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@}
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 PIVOT, the default, causes each TABLES subcommand to be displayed in a
423 pivot table format. NOPIVOT causes the old-style crosstabulation format
427 AVALUE, the default, causes values to be sorted in ascending order.
428 DVALUE asserts a descending sort order.
431 INDEX/NOINDEX is currently ignored.
434 BOX/NOBOX is currently ignored.
437 The CELLS subcommand controls the contents of each cell in the displayed
438 crosstabulation table. The possible settings are:
454 Standardized residual.
456 Adjusted standardized residual.
460 Suppress cells entirely.
463 @samp{/CELLS} without any settings specified requests COUNT, ROW,
464 COLUMN, and TOTAL. If CELLS is not specified at all then only COUNT
467 The STATISTICS subcommand selects statistics for computation:
474 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
475 correction, linear-by-linear association.
479 Contingency coefficient.
483 Uncertainty coefficient.
499 Spearman correlation, Pearson's r.
506 Selected statistics are only calculated when appropriate for the
507 statistic. Certain statistics require tables of a particular size, and
508 some statistics are calculated only in integer mode.
510 @samp{/STATISTICS} without any settings selects CHISQ. If the
511 STATISTICS subcommand is not given, no statistics are calculated.
513 @strong{Please note:} Currently the implementation of CROSSTABS has the
518 Pearson's R (but not Spearman) is off a little.
520 T values for Spearman's R and Pearson's R are wrong.
522 Significance of symmetric and directional measures is not calculated.
524 Asymmetric ASEs and T values for lambda are wrong.
526 ASE of Goodman and Kruskal's tau is not calculated.
528 ASE of symmetric somers' d is wrong.
530 Approximate T of uncertainty coefficient is wrong.
533 Fixes for any of these deficiencies would be welcomed.
539 @cindex factor analysis
540 @cindex principal components analysis
541 @cindex principal axis factoring
542 @cindex data reduction
545 FACTOR VARIABLES=var_list
547 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
549 [ /EXTRACTION=@{PC, PAF@}]
551 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
553 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
557 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
559 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
561 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
564 The FACTOR command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
565 common factors in the data or for data reduction purposes.
567 The VARIABLES subcommand is required. It lists the variables which are to partake in the analysis.
569 The /EXTRACTION subcommand is used to specify the way in which factors (components) are extracted from the data.
570 If PC is specified, then Principal Components Analysis is used. If PAF is specified, then Principal Axis Factoring is
571 used. By default Principal Components Analysis will be used.
573 The /ROTATION subcommand is used to specify the method by which the extracted solution will be rotated.
574 Three methods are available: VARIMAX (which is the default), EQUAMAX, and QUARTIMAX.
575 If don't want any rotation to be performed, the word NOROTATE will prevent the command from performing any
576 rotation on the data. Oblique rotations are not supported.
578 The /METHOD subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
579 to be analysed. By default, the correlation matrix is analysed.
581 The /PRINT subcommand may be used to select which features of the analysis are reported:
585 A table of mean values, standard deviations and total weights are printed.
587 Initial communalities and eigenvalues are printed.
589 Extracted communalities and eigenvalues are printed.
591 Rotated communalities and eigenvalues are printed.
593 The correlation matrix is printed.
595 The covariance matrix is printed.
597 The determinant of the correlation or covariance matrix is printed.
599 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
601 The significance of the elements of correlation matrix is printed.
603 All of the above are printed.
605 Identical to INITIAL and EXTRACTION.
608 If /PLOT=EIGEN is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualising
609 which factors (components) should be retained.
611 The /FORMAT subcommand determined how data are to be displayed in loading matrices. If SORT is specified, then the variables
612 are sorted in descending order of significance. If BLANK(@var{n}) is specified, then coefficients whose absolute value is less
613 than @var{n} will not be printed. If the keyword DEFAULT is given, or if no /FORMAT subcommand is given, then no sorting is
614 performed, and all coefficients will be printed.
616 The /CRITERIA subcommand is used to specify how the number of extracted factors (components) are chosen. If FACTORS(@var{n}) is
617 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the MINEIGEN setting will
618 be used. MINEIGEN(@var{l}) requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
619 The default value of @var{l} is 1. The ECONVERGE and ITERATE settings have effect only when iterative algorithms for factor
620 extraction (such as Principal Axis Factoring) are used. ECONVERGE(@var{delta}) specifies that iteration should cease when
621 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
622 default value of @var{delta} is 0.001.
