specified number of ranges.
185 For instance, @code{/NTILES=4} would cause quartiles to be reported.
188 The HISTOGRAM subcommand causes the output to include a histogram for
189 each specified numeric variable. The X axis by default ranges from
190 the minimum to the maximum value observed in the data, but the MINIMUM
191 and MAXIMUM keywords can set an explicit range. Specify NORMAL to
192 superimpose a normal curve on the histogram. Histograms are not
193 created for string variables.
196 The PIECHART adds a pie chart for each variable to the data. Each
197 slice represents one value, with the size of the slice proportional to
198 the value's frequency. By default, all non-missing values are given
199 slices. The MINIMUM and MAXIMUM keywords can be used to limit the
200 displayed slices to a given range of values. The MISSING keyword adds
201 slices for missing values.
203 The FREQ and PERCENT options on HISTOGRAM and PIECHART are accepted
204 but not currently honored.
207 @comment node-name, next, previous, up
211 @cindex Normality, testing for
215 VARIABLES=var_list [BY factor_list ]
216 /STATISTICS=@{DESCRIPTIVES, EXTREME[(n)], ALL, NONE@}
217 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, ALL, NONE@}
219 /COMPARE=@{GROUPS,VARIABLES@}
222 /PERCENTILE=[value_list]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
223 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
224 [@{NOREPORT,REPORT@}]
228 The @cmd{EXAMINE} command is used to test how closely a distribution is to a
229 normal distribution. It also shows you outliers and extreme values.
231 The VARIABLES subcommand specifies the dependent variables and the
232 independent variable to use as factors for the analysis. Variables
233 listed before the first BY keyword are the dependent variables.
234 The dependent variables may optionally be followed by a list of
235 factors which tell PSPP how to break down the analysis for each
236 dependent variable. The format for each factor is
242 The STATISTICS subcommand specifies the analysis to be done.
243 DESCRIPTIVES will produce a table showing some parametric and
244 non-parametrics statistics. EXTREME produces a table showing extreme
245 values of the dependent variable. A number in parentheses determines
246 how many upper and lower extremes to show. The default number is 5.
252 The PLOT subcommand specifies which plots are to be produced if any.
253 Available plots are HISTOGRAM, NPPLOT and BOXPLOT.
255 The COMPARE subcommand is only relevant if producing boxplots, and it is only
256 useful there is more than one dependent variable and at least one factor. If
257 /COMPARE=GROUPS is specified, then one plot per dependent variable is produced,
258 containing boxplots for all the factors.
259 If /COMPARE=VARIABLES is specified, then one plot per factor is produced, each
260 each containing one boxplot per dependent variable.
261 If the /COMPARE subcommand is ommitted, then PSPP uses the default value of
264 The ID subcommand also pertains to boxplots. If given, it must
265 specify a variable name. Outliers and extreme cases plotted in
266 boxplots will be labelled with the case from that variable. Numeric or
267 string variables are permissible. If the ID subcommand is not given,
268 then the casenumber will be used for labelling.
270 The CINTERVAL subcommand specifies the confidence interval to use in
271 calculation of the descriptives command. The default it 95%.
274 The PERCENTILES subcommand specifies which percentiles are to be calculated,
275 and which algorithm to use for calculating them. The default is to
276 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
279 The TOTAL and NOTOTAL subcommands are mutually exclusive. If NOTOTAL
280 is given and factors have been specified in the VARIABLES subcommand,
281 then then statistics for the unfactored dependent variables are
282 produced in addition to the factored variables. If there are no
283 factors specified then TOTAL and NOTOTAL have no effect.
286 If many dependent variable are given, or factors are given for which
287 there are many distinct values, then @cmd{EXAMINE} will produce a very
288 large quantity of output.
291 @section CORRELATIONS
296 /VARIABLES = varlist [ WITH varlist ]
301 /VARIABLES = varlist [ WITH varlist ]
302 /VARIABLES = varlist [ WITH varlist ]
305 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
306 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
307 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
311 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
312 for a set of variables. The significance of the coefficients are also given.
314 At least one VARIABLES subcommand is required. If the WITH keyword is used, then a non-square
315 correlation table will be produced.
316 The variables preceding WITH, will be used as the rows of the table, and the variables following
317 will be the columns of the table.
318 If no WITH subcommand is given, then a square, symmetrical table using all variables is produced.
321 The @cmd{MISSING} subcommand determines the handling of missing variables.
322 If INCLUDE is set, then user-missing values are included in the
323 calculations, but system-missing values are not.
