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.
12 * CORRELATIONS:: Correlation tables.
13 * CROSSTABS:: Crosstabulation tables.
14 * FACTOR:: Factor analysis and Principal Components analysis.
15 * LOGISTIC REGRESSION:: Bivariate Logistic Regression.
16 * MEANS:: Average values and other statistics.
17 * NPAR TESTS:: Nonparametric tests.
18 * T-TEST:: Test hypotheses about means.
19 * ONEWAY:: One way analysis of variance.
20 * QUICK CLUSTER:: K-Means clustering.
21 * RANK:: Compute rank scores.
22 * REGRESSION:: Linear regression.
23 * RELIABILITY:: Reliability analysis.
24 * ROC:: Receiver Operating Characteristic.
33 /VARIABLES=@var{var_list}
34 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
35 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
37 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
38 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
39 SESKEWNESS,SEKURTOSIS@}
40 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
41 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
45 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
47 statistics requested by the user. In addition, it can optionally
50 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
51 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
53 All other subcommands are optional:
55 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
56 @subcmd{INCLUDE} is set, then user-missing values are included in the
57 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
58 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
59 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
60 the entire case is excluded whenever any value in that case has a
61 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
63 The @subcmd{FORMAT} subcommand affects the output format. Currently the
64 @subcmd{LABELS/NOLABELS} and @subcmd{NOINDEX/INDEX} settings are not used.
65 When @subcmd{SERIAL} is
66 set, both valid and missing number of cases are listed in the output;
67 when @subcmd{NOSERIAL} is set, only valid cases are listed.
69 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
70 the specified variables. The Z scores are saved to new variables.
71 Variable names are generated by trying first the original variable name
72 with Z prepended and truncated to a maximum of 8 characters, then the
73 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
74 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
75 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
76 list by enclosing them in parentheses after each variable.
77 When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
78 treating temporary transformations as permanent.
80 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
84 All of the statistics below.
88 Standard error of the mean.
91 @item @subcmd{VARIANCE}
93 @item @subcmd{KURTOSIS}
94 Kurtosis and standard error of the kurtosis.
95 @item @subcmd{SKEWNESS}
96 Skewness and standard error of the skewness.
106 Mean, standard deviation of the mean, minimum, maximum.
108 Standard error of the kurtosis.
110 Standard error of the skewness.
113 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
114 of the possible values should be self-explanatory. @subcmd{NAME} causes the
115 statistics to be sorted by name. By default, the statistics are listed
116 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
117 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
118 sort order, respectively.
126 /VARIABLES=@var{var_list}
127 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
128 @{AVALUE,DVALUE,AFREQ,DFREQ@}
129 /MISSING=@{EXCLUDE,INCLUDE@}
130 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
131 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
132 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
134 /PERCENTILES=percent@dots{}
135 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
136 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
137 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
138 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
139 /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
141 /ORDER=@{ANALYSIS,VARIABLE@}
144 (These options are not currently implemented.)
149 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
151 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
152 (including median and mode) and percentiles, and various graphical representations
153 of the frequency distribution.
155 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
156 variables to be analyzed.
158 The @subcmd{FORMAT} subcommand controls the output format. It has several
163 @subcmd{TABLE}, the default, causes a frequency table to be output for every
164 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
165 with a numeric argument causes them to be output except when there are
166 more than the specified number of values in the table.
169 Normally frequency tables are sorted in ascending order by value. This
170 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
171 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
172 respectively, by frequency count.
175 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
176 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
177 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
178 are included. System-missing values are never included in statistics,
179 but are listed in frequency tables.
181 The available @subcmd{STATISTICS} are the same as available
182 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
183 of @subcmd{MEDIAN}, the data's median
184 value, and MODE, the mode. (If there are multiple modes, the smallest
185 value is reported.) By default, the mean, standard deviation of the
186 mean, minimum, and maximum are reported for each variable.
189 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
190 The percentiles should be presented at a list of numbers between 0
192 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
193 boundaries of the data set divided into the specified number of ranges.
194 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
197 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
198 each specified numeric variable. The X axis by default ranges from
199 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
200 and @subcmd{MAXIMUM} keywords can set an explicit range.
201 @footnote{The number of
202 bins is chosen according to the Freedman-Diaconis rule:
203 @math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
204 and @math{n} is the number of samples. Note that
205 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
206 Histograms are not created for string variables.
208 Specify @subcmd{NORMAL} to superimpose a normal curve on the
212 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
213 slice represents one value, with the size of the slice proportional to
214 the value's frequency. By default, all non-missing values are given
216 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
217 displayed slices to a given range of values.