623 The ITERATE(@var{m}) setting sets the maximum number of iterations to @var{m}. The default value of @var{m} is 25.
625 The @cmd{MISSING} subcommand determines the handling of missing variables.
626 If INCLUDE is set, then user-missing values are included in the
627 calculations, but system-missing values are not.
628 If EXCLUDE is set, which is the default, user-missing
629 values are excluded as well as system-missing values.
631 If LISTWISE is set, then the entire case is excluded from analysis
632 whenever any variable specified in the @cmd{VARIABLES} subcommand
633 contains a missing value.
634 If PAIRWISE is set, then a case is considered missing only if either of the
635 values for the particular coefficient are missing.
636 The default is LISTWISE.
643 @cindex nonparametric tests
648 nonparametric test subcommands
653 [ /STATISTICS=@{DESCRIPTIVES@} ]
655 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
657 [ /METHOD=EXACT [ TIMER [(n)] ] ]
660 NPAR TESTS performs nonparametric tests.
661 Non parametric tests make very few assumptions about the distribution of the
663 One or more tests may be specified by using the corresponding subcommand.
664 If the /STATISTICS subcommand is also specified, then summary statistics are
665 produces for each variable that is the subject of any test.
667 Certain tests may take a long time to execute, if an exact figure is required.
668 Therefore, by default asymptotic approximations are used unless the
669 subcommand /METHOD=EXACT is specified.
670 Exact tests give more accurate results, but may take an unacceptably long
671 time to perform. If the TIMER keyword is used, it sets a maximum time,
672 after which the test will be abandoned, and a warning message printed.
673 The time, in minutes, should be specified in parentheses after the TIMER keyword.
674 If the TIMER keyword is given without this figure, then a default value of 5 minutes
679 * BINOMIAL:: Binomial Test
680 * CHISQUARE:: Chisquare Test
681 * COCHRAN:: Cochran Q Test
682 * FRIEDMAN:: Friedman Test
683 * KENDALL:: Kendall's W Test
684 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
685 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
686 * MANN-WHITNEY:: Mann Whitney U Test
687 * MCNEMAR:: McNemar Test
688 * MEDIAN:: Median Test
690 * SIGN:: The Sign Test
691 * WILCOXON:: Wilcoxon Signed Ranks Test
696 @subsection Binomial test
698 @cindex binomial test
701 [ /BINOMIAL[(p)]=var_list[(value1[, value2)] ] ]
704 The /BINOMIAL subcommand compares the observed distribution of a dichotomous
705 variable with that of a binomial distribution.
706 The variable @var{p} specifies the test proportion of the binomial
708 The default value of 0.5 is assumed if @var{p} is omitted.
710 If a single value appears after the variable list, then that value is
711 used as the threshold to partition the observed values. Values less
712 than or equal to the threshold value form the first category. Values
713 greater than the threshold form the second category.
715 If two values appear after the variable list, then they will be used
716 as the values which a variable must take to be in the respective
718 Cases for which a variable takes a value equal to neither of the specified
719 values, take no part in the test for that variable.
721 If no values appear, then the variable must assume dichotomous
723 If more than two distinct, non-missing values for a variable
724 under test are encountered then an error occurs.
726 If the test proportion is equal to 0.5, then a two tailed test is
727 reported. For any other test proportion, a one tailed test is
729 For one tailed tests, if the test proportion is less than
730 or equal to the observed proportion, then the significance of
731 observing the observed proportion or more is reported.
732 If the test proportion is more than the observed proportion, then the
733 significance of observing the observed proportion or less is reported.
734 That is to say, the test is always performed in the observed
737 PSPP uses a very precise approximation to the gamma function to
738 compute the binomial significance. Thus, exact results are reported
739 even for very large sample sizes.
744 @subsection Chisquare Test
746 @cindex chisquare test
750 [ /CHISQUARE=var_list[(lo,hi)] [/EXPECTED=@{EQUAL|f1, f2 @dots{} fn@}] ]
754 The /CHISQUARE subcommand produces a chi-square statistic for the differences
755 between the expected and observed frequencies of the categories of a variable.