324 If EXCLUDE is set, which is the default, user-missing
325 values are excluded as well as system-missing values.
328 If LISTWISE is set, then the entire case is excluded from analysis
329 whenever any variable specified in any @cmd{/VARIABLES} subcommand
330 contains a missing value.
331 If PAIRWISE is set, then a case is considered missing only if either of the
332 values for the particular coefficient are missing.
333 The default is PAIRWISE.
335 The PRINT subcommand is used to control how the reported significance values are printed.
336 If the TWOTAIL option is used, then a two-tailed test of significance is
337 printed. If the ONETAIL option is given, then a one-tailed test is used.
338 The default is TWOTAIL.
340 If the NOSIG option is specified, then correlation coefficients with significance less than
341 0.05 are highlighted.
342 If SIG is specified, then no highlighting is performed. This is the default.
345 The STATISTICS subcommand requests additional statistics to be displayed. The keyword
346 DESCRIPTIVES requests that the mean, number of non-missing cases, and the non-biased
347 estimator of the standard deviation are displayed.
348 These statistics will be displayed in a separated table, for all the variables listed
349 in any /VARIABLES subcommand.
350 The XPROD keyword requests cross-product deviations and covariance estimators to
351 be displayed for each pair of variables.
352 The keyword ALL is the union of DESCRIPTIVES and XPROD.
360 /TABLES=var_list BY var_list [BY var_list]@dots{}
361 /MISSING=@{TABLE,INCLUDE,REPORT@}
362 /WRITE=@{NONE,CELLS,ALL@}
363 /FORMAT=@{TABLES,NOTABLES@}
364 @{LABELS,NOLABELS,NOVALLABS@}
369 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
370 ASRESIDUAL,ALL,NONE@}
371 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
372 KAPPA,ETA,CORR,ALL,NONE@}
375 /VARIABLES=var_list (low,high)@dots{}
378 The @cmd{CROSSTABS} procedure displays crosstabulation
379 tables requested by the user. It can calculate several statistics for
380 each cell in the crosstabulation tables. In addition, a number of
381 statistics can be calculated for each table itself.
383 The TABLES subcommand is used to specify the tables to be reported. Any
384 number of dimensions is permitted, and any number of variables per
385 dimension is allowed. The TABLES subcommand may be repeated as many
386 times as needed. This is the only required subcommand in @dfn{general
389 Occasionally, one may want to invoke a special mode called @dfn{integer
390 mode}. Normally, in general mode, PSPP automatically determines
391 what values occur in the data. In integer mode, the user specifies the
392 range of values that the data assumes. To invoke this mode, specify the
393 VARIABLES subcommand, giving a range of data values in parentheses for
394 each variable to be used on the TABLES subcommand. Data values inside
395 the range are truncated to the nearest integer, then assigned to that
396 value. If values occur outside this range, they are discarded. When it
397 is present, the VARIABLES subcommand must precede the TABLES
400 In general mode, numeric and string variables may be specified on
401 TABLES. In integer mode, only numeric variables are allowed.
403 The MISSING subcommand determines the handling of user-missing values.
404 When set to TABLE, the default, missing values are dropped on a table by
405 table basis. When set to INCLUDE, user-missing values are included in
406 tables and statistics. When set to REPORT, which is allowed only in
407 integer mode, user-missing values are included in tables but marked with
408 an @samp{M} (for ``missing'') and excluded from statistical
411 Currently the WRITE subcommand is ignored.
413 The FORMAT subcommand controls the characteristics of the
414 crosstabulation tables to be displayed. It has a number of possible
419 TABLES, the default, causes crosstabulation tables to be output.
420 NOTABLES suppresses them.
423 LABELS, the default, allows variable labels and value labels to appear
424 in the output. NOLABELS suppresses them. NOVALLABS displays variable
425 labels but suppresses value labels.
428 PIVOT, the default, causes each TABLES subcommand to be displayed in a
429 pivot table format. NOPIVOT causes the old-style crosstabulation format
433 AVALUE, the default, causes values to be sorted in ascending order.
434 DVALUE asserts a descending sort order.
437 INDEX/NOINDEX is currently ignored.
440 BOX/NOBOX is currently ignored.
443 The CELLS subcommand controls the contents of each cell in the displayed
444 crosstabulation table. The possible settings are:
460 Standardized residual.
462 Adjusted standardized residual.
466 Suppress cells entirely.
469 @samp{/CELLS} without any settings specified requests COUNT, ROW,
470 COLUMN, and TOTAL. If CELLS is not specified at all then only COUNT
473 The STATISTICS subcommand selects statistics for computation:
480 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
481 correction, linear-by-linear association.