218 The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
219 piechart. This is the default.
220 If instead, @subcmd{MISSING} is specified, then a single slice
221 will be included representing all system missing and user-missing cases.
224 The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
225 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
226 categories whose counts which lie outside the specified limits.
227 The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
228 of each category, whereas the @subcmd{PERCENT} option will display relative
231 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
232 @subcmd{PIECHART} are accepted but not currently honoured.
234 The @subcmd{ORDER} subcommand is accepted but ignored.
240 @cindex Exploratory data analysis
241 @cindex normality, testing
245 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
246 [BY @var{factor1} [BY @var{subfactor1}]
247 [ @var{factor2} [BY @var{subfactor2}]]
249 [ @var{factor3} [BY @var{subfactor3}]]
251 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
252 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
254 /COMPARE=@{GROUPS,VARIABLES@}
255 /ID=@var{identity_variable}
257 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
258 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
259 [@{NOREPORT,REPORT@}]
263 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
264 In particular, it is useful for testing how closely a distribution follows a
265 normal distribution, and for finding outliers and extreme values.
267 The @subcmd{VARIABLES} subcommand is mandatory.
268 It specifies the dependent variables and optionally variables to use as
269 factors for the analysis.
270 Variables listed before the first @subcmd{BY} keyword (if any) are the
272 The dependent variables may optionally be followed by a list of
273 factors which tell @pspp{} how to break down the analysis for each
276 Following the dependent variables, factors may be specified.
277 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
278 The format for each factor is
280 @var{factorvar} [BY @var{subfactorvar}].
282 Each unique combination of the values of @var{factorvar} and
283 @var{subfactorvar} divide the dataset into @dfn{cells}.
284 Statistics will be calculated for each cell
285 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
287 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
288 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
289 non-parametrics statistics.
290 @subcmd{EXTREME} produces a table showing the extremities of each cell.
291 A number in parentheses, @var{n} determines
292 how many upper and lower extremities to show.
293 The default number is 5.
295 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
296 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
297 as well as for each cell.
298 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
299 (unless no factor variables have been given).
300 These subcommands have no effect if there have been no factor variables
306 @cindex spreadlevel plot
307 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
308 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
309 @subcmd{SPREADLEVEL}.
310 The first three can be used to visualise how closely each cell conforms to a
311 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
312 how the variance of differs between factors.
313 Boxplots will also show you the outliers and extreme values.
314 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
315 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
316 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
318 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
319 median. It takes an optional parameter @var{t}, which specifies how the data
320 should be transformed prior to plotting.
321 The given value @var{t} is a power to which the data is raised. For example, if
322 @var{t} is given as 2, then the data will be squared.
323 Zero, however is a special value. If @var{t} is 0 or
324 is omitted, then data will be transformed by taking its natural logarithm instead of
325 raising to the power of @var{t}.
327 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
328 useful there is more than one dependent variable and at least one factor.
330 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
331 each of which contain boxplots for all the cells.
332 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
333 each containing one boxplot per dependent variable.
334 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
335 @subcmd{/COMPARE=GROUPS} were given.
337 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
338 @subcmd{/STATISTICS=EXTREME} has been given.
339 If given, it should provide the name of a variable which is to be used
340 to labels extreme values and outliers.
341 Numeric or string variables are permissible.
342 If the @subcmd{ID} subcommand is not given, then the case number will be used for
345 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
346 calculation of the descriptives command. The default is 95%.
349 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
350 and which algorithm to use for calculating them. The default is to
351 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
352 @subcmd{HAVERAGE} algorithm.
354 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
355 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
356 then then statistics for the unfactored dependent variables are
357 produced in addition to the factored variables. If there are no
358 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
361 The following example will generate descriptive statistics and histograms for
362 two variables @var{score1} and @var{score2}.
363 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
364 Therefore, the descriptives and histograms will be generated for each
366 of @var{gender} @emph{and} for each distinct combination of the values
367 of @var{gender} and @var{race}.
368 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
369 @var{score1} and @var{score2} covering the whole dataset are not produced.
371 EXAMINE @var{score1} @var{score2} BY
373 @var{gender} BY @var{culture}
374 /STATISTICS = DESCRIPTIVES
379 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
381 EXAMINE @var{height} @var{weight} BY
383 /STATISTICS = EXTREME (3)
388 In this example, we look at the height and weight of a sample of individuals and
389 how they differ between male and female.