756 Optionally, a range of values may appear after the variable list.
757 If a range is given, then non integer values are truncated, and values
758 outside the specified range are excluded from the analysis.
760 The /EXPECTED subcommand specifies the expected values of each
762 There must be exactly one non-zero expected value, for each observed
763 category, or the EQUAL keywork must be specified.
764 You may use the notation @var{n}*@var{f} to specify @var{n}
765 consecutive expected categories all taking a frequency of @var{f}.
766 The frequencies given are proportions, not absolute frequencies. The
767 sum of the frequencies need not be 1.
768 If no /EXPECTED subcommand is given, then then equal frequencies
773 @subsection Cochran Q Test
775 @cindex Cochran Q test
779 [ /COCHRAN = varlist ]
782 The Cochran Q test is used to test for differences between three or more groups.
783 The data for @var{varlist} in all cases must assume exactly two distinct values (other than missing values).
785 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
788 @subsection Friedman Test
790 @cindex Friedman test
793 [ /FRIEDMAN = varlist ]
796 The Friedman test is used to test for differences between repeated measures when there is no indication that the distributions are normally distributed.
798 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.
801 @subsection Kendall's W Test
803 @cindex Kendall's W test
804 @cindex coefficient of concordance
807 [ /KENDALL = varlist ]
810 The Kendall test investigates whether an arbitrary number of related samples come from the
812 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
813 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
814 unity indicates complete agreement.
817 @node KOLMOGOROV-SMIRNOV
818 @subsection Kolmogorov-Smirnov Test
819 @vindex KOLMOGOROV-SMIRNOV
821 @cindex Kolmogorov-Smirnov test
824 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = varlist ]
827 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
828 drawn from a particular distribution. Four distributions are supported, @i{viz:}
829 Normal, Uniform, Poisson and Exponential.
831 Ideally you should provide the parameters of the distribution against which you wish to test
832 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
833 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
835 However, if the parameters are omitted they will be imputed from the data. Imputing the
836 parameters reduces the power of the test so should be avoided if possible.
838 In the following example, two variables @var{score} and @var{age} are tested to see if
839 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
842 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
844 If the variables need to be tested against different distributions, then a seperate
845 subcommand must be used. For example the following syntax tests @var{score} against
846 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
847 is tested against a normal distribution of mean 40 and standard deviation 1.5.
850 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
851 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
854 The abbreviated subcommand K-S may be used in place of KOLMOGOROV-SMIRNOV.
857 @subsection Kruskal-Wallis Test
858 @vindex KRUSKAL-WALLIS
860 @cindex Kruskal-Wallis test
863 [ /KRUSKAL-WALLIS = varlist BY var (lower, upper) ]
866 The Kruskal-Wallis test is used to compare data from an
867 arbitrary number of populations. It does not assume normality.
868 The data to be compared are specified by @var{varlist}.
869 The categorical variable determining the groups to which the
870 data belongs is given by @var{var}. The limits @var{lower} and
871 @var{upper} specify the valid range of @var{var}. Any cases for
872 which @var{var} falls outside [@var{lower}, @var{upper}] will be
875 The mean rank of each group as well as the chi-squared value and significance
876 of the test will be printed.
877 The abbreviated subcommand K-W may be used in place of KRUSKAL-WALLIS.
881 @subsection Mann-Whitney U Test
884 @cindex Mann-Whitney U test
885 @cindex U, Mann-Whitney U
888 [ /MANN-WHITNEY = varlist BY var (group1, group2) ]
891 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
892 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}.
893 @var{Var} may be either a string or an alpha variable.
894 @var{Group1} and @var{group2} specify the
895 two values of @var{var} which determine the groups of the test data.
896 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
898 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
899 The abbreviated subcommand M-W may be used in place of MANN-WHITNEY.
902 @subsection McNemar Test
907 [ /MCNEMAR varlist [ WITH varlist [ (PAIRED) ]]]
910 Use McNemar's test to analyse the significance of the difference between
911 pairs of correlated proportions.
913 If the @code{WITH} keyword is omitted, then tests for all
914 combinations of the listed variables are performed.