485 Contingency coefficient.
489 Uncertainty coefficient.
505 Spearman correlation, Pearson's r.
512 Selected statistics are only calculated when appropriate for the
513 statistic. Certain statistics require tables of a particular size, and
514 some statistics are calculated only in integer mode.
516 @samp{/STATISTICS} without any settings selects CHISQ. If the
517 STATISTICS subcommand is not given, no statistics are calculated.
519 @strong{Please note:} Currently the implementation of CROSSTABS has the
524 Pearson's R (but not Spearman) is off a little.
526 T values for Spearman's R and Pearson's R are wrong.
528 Significance of symmetric and directional measures is not calculated.
530 Asymmetric ASEs and T values for lambda are wrong.
532 ASE of Goodman and Kruskal's tau is not calculated.
534 ASE of symmetric somers' d is wrong.
536 Approximate T of uncertainty coefficient is wrong.
539 Fixes for any of these deficiencies would be welcomed.
545 @cindex factor analysis
546 @cindex principal components analysis
547 @cindex principal axis factoring
548 @cindex data reduction
551 FACTOR VARIABLES=var_list
553 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
555 [ /EXTRACTION=@{PC, PAF@}]
557 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
559 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [SIG] [ALL] [DEFAULT] ]
563 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
565 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
567 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
570 The FACTOR command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
571 common factors in the data or for data reduction purposes.
573 The VARIABLES subcommand is required. It lists the variables which are to partake in the analysis.
575 The /EXTRACTION subcommand is used to specify the way in which factors (components) are extracted from the data.
576 If PC is specified, then Principal Components Analysis is used. If PAF is specified, then Principal Axis Factoring is
577 used. By default Principal Components Analysis will be used.
579 The /ROTATION subcommand is used to specify the method by which the extracted solution will be rotated.
580 Three methods are available: VARIMAX (which is the default), EQUAMAX, and QUARTIMAX.
581 If don't want any rotation to be performed, the word NOROTATE will prevent the command from performing any
582 rotation on the data. Oblique rotations are not supported.
584 The /METHOD subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
585 to be analysed. By default, the correlation matrix is analysed.
587 The /PRINT subcommand may be used to select which features of the analysis are reported:
591 A table of mean values, standard deviations and total weights are printed.
593 Initial communalities and eigenvalues are printed.
595 Extracted communalities and eigenvalues are printed.
597 Rotated communalities and eigenvalues are printed.
599 The correlation matrix is printed.
601 The covariance matrix is printed.
603 The determinant of the correlation or covariance matrix is printed.
605 The significance of the elements of correlation matrix is printed.
607 All of the above are printed.
609 Identical to INITIAL and EXTRACTION.
612 If /PLOT=EIGEN is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualising
613 which factors (components) should be retained.
615 The /FORMAT subcommand determined how data are to be displayed in loading matrices. If SORT is specified, then the variables
616 are sorted in descending order of significance. If BLANK(@var{n}) is specified, then coefficients whose absolute value is less
617 than @var{n} will not be printed. If the keyword DEFAULT is given, or if no /FORMAT subcommand is given, then no sorting is
618 performed, and all coefficients will be printed.
620 The /CRITERIA subcommand is used to specify how the number of extracted factors (components) are chosen. If FACTORS(@var{n}) is
621 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the MINEIGEN setting will
622 be used. MINEIGEN(@var{l}) requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
623 The default value of @var{l} is 1. The ECONVERGE and ITERATE settings have effect only when iterative algorithms for factor
624 extraction (such as Principal Axis Factoring) are used. ECONVERGE(@var{delta}) specifies that iteration should cease when
625 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
626 default value of @var{delta} is 0.001.
627 The ITERATE(@var{m}) setting sets the maximum number of iterations to @var{m}. The default value of @var{m} is 25.
629 The @cmd{MISSING} subcommand determines the handling of missing variables.
630 If INCLUDE is set, then user-missing values are included in the
631 calculations, but system-missing values are not.
632 If EXCLUDE is set, which is the default, user-missing
633 values are excluded as well as system-missing values.
635 If LISTWISE is set, then the entire case is excluded from analysis
636 whenever any variable specified in the @cmd{VARIABLES} subcommand
637 contains a missing value.
638 If PAIRWISE is set, then a case is considered missing only if either of the
639 values for the particular coefficient are missing.