390 A table showing the 3 largest and the 3 smallest values of @var{height} and
391 @var{weight} for each gender, and for the whole dataset will be shown.
392 Boxplots will also be produced.
393 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
394 shown in the same graphic, allowing us to easily see the difference between
396 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
397 used to label the extreme values.
400 If many dependent variables are specified, or if factor variables are
402 there are many distinct values, then @cmd{EXAMINE} will produce a very
403 large quantity of output.
409 @cindex Exploratory data analysis
410 @cindex normality, testing
414 /HISTOGRAM [(NORMAL)]= @var{var}
415 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
416 /BAR = @{@var{summary-function}(@var{var1}) | @var{count-function}@} BY @var{var2} [BY @var{var3}]
417 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
418 [@{NOREPORT,REPORT@}]
422 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
423 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
424 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
428 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the data. The different
429 values of the optional third variable @var{var3} will result in different colours and/or
430 markers for the plot. The following is an example for producing a scatterplot.
434 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
437 This example will produce a scatterplot where @var{height} is plotted versus @var{weight}. Depending
438 on the value of the @var{gender} variable, the colour of the datapoint is different. With
439 this plot it is possible to analyze gender differences for @var{height} vs.@: @var{weight} relation.
443 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
445 The keyword @subcmd{NORMAL} may be specified in parentheses, to indicate that the ideal normal curve
446 should be superimposed over the histogram.
447 For an alternative method to produce histograms @pxref{EXAMINE}. The
448 following example produces a histogram plot for the variable @var{weight}.
452 /HISTOGRAM = @var{weight}.
456 The subcommand @subcmd{BAR} produces a bar chart.
457 This subcommand requires that a @var{count-function} be specified (with no arguments) or a @var{summary-function} with a variable @var{var1} in parentheses.
458 Following the summary or count function, the keyword @subcmd{BY} should be specified and then a catagorical variable, @var{var2}.
459 The values of the variable @var{var2} determine the labels of the bars to be plotted.
460 Optionally a second categorical variable @var{var3} may be specified in which case a clustered (grouped) bar chart is produced.
462 Valid count functions are
465 The weighted counts of the cases in each category.
467 The weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
469 The cumulative weighted counts of the cases in each category.
471 The cumulative weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
474 The summary function is applied to @var{var1} across all cases in each category.
475 The recognised summary functions are:
487 The following examples assume a dataset which is the results of a survey.
488 Each respondent has indicated annual income, their sex and city of residence.
489 One could create a bar chart showing how the mean income varies between of residents of different cities, thus:
491 GRAPH /BAR = MEAN(@var{income}) BY @var{city}.
494 This can be extended to also indicate how income in each city differs between the sexes.
496 GRAPH /BAR = MEAN(@var{income}) BY @var{city} BY @var{sex}.
499 One might also want to see how many respondents there are from each city. This can be achieved as follows:
501 GRAPH /BAR = COUNT BY @var{city}.
504 Bar charts can also be produced using the @ref{FREQUENCIES} and @ref{CROSSTABS} commands.
507 @section CORRELATIONS
512 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
517 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
518 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
521 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
522 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
523 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
527 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
528 for a set of variables. The significance of the coefficients are also given.
530 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
531 keyword is used, then a non-square correlation table will be produced.
532 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
533 and the variables following will be the columns of the table.
534 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
537 The @cmd{MISSING} subcommand determines the handling of missing variables.
538 If @subcmd{INCLUDE} is set, then user-missing values are included in the
539 calculations, but system-missing values are not.
540 If @subcmd{EXCLUDE} is set, which is the default, user-missing
541 values are excluded as well as system-missing values.
543 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
544 whenever any variable specified in any @cmd{/VARIABLES} subcommand
545 contains a missing value.
546 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
547 values for the particular coefficient are missing.
548 The default is @subcmd{PAIRWISE}.
550 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
551 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
552 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
553 The default is @subcmd{TWOTAIL}.
555 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
556 0.05 are highlighted.
557 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
560 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
561 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
562 estimator of the standard deviation are displayed.
563 These statistics will be displayed in a separated table, for all the variables listed
564 in any @subcmd{/VARIABLES} subcommand.
565 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
566 be displayed for each pair of variables.