915 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
916 is also given, then the number of variables preceding @code{WITH}
917 must be the same as the number following it.
918 In this case, tests for each respective pair of variables are
920 If the @code{WITH} keyword is given, but the
921 @code{(PAIRED)} keyword is omitted, then tests for each combination
922 of variable preceding @code{WITH} against variable following
923 @code{WITH} are performed.
925 The data in each variable must be dichotomous. If there are more
926 than two distinct variables an error will occur and the test will
930 @subsection Median Test
935 [ /MEDIAN [(value)] = varlist BY variable (value1, value2) ]
938 The median test is used to test whether independent samples come from
939 populations with a common median.
940 The median of the populations against which the samples are to be tested
941 may be given in parentheses immediately after the
942 /MEDIAN subcommand. If it is not given, the median will be imputed from the
943 union of all the samples.
945 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
946 keyword @code{BY} must come next, and then the grouping variable. Two values
947 in parentheses should follow. If the first value is greater than the second,
948 then a 2 sample test is performed using these two values to determine the groups.
949 If however, the first variable is less than the second, then a @i{k} sample test is
950 conducted and the group values used are all values encountered which lie in the
951 range [@var{value1},@var{value2}].
955 @subsection Runs Test
960 [ /RUNS (@{MEAN, MEDIAN, MODE, value@}) = varlist ]
963 The /RUNS subcommand tests whether a data sequence is randomly ordered.
965 It works by examining the number of times a variable's value crosses a given threshold.
966 The desired threshold must be specified within parentheses.
967 It may either be specified as a number or as one of MEAN, MEDIAN or MODE.
968 Following the threshold specification comes the list of variables whose values are to be
971 The subcommand shows the number of runs, the asymptotic significance based on the
975 @subsection Sign Test
980 [ /SIGN varlist [ WITH varlist [ (PAIRED) ]]]
983 The /SIGN subcommand tests for differences between medians of the
985 The test does not make any assumptions about the
986 distribution of the data.
988 If the @code{WITH} keyword is omitted, then tests for all
989 combinations of the listed variables are performed.
990 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
991 is also given, then the number of variables preceding @code{WITH}
992 must be the same as the number following it.
993 In this case, tests for each respective pair of variables are
995 If the @code{WITH} keyword is given, but the
996 @code{(PAIRED)} keyword is omitted, then tests for each combination
997 of variable preceding @code{WITH} against variable following
998 @code{WITH} are performed.
1001 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1002 @comment node-name, next, previous, up
1004 @cindex wilcoxon matched pairs signed ranks test
1007 [ /WILCOXON varlist [ WITH varlist [ (PAIRED) ]]]
1010 The /WILCOXON subcommand tests for differences between medians of the
1012 The test does not make any assumptions about the variances of the samples.
1013 It does however assume that the distribution is symetrical.
1015 If the @code{WITH} keyword is omitted, then tests for all
1016 combinations of the listed variables are performed.
1017 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1018 is also given, then the number of variables preceding @code{WITH}
1019 must be the same as the number following it.
1020 In this case, tests for each respective pair of variables are
1022 If the @code{WITH} keyword is given, but the
1023 @code{(PAIRED)} keyword is omitted, then tests for each combination
1024 of variable preceding @code{WITH} against variable following
1025 @code{WITH} are performed.
1028 @comment node-name, next, previous, up
1035 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1036 /CRITERIA=CIN(confidence)
1044 (Independent Samples mode.)
1045 GROUPS=var(value1 [, value2])
1049 (Paired Samples mode.)
1050 PAIRS=var_list [WITH var_list [(PAIRED)] ]
1055 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1057 It operates in one of three modes:
1059 @item One Sample mode.
1060 @item Independent Groups mode.
1065 Each of these modes are described in more detail below.
1066 There are two optional subcommands which are common to all modes.
1068 The @cmd{/CRITERIA} subcommand tells PSPP the confidence interval used
1069 in the tests. The default value is 0.95.
1072 The @cmd{MISSING} subcommand determines the handling of missing
1074 If INCLUDE is set, then user-missing values are included in the
1075 calculations, but system-missing values are not.
1076 If EXCLUDE is set, which is the default, user-missing
1077 values are excluded as well as system-missing values.