640 The default is LISTWISE.
647 @cindex nonparametric tests
652 nonparametric test subcommands
657 [ /STATISTICS=@{DESCRIPTIVES@} ]
659 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
661 [ /METHOD=EXACT [ TIMER [(n)] ] ]
664 NPAR TESTS performs nonparametric tests.
665 Non parametric tests make very few assumptions about the distribution of the
667 One or more tests may be specified by using the corresponding subcommand.
668 If the /STATISTICS subcommand is also specified, then summary statistics are
669 produces for each variable that is the subject of any test.
671 Certain tests may take a long time to execute, if an exact figure is required.
672 Therefore, by default asymptotic approximations are used unless the
673 subcommand /METHOD=EXACT is specified.
674 Exact tests give more accurate results, but may take an unacceptably long
675 time to perform. If the TIMER keyword is used, it sets a maximum time,
676 after which the test will be abandoned, and a warning message printed.
677 The time, in minutes, should be specified in parentheses after the TIMER keyword.
678 If the TIMER keyword is given without this figure, then a default value of 5 minutes
683 * BINOMIAL:: Binomial Test
684 * CHISQUARE:: Chisquare Test
685 * COCHRAN:: Cochran Q Test
686 * FRIEDMAN:: Friedman Test
687 * KENDALL:: Kendall's W Test
688 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
689 * MANN-WHITNEY:: Mann Whitney U Test
690 * MCNEMAR:: McNemar Test
692 * SIGN:: The Sign Test
693 * WILCOXON:: Wilcoxon Signed Ranks Test
698 @subsection Binomial test
700 @cindex binomial test
703 [ /BINOMIAL[(p)]=var_list[(value1[, value2)] ] ]
706 The /BINOMIAL subcommand compares the observed distribution of a dichotomous
707 variable with that of a binomial distribution.
708 The variable @var{p} specifies the test proportion of the binomial
710 The default value of 0.5 is assumed if @var{p} is omitted.
712 If a single value appears after the variable list, then that value is
713 used as the threshold to partition the observed values. Values less
714 than or equal to the threshold value form the first category. Values
715 greater than the threshold form the second category.
717 If two values appear after the variable list, then they will be used
718 as the values which a variable must take to be in the respective
720 Cases for which a variable takes a value equal to neither of the specified
721 values, take no part in the test for that variable.
723 If no values appear, then the variable must assume dichotomous
725 If more than two distinct, non-missing values for a variable
726 under test are encountered then an error occurs.
728 If the test proportion is equal to 0.5, then a two tailed test is
729 reported. For any other test proportion, a one tailed test is
731 For one tailed tests, if the test proportion is less than
732 or equal to the observed proportion, then the significance of
733 observing the observed proportion or more is reported.
734 If the test proportion is more than the observed proportion, then the
735 significance of observing the observed proportion or less is reported.
736 That is to say, the test is always performed in the observed
739 PSPP uses a very precise approximation to the gamma function to
740 compute the binomial significance. Thus, exact results are reported
741 even for very large sample sizes.
746 @subsection Chisquare Test
748 @cindex chisquare test
752 [ /CHISQUARE=var_list[(lo,hi)] [/EXPECTED=@{EQUAL|f1, f2 @dots{} fn@}] ]
756 The /CHISQUARE subcommand produces a chi-square statistic for the differences
757 between the expected and observed frequencies of the categories of a variable.
758 Optionally, a range of values may appear after the variable list.
759 If a range is given, then non integer values are truncated, and values
760 outside the specified range are excluded from the analysis.
762 The /EXPECTED subcommand specifies the expected values of each
764 There must be exactly one non-zero expected value, for each observed
765 category, or the EQUAL keywork must be specified.
766 You may use the notation @var{n}*@var{f} to specify @var{n}
767 consecutive expected categories all taking a frequency of @var{f}.
768 The frequencies given are proportions, not absolute frequencies. The
769 sum of the frequencies need not be 1.
770 If no /EXPECTED subcommand is given, then then equal frequencies
775 @subsection Cochran Q Test
777 @cindex Cochran Q test
781 [ /COCHRAN = varlist ]
784 The Cochran Q test is used to test for differences between three or more groups.
785 The data for @var{varlist} in all cases must assume exactly two distinct values (other than missing values).
787 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
790 @subsection Friedman Test
792 @cindex Friedman test
795 [ /FRIEDMAN = varlist ]
798 The Friedman test is used to test for differences between repeated measures when there is no indication that the distributions are normally distributed.
800 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.