567 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
575 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
576 /MISSING=@{TABLE,INCLUDE,REPORT@}
577 /WRITE=@{NONE,CELLS,ALL@}
578 /FORMAT=@{TABLES,NOTABLES@}
583 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
584 ASRESIDUAL,ALL,NONE@}
585 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
586 KAPPA,ETA,CORR,ALL,NONE@}
590 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
593 The @cmd{CROSSTABS} procedure displays crosstabulation
594 tables requested by the user. It can calculate several statistics for
595 each cell in the crosstabulation tables. In addition, a number of
596 statistics can be calculated for each table itself.
598 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
599 number of dimensions is permitted, and any number of variables per
600 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
601 times as needed. This is the only required subcommand in @dfn{general
604 Occasionally, one may want to invoke a special mode called @dfn{integer
605 mode}. Normally, in general mode, @pspp{} automatically determines
606 what values occur in the data. In integer mode, the user specifies the
607 range of values that the data assumes. To invoke this mode, specify the
608 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
609 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
610 the range are truncated to the nearest integer, then assigned to that
611 value. If values occur outside this range, they are discarded. When it
612 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
615 In general mode, numeric and string variables may be specified on
616 TABLES. In integer mode, only numeric variables are allowed.
618 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
619 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
620 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
621 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
622 integer mode, user-missing values are included in tables but marked with
623 an @samp{M} (for ``missing'') and excluded from statistical
626 Currently the @subcmd{WRITE} subcommand is ignored.
628 The @subcmd{FORMAT} subcommand controls the characteristics of the
629 crosstabulation tables to be displayed. It has a number of possible
634 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
635 @subcmd{NOTABLES} suppresses them.
638 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
639 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
643 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
644 @subcmd{DVALUE} asserts a descending sort order.
647 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
650 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
653 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
654 crosstabulation table. The possible settings are:
670 Standardized residual.
672 Adjusted standardized residual.
676 Suppress cells entirely.
679 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
680 @subcmd{COLUMN}, and @subcmd{TOTAL}.
681 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
684 The @subcmd{STATISTICS} subcommand selects statistics for computation:
691 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
692 correction, linear-by-linear association.
696 Contingency coefficient.
700 Uncertainty coefficient.
716 Spearman correlation, Pearson's r.
723 Selected statistics are only calculated when appropriate for the
724 statistic. Certain statistics require tables of a particular size, and
725 some statistics are calculated only in integer mode.
727 @samp{/STATISTICS} without any settings selects CHISQ. If the
728 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
731 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
732 variables on each table.
733 If a table has more than two variables, the counts for the third and subsequent levels
734 will be aggregated and the chart will be produces as if there were only two variables.
737 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
738 following limitations:
742 Significance of some symmetric and directional measures is not calculated.
744 Asymptotic standard error is not calculated for
745 Goodman and Kruskal's tau or symmetric Somers' d.
747 Approximate T is not calculated for symmetric uncertainty coefficient.
750 Fixes for any of these deficiencies would be welcomed.
756 @cindex factor analysis
757 @cindex principal components analysis
758 @cindex principal axis factoring
759 @cindex data reduction
762 FACTOR VARIABLES=@var{var_list}
764 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
766 [ /ANALYSIS=@var{var_list} ]
768 [ /EXTRACTION=@{PC, PAF@}]
770 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
772 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
776 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
778 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
780 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
783 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
784 common factors in the data or for data reduction purposes.
786 The @subcmd{VARIABLES} subcommand is required. It lists the variables
787 which are to partake in the analysis. (The @subcmd{ANALYSIS}
788 subcommand may optionally further limit the variables that
789 participate; it is not useful and implemented only for compatibility.)
791 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
792 If @subcmd{PC} is specified, then Principal Components Analysis is used.
793 If @subcmd{PAF} is specified, then Principal Axis Factoring is
794 used. By default Principal Components Analysis will be used.
796 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
797 Three orthogonal rotation methods are available:
798 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
799 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
800 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
801 The default value of @var{k} is 5.
802 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
803 rotation on the data.
805 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
806 to be analysed. By default, the correlation matrix is analysed.