1078 This is the default.
1080 If LISTWISE is set, then the entire case is excluded from analysis
1081 whenever any variable specified in the @cmd{/VARIABLES}, @cmd{/PAIRS} or
1082 @cmd{/GROUPS} subcommands contains a missing value.
1083 If ANALYSIS is set, then missing values are excluded only in the analysis for
1084 which they would be needed. This is the default.
1088 * One Sample Mode:: Testing against a hypothesised mean
1089 * Independent Samples Mode:: Testing two independent groups for equal mean
1090 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1093 @node One Sample Mode
1094 @subsection One Sample Mode
1096 The @cmd{TESTVAL} subcommand invokes the One Sample mode.
1097 This mode is used to test a population mean against a hypothesised
1099 The value given to the @cmd{TESTVAL} subcommand is the value against
1100 which you wish to test.
1101 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
1102 tell PSPP which variables you wish to test.
1104 @node Independent Samples Mode
1105 @comment node-name, next, previous, up
1106 @subsection Independent Samples Mode
1108 The @cmd{GROUPS} subcommand invokes Independent Samples mode or
1110 This mode is used to test whether two groups of values have the
1111 same population mean.
1112 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
1113 tell PSPP the dependent variables you wish to test.
1115 The variable given in the @cmd{GROUPS} subcommand is the independent
1116 variable which determines to which group the samples belong.
1117 The values in parentheses are the specific values of the independent
1118 variable for each group.
1119 If the parentheses are omitted and no values are given, the default values
1120 of 1.0 and 2.0 are assumed.
1122 If the independent variable is numeric,
1123 it is acceptable to specify only one value inside the parentheses.
1124 If you do this, cases where the independent variable is
1125 greater than or equal to this value belong to the first group, and cases
1126 less than this value belong to the second group.
1127 When using this form of the @cmd{GROUPS} subcommand, missing values in
1128 the independent variable are excluded on a listwise basis, regardless
1129 of whether @cmd{/MISSING=LISTWISE} was specified.
1132 @node Paired Samples Mode
1133 @comment node-name, next, previous, up
1134 @subsection Paired Samples Mode
1136 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1137 Use this mode when repeated measures have been taken from the same
1139 If the @code{WITH} keyword is omitted, then tables for all
1140 combinations of variables given in the @cmd{PAIRS} subcommand are
1142 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1143 is also given, then the number of variables preceding @code{WITH}
1144 must be the same as the number following it.
1145 In this case, tables for each respective pair of variables are
1147 In the event that the @code{WITH} keyword is given, but the
1148 @code{(PAIRED)} keyword is omitted, then tables for each combination
1149 of variable preceding @code{WITH} against variable following
1150 @code{WITH} are generated.
1154 @comment node-name, next, previous, up
1158 @cindex analysis of variance
1163 [/VARIABLES = ] var_list BY var
1164 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1165 /CONTRAST= value1 [, value2] ... [,valueN]
1166 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1167 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([value])@}
1170 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1171 variables factored by a single independent variable.
1172 It is used to compare the means of a population
1173 divided into more than two groups.
1175 The dependent variables to be analysed should be given in the @code{VARIABLES}
1177 The list of variables must be followed by the @code{BY} keyword and
1178 the name of the independent (or factor) variable.
1180 You can use the @code{STATISTICS} subcommand to tell PSPP to display
1181 ancilliary information. The options accepted are:
1184 Displays descriptive statistics about the groups factored by the independent
1187 Displays the Levene test of Homogeneity of Variance for the
1188 variables and their groups.
1191 The @code{CONTRAST} subcommand is used when you anticipate certain
1192 differences between the groups.
1193 The subcommand must be followed by a list of numerals which are the
1194 coefficients of the groups to be tested.
1195 The number of coefficients must correspond to the number of distinct
1196 groups (or values of the independent variable).
1197 If the total sum of the coefficients are not zero, then PSPP will
1198 display a warning, but will proceed with the analysis.
1199 The @code{CONTRAST} subcommand may be given up to 10 times in order
1200 to specify different contrast tests.
1201 The @code{MISSING} subcommand defines how missing values are handled.
1202 If LISTWISE is specified then cases which have missing values for
1203 the independent variable or any dependent variable will be ignored.