803 @subsection Kendall's W Test
805 @cindex Kendall's W test
806 @cindex coefficient of concordance
809 [ /KENDALL = varlist ]
812 The Kendall test investigates whether an arbitrary number of related samples come from the
814 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
815 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
816 unity indicates complete agreement.
820 @subsection Kruskal-Wallis Test
821 @vindex KRUSKAL-WALLIS
823 @cindex Kruskal-Wallis test
826 [ /KRUSKAL-WALLIS = varlist BY var (lower, upper) ]
829 The Kruskal-Wallis test is used to compare data from an
830 arbitrary number of populations. It does not assume normality.
831 The data to be compared are specified by @var{varlist}.
832 The categorical variable determining the groups to which the
833 data belongs is given by @var{var}. The limits @var{lower} and
834 @var{upper} specify the valid range of @var{var}. Any cases for
835 which @var{var} falls outside [@var{lower}, @var{upper}] will be
838 The mean rank of each group as well as the chi-squared value and significance
839 of the test will be printed.
840 The abbreviated subcommand K-W may be used in place of KRUSKAL-WALLIS.
844 @subsection Mann-Whitney U Test
847 @cindex Mann-Whitney U test
848 @cindex U, Mann-Whitney U
851 [ /MANN-WHITNEY = varlist BY var (group1, group2) ]
854 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
855 The variables to be tested should be specified in @var{varlist} and the grouping variable, that determines to which group the test variables belong, in @var{var}.
856 @var{Var} may be either a string or an alpha variable.
857 @var{Group1} and @var{group2} specify the
858 two values of @var{var} which determine the groups of the test data.
859 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
861 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
862 The abbreviated subcommand M-W may be used in place of MANN-WHITNEY.
865 @subsection McNemar Test
870 [ /MCNEMAR varlist [ WITH varlist [ (PAIRED) ]]]
873 Use McNemar's test to analyse the significance of the difference between
874 pairs of correlated proportions.
876 If the @code{WITH} keyword is omitted, then tests for all
877 combinations of the listed variables are performed.
878 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
879 is also given, then the number of variables preceding @code{WITH}
880 must be the same as the number following it.
881 In this case, tests for each respective pair of variables are
883 If the @code{WITH} keyword is given, but the
884 @code{(PAIRED)} keyword is omitted, then tests for each combination
885 of variable preceding @code{WITH} against variable following
886 @code{WITH} are performed.
888 The data in each variable must be dichotomous. If there are more
889 than two distinct variables an error will occur and the test will
893 @subsection Runs Test
898 [ /RUNS (@{MEAN, MEDIAN, MODE, value@}) varlist ]
901 The /RUNS subcommand tests whether a data sequence is randomly ordered.
903 It works by examining the number of times a variable's value crosses a given threshold.
904 The desired threshold must be specified within parentheses.
905 It may either be specified as a number or as one of MEAN, MEDIAN or MODE.
906 Following the threshold specification comes the list of variables whose values are to be
909 The subcommand shows the number of runs, the asymptotic significance based on the
913 @subsection Sign Test
918 [ /SIGN varlist [ WITH varlist [ (PAIRED) ]]]
921 The /SIGN subcommand tests for differences between medians of the
923 The test does not make any assumptions about the
924 distribution of the data.
926 If the @code{WITH} keyword is omitted, then tests for all
927 combinations of the listed variables are performed.
928 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
929 is also given, then the number of variables preceding @code{WITH}
930 must be the same as the number following it.
931 In this case, tests for each respective pair of variables are
933 If the @code{WITH} keyword is given, but the
934 @code{(PAIRED)} keyword is omitted, then tests for each combination
935 of variable preceding @code{WITH} against variable following
936 @code{WITH} are performed.
939 @subsection Wilcoxon Matched Pairs Signed Ranks Test
940 @comment node-name, next, previous, up
942 @cindex wilcoxon matched pairs signed ranks test
945 [ /WILCOXON varlist [ WITH varlist [ (PAIRED) ]]]
948 The /WILCOXON subcommand tests for differences between medians of the
950 The test does not make any assumptions about the variances of the samples.
951 It does however assume that the distribution is symetrical.
953 If the @code{WITH} keyword is omitted, then tests for all
954 combinations of the listed variables are performed.
955 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
956 is also given, then the number of variables preceding @code{WITH}
957 must be the same as the number following it.
958 In this case, tests for each respective pair of variables are
960 If the @code{WITH} keyword is given, but the
961 @code{(PAIRED)} keyword is omitted, then tests for each combination
962 of variable preceding @code{WITH} against variable following
963 @code{WITH} are performed.