808 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
811 @item @subcmd{UNIVARIATE}
812 A table of mean values, standard deviations and total weights are printed.
813 @item @subcmd{INITIAL}
814 Initial communalities and eigenvalues are printed.
815 @item @subcmd{EXTRACTION}
816 Extracted communalities and eigenvalues are printed.
817 @item @subcmd{ROTATION}
818 Rotated communalities and eigenvalues are printed.
819 @item @subcmd{CORRELATION}
820 The correlation matrix is printed.
821 @item @subcmd{COVARIANCE}
822 The covariance matrix is printed.
824 The determinant of the correlation or covariance matrix is printed.
826 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
828 The significance of the elements of correlation matrix is printed.
830 All of the above are printed.
831 @item @subcmd{DEFAULT}
832 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
835 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
836 which factors (components) should be retained.
838 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
839 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
840 than @var{n} will not be printed. If the keyword @subcmd{DEFAULT} is given, or if no @subcmd{/FORMAT} subcommand is given, then no sorting is
841 performed, and all coefficients will be printed.
843 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
844 If @subcmd{FACTORS(@var{n})} is
845 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
847 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
848 The default value of @var{l} is 1.
849 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
850 extraction (such as Principal Axis Factoring) are used.
851 @subcmd{ECONVERGE(@var{delta})} specifies that
852 iteration should cease when
853 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
854 default value of @var{delta} is 0.001.
855 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
856 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
858 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
859 If @subcmd{EXTRACTION} follows, it affects convergence.
860 If @subcmd{ROTATION} follows, it affects rotation.
861 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
862 The default value of @var{m} is 25.
864 The @cmd{MISSING} subcommand determines the handling of missing variables.
865 If @subcmd{INCLUDE} is set, then user-missing values are included in the
866 calculations, but system-missing values are not.
867 If @subcmd{EXCLUDE} is set, which is the default, user-missing
868 values are excluded as well as system-missing values.
870 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
871 whenever any variable specified in the @cmd{VARIABLES} subcommand
872 contains a missing value.
873 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
874 values for the particular coefficient are missing.
875 The default is @subcmd{LISTWISE}.
877 @node LOGISTIC REGRESSION
878 @section LOGISTIC REGRESSION
880 @vindex LOGISTIC REGRESSION
881 @cindex logistic regression
882 @cindex bivariate logistic regression
885 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
887 [/CATEGORICAL = @var{categorical_predictors}]
889 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
891 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
893 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
894 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
895 [CUT(@var{cut_point})]]
897 [/MISSING = @{INCLUDE|EXCLUDE@}]
900 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
901 variable in terms of one or more predictor variables.
903 The minimum command is
905 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
907 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
908 are the predictor variables whose coefficients the procedure estimates.
910 By default, a constant term is included in the model.
911 Hence, the full model is
914 = b_0 + b_1 {\bf x_1}
920 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
921 Simple variables as well as interactions between variables may be listed here.
923 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
924 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
926 An iterative Newton-Raphson procedure is used to fit the model.
927 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
928 and other parameters.
929 The value of @var{cut_point} is used in the classification table. It is the
930 threshold above which predicted values are considered to be 1. Values
931 of @var{cut_point} must lie in the range [0,1].
932 During iterations, if any one of the stopping criteria are satisfied, the procedure is
934 The stopping criteria are:
936 @item The number of iterations exceeds @var{max_iterations}.
937 The default value of @var{max_iterations} is 20.
938 @item The change in the all coefficient estimates are less than @var{min_delta}.
939 The default value of @var{min_delta} is 0.001.
940 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
941 The default value of @var{min_delta} is zero.
942 This means that this criterion is disabled.
943 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
944 In other words, the probabilities are close to zero or one.
945 The default value of @var{min_epsilon} is 0.00000001.
949 The @subcmd{PRINT} subcommand controls the display of optional statistics.
950 Currently there is one such option, @subcmd{CI}, which indicates that the
951 confidence interval of the odds ratio should be displayed as well as its value.
952 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
953 confidence level of the desired confidence interval.
955 The @subcmd{MISSING} subcommand determines the handling of missing
957 If @subcmd{INCLUDE} is set, then user-missing values are included in the
958 calculations, but system-missing values are not.
959 If @subcmd{EXCLUDE} is set, which is the default, user-missing
960 values are excluded as well as system-missing values.
972 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
974 [ /@{@var{var_list}@}
975 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
977 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
978 [VARIANCE] [KURT] [SEKURT]
979 [SKEW] [SESKEW] [FIRST] [LAST]
980 [HARMONIC] [GEOMETRIC]
985 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
988 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
989 statistics, either for the dataset as a whole or for categories of data.
991 The simplest form of the command is
995 @noindent which calculates the mean, count and standard deviation for @var{v}.