1204 If ANALYSIS is specified, then cases will be ignored if the independent
1205 variable is missing or if the dependent variable currently being
1206 analysed is missing. The default is ANALYSIS.
1207 A setting of EXCLUDE means that variables whose values are
1208 user-missing are to be excluded from the analysis. A setting of
1209 INCLUDE means they are to be included. The default is EXCLUDE.
1211 Using the @code{POSTHOC} subcommand you can perform multiple
1212 pairwise comparisons on the data. The following comparison methods
1216 Least Significant Difference.
1218 Tukey Honestly Significant Difference.
1226 The Games-Howell test.
1230 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1231 that @var{value} should be used as the
1232 confidence level for which the posthoc tests will be performed.
1233 The default is 0.05.
1236 @comment node-name, next, previous, up
1237 @section QUICK CLUSTER
1238 @vindex QUICK CLUSTER
1240 @cindex K-means clustering
1244 QUICK CLUSTER var_list
1245 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1246 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1249 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1250 dataset. This is useful when you wish to allocate cases into clusters
1251 of similar values and you already know the number of clusters.
1253 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1254 of the variables which contain the cluster data. Normally you will also
1255 want to specify @samp{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1256 number of clusters. If this is not given, then @var{k} defaults to 2.
1258 The command uses an iterative algorithm to determine the clusters for
1259 each case. It will continue iterating until convergence, or until @var{max_iter}
1260 iterations have been done. The default value of @var{max_iter} is 2.
1262 The @cmd{MISSING} subcommand determines the handling of missing variables.
1263 If INCLUDE is set, then user-missing values are considered at their face
1264 value and not as missing values.
1265 If EXCLUDE is set, which is the default, user-missing
1266 values are excluded as well as system-missing values.
1268 If LISTWISE is set, then the entire case is excluded from the analysis
1269 whenever any of the clustering variables contains a missing value.
1270 If PAIRWISE is set, then a case is considered missing only if all the
1271 clustering variables contain missing values. Otherwise it is clustered
1272 on the basis of the non-missing values.
1273 The default is LISTWISE.
1277 @comment node-name, next, previous, up
1284 [VARIABLES=] var_list [@{A,D@}] [BY var_list]
1285 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1286 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1288 /MISSING=@{EXCLUDE,INCLUDE@}
1290 /RANK [INTO var_list]
1291 /NTILES(k) [INTO var_list]
1292 /NORMAL [INTO var_list]
1293 /PERCENT [INTO var_list]
1294 /RFRACTION [INTO var_list]
1295 /PROPORTION [INTO var_list]
1297 /SAVAGE [INTO var_list]
1300 The @cmd{RANK} command ranks variables and stores the results into new
1303 The VARIABLES subcommand, which is mandatory, specifies one or
1304 more variables whose values are to be ranked.
1305 After each variable, @samp{A} or @samp{D} may appear, indicating that
1306 the variable is to be ranked in ascending or descending order.
1307 Ascending is the default.
1308 If a BY keyword appears, it should be followed by a list of variables
1309 which are to serve as group variables.
1310 In this case, the cases are gathered into groups, and ranks calculated
1313 The TIES subcommand specifies how tied values are to be treated. The
1314 default is to take the mean value of all the tied cases.
1316 The FRACTION subcommand specifies how proportional ranks are to be
1317 calculated. This only has any effect if NORMAL or PROPORTIONAL rank
1318 functions are requested.
1320 The PRINT subcommand may be used to specify that a summary of the rank
1321 variables created should appear in the output.
1323 The function subcommands are RANK, NTILES, NORMAL, PERCENT, RFRACTION,
1324 PROPORTION and SAVAGE. Any number of function subcommands may appear.
1325 If none are given, then the default is RANK.
1326 The NTILES subcommand must take an integer specifying the number of
1327 partitions into which values should be ranked.
1328 Each subcommand may be followed by the INTO keyword and a list of
1329 variables which are the variables to be created and receive the rank
1330 scores. There may be as many variables specified as there are
1331 variables named on the VARIABLES subcommand. If fewer are specified,
1332 then the variable names are automatically created.