966 @comment node-name, next, previous, up
973 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
974 /CRITERIA=CIN(confidence)
982 (Independent Samples mode.)
983 GROUPS=var(value1 [, value2])
987 (Paired Samples mode.)
988 PAIRS=var_list [WITH var_list [(PAIRED)] ]
993 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
995 It operates in one of three modes:
997 @item One Sample mode.
998 @item Independent Groups mode.
1003 Each of these modes are described in more detail below.
1004 There are two optional subcommands which are common to all modes.
1006 The @cmd{/CRITERIA} subcommand tells PSPP the confidence interval used
1007 in the tests. The default value is 0.95.
1010 The @cmd{MISSING} subcommand determines the handling of missing
1012 If INCLUDE is set, then user-missing values are included in the
1013 calculations, but system-missing values are not.
1014 If EXCLUDE is set, which is the default, user-missing
1015 values are excluded as well as system-missing values.
1016 This is the default.
1018 If LISTWISE is set, then the entire case is excluded from analysis
1019 whenever any variable specified in the @cmd{/VARIABLES}, @cmd{/PAIRS} or
1020 @cmd{/GROUPS} subcommands contains a missing value.
1021 If ANALYSIS is set, then missing values are excluded only in the analysis for
1022 which they would be needed. This is the default.
1026 * One Sample Mode:: Testing against a hypothesised mean
1027 * Independent Samples Mode:: Testing two independent groups for equal mean
1028 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1031 @node One Sample Mode
1032 @subsection One Sample Mode
1034 The @cmd{TESTVAL} subcommand invokes the One Sample mode.
1035 This mode is used to test a population mean against a hypothesised
1037 The value given to the @cmd{TESTVAL} subcommand is the value against
1038 which you wish to test.
1039 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
1040 tell PSPP which variables you wish to test.
1042 @node Independent Samples Mode
1043 @comment node-name, next, previous, up
1044 @subsection Independent Samples Mode
1046 The @cmd{GROUPS} subcommand invokes Independent Samples mode or
1048 This mode is used to test whether two groups of values have the
1049 same population mean.
1050 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
1051 tell PSPP the dependent variables you wish to test.
1053 The variable given in the @cmd{GROUPS} subcommand is the independent
1054 variable which determines to which group the samples belong.
1055 The values in parentheses are the specific values of the independent
1056 variable for each group.
1057 If the parentheses are omitted and no values are given, the default values
1058 of 1.0 and 2.0 are assumed.
1060 If the independent variable is numeric,
1061 it is acceptable to specify only one value inside the parentheses.
1062 If you do this, cases where the independent variable is
1063 greater than or equal to this value belong to the first group, and cases
1064 less than this value belong to the second group.
1065 When using this form of the @cmd{GROUPS} subcommand, missing values in
1066 the independent variable are excluded on a listwise basis, regardless
1067 of whether @cmd{/MISSING=LISTWISE} was specified.
1070 @node Paired Samples Mode
1071 @comment node-name, next, previous, up
1072 @subsection Paired Samples Mode
1074 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1075 Use this mode when repeated measures have been taken from the same
1077 If the @code{WITH} keyword is omitted, then tables for all
1078 combinations of variables given in the @cmd{PAIRS} subcommand are
1080 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1081 is also given, then the number of variables preceding @code{WITH}
1082 must be the same as the number following it.
1083 In this case, tables for each respective pair of variables are
1085 In the event that the @code{WITH} keyword is given, but the
1086 @code{(PAIRED)} keyword is omitted, then tables for each combination
1087 of variable preceding @code{WITH} against variable following
1088 @code{WITH} are generated.
1092 @comment node-name, next, previous, up
1096 @cindex analysis of variance
1101 [/VARIABLES = ] var_list BY var
1102 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1103 /CONTRAST= value1 [, value2] ... [,valueN]
1104 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1105 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([value])@}
1108 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1109 variables factored by a single independent variable.
1110 It is used to compare the means of a population
1111 divided into more than two groups.
1113 The dependent variables to be analysed should be given in the @code{VARIABLES}
1115 The list of variables must be followed by the @code{BY} keyword and
1116 the name of the independent (or factor) variable.
1118 You can use the @code{STATISTICS} subcommand to tell PSPP to display
1119 ancilliary information. The options accepted are:
1122 Displays descriptive statistics about the groups factored by the independent
1125 Displays the Levene test of Homogeneity of Variance for the
1126 variables and their groups.
1129 The @code{CONTRAST} subcommand is used when you anticipate certain
1130 differences between the groups.