996 If you specify a grouping variable, for example
998 MEANS @var{v} BY @var{g}.
1000 @noindent then the means, counts and standard deviations for @var{v} after having
1001 been grouped by @var{g} will be calculated.
1002 Instead of the mean, count and standard deviation, you could specify the statistics
1003 in which you are interested:
1005 MEANS @var{x} @var{y} BY @var{g}
1006 /CELLS = HARMONIC SUM MIN.
1008 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
1011 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
1015 @cindex arithmetic mean
1016 The arithmetic mean.
1017 @item @subcmd{COUNT}
1018 The count of the values.
1019 @item @subcmd{STDDEV}
1020 The standard deviation.
1021 @item @subcmd{SEMEAN}
1022 The standard error of the mean.
1024 The sum of the values.
1029 @item @subcmd{RANGE}
1030 The difference between the maximum and minimum values.
1031 @item @subcmd{VARIANCE}
1033 @item @subcmd{FIRST}
1034 The first value in the category.
1036 The last value in the category.
1039 @item @subcmd{SESKEW}
1040 The standard error of the skewness.
1043 @item @subcmd{SEKURT}
1044 The standard error of the kurtosis.
1045 @item @subcmd{HARMONIC}
1046 @cindex harmonic mean
1048 @item @subcmd{GEOMETRIC}
1049 @cindex geometric mean
1053 In addition, three special keywords are recognized:
1055 @item @subcmd{DEFAULT}
1056 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
1058 All of the above statistics will be calculated.
1060 No statistics will be calculated (only a summary will be shown).
1064 More than one @dfn{table} can be specified in a single command.
1065 Each table is separated by a @samp{/}. For
1069 @var{c} @var{d} @var{e} BY @var{x}
1070 /@var{a} @var{b} BY @var{x} @var{y}
1071 /@var{f} BY @var{y} BY @var{z}.
1073 has three tables (the @samp{TABLE =} is optional).
1074 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1075 and a single categorical variable @var{x}.
1076 The second table has two dependent variables @var{a} and @var{b},
1077 and two categorical variables @var{x} and @var{y}.
1078 The third table has a single dependent variables @var{f}
1079 and a categorical variable formed by the combination of @var{y} and @var{z}.
1082 By default values are omitted from the analysis only if missing values
1083 (either system missing or user missing)
1084 for any of the variables directly involved in their calculation are
1086 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1087 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1089 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1090 in the table specification currently being processed, regardless of
1091 whether it is needed to calculate the statistic.
1093 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1094 variables or in the categorical variables should be taken at their face
1095 value, and not excluded.
1097 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1098 variables should be taken at their face value, however cases which
1099 have user missing values for the categorical variables should be omitted
1100 from the calculation.
1106 @cindex nonparametric tests
1111 nonparametric test subcommands
1116 [ /STATISTICS=@{DESCRIPTIVES@} ]
1118 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1120 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1123 @cmd{NPAR TESTS} performs nonparametric tests.
1124 Non parametric tests make very few assumptions about the distribution of the
1126 One or more tests may be specified by using the corresponding subcommand.
1127 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1128 produces for each variable that is the subject of any test.
1130 Certain tests may take a long time to execute, if an exact figure is required.
1131 Therefore, by default asymptotic approximations are used unless the
1132 subcommand @subcmd{/METHOD=EXACT} is specified.
1133 Exact tests give more accurate results, but may take an unacceptably long
1134 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1135 after which the test will be abandoned, and a warning message printed.
1136 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1137 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1142 * BINOMIAL:: Binomial Test
1143 * CHISQUARE:: Chisquare Test
1144 * COCHRAN:: Cochran Q Test
1145 * FRIEDMAN:: Friedman Test
1146 * KENDALL:: Kendall's W Test
1147 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1148 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1149 * MANN-WHITNEY:: Mann Whitney U Test
1150 * MCNEMAR:: McNemar Test
1151 * MEDIAN:: Median Test
1153 * SIGN:: The Sign Test
1154 * WILCOXON:: Wilcoxon Signed Ranks Test
1159 @subsection Binomial test
1161 @cindex binomial test
1164 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1167 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1168 variable with that of a binomial distribution.
1169 The variable @var{p} specifies the test proportion of the binomial
1171 The default value of 0.5 is assumed if @var{p} is omitted.
1173 If a single value appears after the variable list, then that value is
1174 used as the threshold to partition the observed values. Values less
1175 than or equal to the threshold value form the first category. Values
1176 greater than the threshold form the second category.