1334 The MISSING subcommand determines how user missing values are to be
1335 treated. A setting of EXCLUDE means that variables whose values are
1336 user-missing are to be excluded from the rank scores. A setting of
1337 INCLUDE means they are to be included. The default is EXCLUDE.
1339 @include regression.texi
1343 @section RELIABILITY
1349 /SCALE (@var{name}) = @{var_list, ALL@}
1350 /MODEL=@{ALPHA, SPLIT[(N)]@}
1351 /SUMMARY=@{TOTAL,ALL@}
1352 /MISSING=@{EXCLUDE,INCLUDE@}
1355 @cindex Cronbach's Alpha
1356 The @cmd{RELIABILTY} command performs reliablity analysis on the data.
1358 The VARIABLES subcommand is required. It determines the set of variables
1359 upon which analysis is to be performed.
1361 The SCALE subcommand determines which variables reliability is to be
1362 calculated for. If it is omitted, then analysis for all variables named
1363 in the VARIABLES subcommand will be used.
1364 Optionally, the @var{name} parameter may be specified to set a string name
1367 The MODEL subcommand determines the type of analysis. If ALPHA is specified,
1368 then Cronbach's Alpha is calculated for the scale. If the model is SPLIT,
1369 then the variables are divided into 2 subsets. An optional parameter
1370 @var{N} may be given, to specify how many variables to be in the first subset.
1371 If @var{N} is omitted, then it defaults to one half of the variables in the
1372 scale, or one half minus one if there are an odd number of variables.
1373 The default model is ALPHA.
1375 By default, any cases with user missing, or system missing values for
1377 in the VARIABLES subcommand will be omitted from analysis.
1378 The MISSING subcommand determines whether user missing values are to
1379 be included or excluded in the analysis.
1381 The SUMMARY subcommand determines the type of summary analysis to be performed.
1382 Currently there is only one type: SUMMARY=TOTAL, which displays per-item
1383 analysis tested against the totals.
1391 @cindex Receiver Operating Characterstic
1392 @cindex Area under curve
1395 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1396 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1397 /PRINT = [ SE ] [ COORDINATES ]
1398 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1399 [ TESTPOS (@{LARGE,SMALL@}) ]
1400 [ CI (@var{confidence}) ]
1401 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1402 /MISSING=@{EXCLUDE,INCLUDE@}
1406 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1407 of a dataset, and to estimate the area under the curve.
1408 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1410 The mandatory @var{var_list} is the list of predictor variables.
1411 The variable @var{state_var} is the variable whose values represent the actual states,
1412 and @var{state_value} is the value of this variable which represents the positive state.
1414 The optional subcommand PLOT is used to determine if and how the ROC curve is drawn.
1415 The keyword CURVE means that the ROC curve should be drawn, and the optional keyword REFERENCE,
1416 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1417 If the keyword NONE is given, then no ROC curve is drawn.
1418 By default, the curve is drawn with no reference line.
1420 The optional subcommand PRINT determines which additional tables should be printed.
1421 Two additional tables are available.
1422 The SE keyword says that standard error of the area under the curve should be printed as well as
1424 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1426 The COORDINATES keyword says that a table of coordinates of the ROC curve should be printed.
1428 The CRITERIA subcommand has four optional parameters:
1430 @item The TESTPOS parameter may be LARGE or SMALL.
1431 LARGE is the default, and says that larger values in the predictor variables are to be
1432 considered positive. SMALL indicates that smaller values should be considered positive.
1434 @item The CI parameter specifies the confidence interval that should be printed.
1435 It has no effect if the SE keyword in the PRINT subcommand has not been given.
1437 @item The DISTRIBUTION parameter determines the method to be used when estimating the area
1439 There are two possibilities, @i{viz}: FREE and NEGEXPO.
1440 The FREE method uses a non-parametric estimate, and the NEGEXPO method a bi-negative
1441 exponential distribution estimate.
1442 The NEGEXPO method should only be used when the number of positive actual states is
1443 equal to the number of negative actual states.
1444 The default is FREE.
1446 @item The CUTOFF parameter is for compatibility and is ignored.
1449 The MISSING subcommand determines whether user missing values are to
1450 be included or excluded in the analysis. The default behaviour is to
1452 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1453 or if the variable @var{state_var} is missing, then the entire case will be