1131 The subcommand must be followed by a list of numerals which are the
1132 coefficients of the groups to be tested.
1133 The number of coefficients must correspond to the number of distinct
1134 groups (or values of the independent variable).
1135 If the total sum of the coefficients are not zero, then PSPP will
1136 display a warning, but will proceed with the analysis.
1137 The @code{CONTRAST} subcommand may be given up to 10 times in order
1138 to specify different contrast tests.
1139 The @code{MISSING} subcommand defines how missing values are handled.
1140 If LISTWISE is specified then cases which have missing values for
1141 the independent variable or any dependent variable will be ignored.
1142 If ANALYSIS is specified, then cases will be ignored if the independent
1143 variable is missing or if the dependent variable currently being
1144 analysed is missing. The default is ANALYSIS.
1145 A setting of EXCLUDE means that variables whose values are
1146 user-missing are to be excluded from the analysis. A setting of
1147 INCLUDE means they are to be included. The default is EXCLUDE.
1149 Using the @code{POSTHOC} subcommand you can perform multiple
1150 pairwise comparisons on the data. The following comparison methods
1154 Least Significant Difference.
1156 Tukey Honestly Significant Difference.
1164 The Games-Howell test.
1168 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1169 that @var{value} should be used as the
1170 confidence level for which the posthoc tests will be performed.
1171 The default is 0.05.
1174 @comment node-name, next, previous, up
1175 @section QUICK CLUSTER
1176 @vindex QUICK CLUSTER
1178 @cindex K-means clustering
1182 QUICK CLUSTER var_list
1183 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1184 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1187 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1188 dataset. This is useful when you wish to allocate cases into clusters
1189 of similar values and you already know the number of clusters.
1191 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1192 of the variables which contain the cluster data. Normally you will also
1193 want to specify @samp{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1194 number of clusters. If this is not given, then @var{k} defaults to 2.
1196 The command uses an iterative algorithm to determine the clusters for
1197 each case. It will continue iterating until convergence, or until @var{max_iter}
1198 iterations have been done. The default value of @var{max_iter} is 2.
1200 The @cmd{MISSING} subcommand determines the handling of missing variables.
1201 If INCLUDE is set, then user-missing values are considered at their face
1202 value and not as missing values.
1203 If EXCLUDE is set, which is the default, user-missing
1204 values are excluded as well as system-missing values.
1206 If LISTWISE is set, then the entire case is excluded from the analysis
1207 whenever any of the clustering variables contains a missing value.
1208 If PAIRWISE is set, then a case is considered missing only if all the
1209 clustering variables contain missing values. Otherwise it is clustered
1210 on the basis of the non-missing values.
1211 The default is LISTWISE.
1215 @comment node-name, next, previous, up
1222 [VARIABLES=] var_list [@{A,D@}] [BY var_list]
1223 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1224 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1226 /MISSING=@{EXCLUDE,INCLUDE@}
1228 /RANK [INTO var_list]
1229 /NTILES(k) [INTO var_list]
1230 /NORMAL [INTO var_list]
1231 /PERCENT [INTO var_list]
1232 /RFRACTION [INTO var_list]
1233 /PROPORTION [INTO var_list]
1235 /SAVAGE [INTO var_list]
1238 The @cmd{RANK} command ranks variables and stores the results into new
1241 The VARIABLES subcommand, which is mandatory, specifies one or
1242 more variables whose values are to be ranked.
1243 After each variable, @samp{A} or @samp{D} may appear, indicating that
1244 the variable is to be ranked in ascending or descending order.
1245 Ascending is the default.
1246 If a BY keyword appears, it should be followed by a list of variables
1247 which are to serve as group variables.
1248 In this case, the cases are gathered into groups, and ranks calculated
1251 The TIES subcommand specifies how tied values are to be treated. The
1252 default is to take the mean value of all the tied cases.
1254 The FRACTION subcommand specifies how proportional ranks are to be
1255 calculated. This only has any effect if NORMAL or PROPORTIONAL rank
1256 functions are requested.
1258 The PRINT subcommand may be used to specify that a summary of the rank
1259 variables created should appear in the output.
1261 The function subcommands are RANK, NTILES, NORMAL, PERCENT, RFRACTION,
1262 PROPORTION and SAVAGE. Any number of function subcommands may appear.
1263 If none are given, then the default is RANK.
1264 The NTILES subcommand must take an integer specifying the number of
1265 partitions into which values should be ranked.