1178 If two values appear after the variable list, then they will be used
1179 as the values which a variable must take to be in the respective
1181 Cases for which a variable takes a value equal to neither of the specified
1182 values, take no part in the test for that variable.
1184 If no values appear, then the variable must assume dichotomous
1186 If more than two distinct, non-missing values for a variable
1187 under test are encountered then an error occurs.
1189 If the test proportion is equal to 0.5, then a two tailed test is
1190 reported. For any other test proportion, a one tailed test is
1192 For one tailed tests, if the test proportion is less than
1193 or equal to the observed proportion, then the significance of
1194 observing the observed proportion or more is reported.
1195 If the test proportion is more than the observed proportion, then the
1196 significance of observing the observed proportion or less is reported.
1197 That is to say, the test is always performed in the observed
1200 @pspp{} uses a very precise approximation to the gamma function to
1201 compute the binomial significance. Thus, exact results are reported
1202 even for very large sample sizes.
1207 @subsection Chisquare Test
1209 @cindex chisquare test
1213 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1217 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1218 between the expected and observed frequencies of the categories of a variable.
1219 Optionally, a range of values may appear after the variable list.
1220 If a range is given, then non integer values are truncated, and values
1221 outside the specified range are excluded from the analysis.
1223 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1225 There must be exactly one non-zero expected value, for each observed
1226 category, or the @subcmd{EQUAL} keyword must be specified.
1227 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1228 consecutive expected categories all taking a frequency of @var{f}.
1229 The frequencies given are proportions, not absolute frequencies. The
1230 sum of the frequencies need not be 1.
1231 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1236 @subsection Cochran Q Test
1238 @cindex Cochran Q test
1239 @cindex Q, Cochran Q
1242 [ /COCHRAN = @var{var_list} ]
1245 The Cochran Q test is used to test for differences between three or more groups.
1246 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1248 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1251 @subsection Friedman Test
1253 @cindex Friedman test
1256 [ /FRIEDMAN = @var{var_list} ]
1259 The Friedman test is used to test for differences between repeated measures when
1260 there is no indication that the distributions are normally distributed.
1262 A list of variables which contain the measured data must be given. The procedure
1263 prints the sum of ranks for each variable, the test statistic and its significance.
1266 @subsection Kendall's W Test
1268 @cindex Kendall's W test
1269 @cindex coefficient of concordance
1272 [ /KENDALL = @var{var_list} ]
1275 The Kendall test investigates whether an arbitrary number of related samples come from the
1277 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1278 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1279 unity indicates complete agreement.
1282 @node KOLMOGOROV-SMIRNOV
1283 @subsection Kolmogorov-Smirnov Test
1284 @vindex KOLMOGOROV-SMIRNOV
1286 @cindex Kolmogorov-Smirnov test
1289 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1292 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1293 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1294 Normal, Uniform, Poisson and Exponential.
1296 Ideally you should provide the parameters of the distribution against which you wish to test
1297 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1298 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1300 However, if the parameters are omitted they will be imputed from the data. Imputing the
1301 parameters reduces the power of the test so should be avoided if possible.
1303 In the following example, two variables @var{score} and @var{age} are tested to see if
1304 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1307 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1309 If the variables need to be tested against different distributions, then a separate
1310 subcommand must be used. For example the following syntax tests @var{score} against
1311 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1312 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1315 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1316 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1319 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1321 @node KRUSKAL-WALLIS
1322 @subsection Kruskal-Wallis Test
1323 @vindex KRUSKAL-WALLIS
1325 @cindex Kruskal-Wallis test
1328 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1331 The Kruskal-Wallis test is used to compare data from an
1332 arbitrary number of populations. It does not assume normality.
1333 The data to be compared are specified by @var{var_list}.
1334 The categorical variable determining the groups to which the
1335 data belongs is given by @var{var}. The limits @var{lower} and
1336 @var{upper} specify the valid range of @var{var}. Any cases for
1337 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1340 The mean rank of each group as well as the chi-squared value and significance
1341 of the test will be printed.
1342 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1346 @subsection Mann-Whitney U Test
1347 @vindex MANN-WHITNEY
1349 @cindex Mann-Whitney U test
1350 @cindex U, Mann-Whitney U
1353 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1356 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1357 The variables to be tested should be specified in @var{var_list} and the grouping variable, that determines to which group the test variables belong, in @var{var}.