1266 Each subcommand may be followed by the INTO keyword and a list of
1267 variables which are the variables to be created and receive the rank
1268 scores. There may be as many variables specified as there are
1269 variables named on the VARIABLES subcommand. If fewer are specified,
1270 then the variable names are automatically created.
1272 The MISSING subcommand determines how user missing values are to be
1273 treated. A setting of EXCLUDE means that variables whose values are
1274 user-missing are to be excluded from the rank scores. A setting of
1275 INCLUDE means they are to be included. The default is EXCLUDE.
1277 @include regression.texi
1281 @section RELIABILITY
1287 /SCALE (@var{name}) = @{var_list, ALL@}
1288 /MODEL=@{ALPHA, SPLIT[(N)]@}
1289 /SUMMARY=@{TOTAL,ALL@}
1290 /MISSING=@{EXCLUDE,INCLUDE@}
1293 @cindex Cronbach's Alpha
1294 The @cmd{RELIABILTY} command performs reliablity analysis on the data.
1296 The VARIABLES subcommand is required. It determines the set of variables
1297 upon which analysis is to be performed.
1299 The SCALE subcommand determines which variables reliability is to be
1300 calculated for. If it is omitted, then analysis for all variables named
1301 in the VARIABLES subcommand will be used.
1302 Optionally, the @var{name} parameter may be specified to set a string name
1305 The MODEL subcommand determines the type of analysis. If ALPHA is specified,
1306 then Cronbach's Alpha is calculated for the scale. If the model is SPLIT,
1307 then the variables are divided into 2 subsets. An optional parameter
1308 @var{N} may be given, to specify how many variables to be in the first subset.
1309 If @var{N} is omitted, then it defaults to one half of the variables in the
1310 scale, or one half minus one if there are an odd number of variables.
1311 The default model is ALPHA.
1313 By default, any cases with user missing, or system missing values for
1315 in the VARIABLES subcommand will be omitted from analysis.
1316 The MISSING subcommand determines whether user missing values are to
1317 be included or excluded in the analysis.
1319 The SUMMARY subcommand determines the type of summary analysis to be performed.
1320 Currently there is only one type: SUMMARY=TOTAL, which displays per-item
1321 analysis tested against the totals.
1329 @cindex Receiver Operating Characterstic
1330 @cindex Area under curve
1333 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1334 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1335 /PRINT = [ SE ] [ COORDINATES ]
1336 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1337 [ TESTPOS (@{LARGE,SMALL@}) ]
1338 [ CI (@var{confidence}) ]
1339 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1340 /MISSING=@{EXCLUDE,INCLUDE@}
1344 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1345 of a dataset, and to estimate the area under the curve.
1346 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1348 The mandatory @var{var_list} is the list of predictor variables.
1349 The variable @var{state_var} is the variable whose values represent the actual states,
1350 and @var{state_value} is the value of this variable which represents the positive state.
1352 The optional subcommand PLOT is used to determine if and how the ROC curve is drawn.
1353 The keyword CURVE means that the ROC curve should be drawn, and the optional keyword REFERENCE,
1354 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1355 If the keyword NONE is given, then no ROC curve is drawn.
1356 By default, the curve is drawn with no reference line.
1358 The optional subcommand PRINT determines which additional tables should be printed.
1359 Two additional tables are available.
1360 The SE keyword says that standard error of the area under the curve should be printed as well as
1362 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1364 The COORDINATES keyword says that a table of coordinates of the ROC curve should be printed.
1366 The CRITERIA subcommand has four optional parameters:
1368 @item The TESTPOS parameter may be LARGE or SMALL.
1369 LARGE is the default, and says that larger values in the predictor variables are to be
1370 considered positive. SMALL indicates that smaller values should be considered positive.
1372 @item The CI parameter specifies the confidence interval that should be printed.
1373 It has no effect if the SE keyword in the PRINT subcommand has not been given.
1375 @item The DISTRIBUTION parameter determines the method to be used when estimating the area
1377 There are two possibilities, @i{viz}: FREE and NEGEXPO.
1378 The FREE method uses a non-parametric estimate, and the NEGEXPO method a bi-negative
1379 exponential distribution estimate.
1380 The NEGEXPO method should only be used when the number of positive actual states is
1381 equal to the number of negative actual states.
1382 The default is FREE.
1384 @item The CUTOFF parameter is for compatibility and is ignored.
1387 The MISSING subcommand determines whether user missing values are to
1388 be included or excluded in the analysis. The default behaviour is to
1390 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1391 or if the variable @var{state_var} is missing, then the entire case will be