1358 @var{Var} may be either a string or an alpha variable.
1359 @var{Group1} and @var{group2} specify the
1360 two values of @var{var} which determine the groups of the test data.
1361 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1363 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1364 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1367 @subsection McNemar Test
1369 @cindex McNemar test
1372 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1375 Use McNemar's test to analyse the significance of the difference between
1376 pairs of correlated proportions.
1378 If the @code{WITH} keyword is omitted, then tests for all
1379 combinations of the listed variables are performed.
1380 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1381 is also given, then the number of variables preceding @code{WITH}
1382 must be the same as the number following it.
1383 In this case, tests for each respective pair of variables are
1385 If the @code{WITH} keyword is given, but the
1386 @code{(PAIRED)} keyword is omitted, then tests for each combination
1387 of variable preceding @code{WITH} against variable following
1388 @code{WITH} are performed.
1390 The data in each variable must be dichotomous. If there are more
1391 than two distinct variables an error will occur and the test will
1395 @subsection Median Test
1400 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1403 The median test is used to test whether independent samples come from
1404 populations with a common median.
1405 The median of the populations against which the samples are to be tested
1406 may be given in parentheses immediately after the
1407 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1408 union of all the samples.
1410 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1411 keyword @code{BY} must come next, and then the grouping variable. Two values
1412 in parentheses should follow. If the first value is greater than the second,
1413 then a 2 sample test is performed using these two values to determine the groups.
1414 If however, the first variable is less than the second, then a @i{k} sample test is
1415 conducted and the group values used are all values encountered which lie in the
1416 range [@var{value1},@var{value2}].
1420 @subsection Runs Test
1425 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1428 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1430 It works by examining the number of times a variable's value crosses a given threshold.
1431 The desired threshold must be specified within parentheses.
1432 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1433 Following the threshold specification comes the list of variables whose values are to be
1436 The subcommand shows the number of runs, the asymptotic significance based on the
1440 @subsection Sign Test
1445 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1448 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1450 The test does not make any assumptions about the
1451 distribution of the data.
1453 If the @code{WITH} keyword is omitted, then tests for all
1454 combinations of the listed variables are performed.
1455 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1456 is also given, then the number of variables preceding @code{WITH}
1457 must be the same as the number following it.
1458 In this case, tests for each respective pair of variables are
1460 If the @code{WITH} keyword is given, but the
1461 @code{(PAIRED)} keyword is omitted, then tests for each combination
1462 of variable preceding @code{WITH} against variable following
1463 @code{WITH} are performed.
1466 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1468 @cindex wilcoxon matched pairs signed ranks test
1471 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1474 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1476 The test does not make any assumptions about the variances of the samples.
1477 It does however assume that the distribution is symmetrical.
1479 If the @subcmd{WITH} keyword is omitted, then tests for all
1480 combinations of the listed variables are performed.
1481 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1482 is also given, then the number of variables preceding @subcmd{WITH}
1483 must be the same as the number following it.
1484 In this case, tests for each respective pair of variables are
1486 If the @subcmd{WITH} keyword is given, but the
1487 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1488 of variable preceding @subcmd{WITH} against variable following
1489 @subcmd{WITH} are performed.
1498 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1499 /CRITERIA=CI(@var{confidence})
1503 TESTVAL=@var{test_value}
1504 /VARIABLES=@var{var_list}
1507 (Independent Samples mode.)
1508 GROUPS=var(@var{value1} [, @var{value2}])
1509 /VARIABLES=@var{var_list}
1512 (Paired Samples mode.)
1513 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1518 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1520 It operates in one of three modes:
1522 @item One Sample mode.
1523 @item Independent Groups mode.
1528 Each of these modes are described in more detail below.
1529 There are two optional subcommands which are common to all modes.
1531 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1532 in the tests. The default value is 0.95.
1535 The @cmd{MISSING} subcommand determines the handling of missing
1537 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1538 calculations, but system-missing values are not.
1539 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1540 values are excluded as well as system-missing values.
1541 This is the default.
1543 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1544 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1545 @subcmd{/GROUPS} subcommands contains a missing value.
1546 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1547 which they would be needed. This is the default.
1551 * One Sample Mode:: Testing against a hypothesized mean
1552 * Independent Samples Mode:: Testing two independent groups for equal mean
1553 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1556 @node One Sample Mode
1557 @subsection One Sample Mode
1559 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1560 This mode is used to test a population mean against a hypothesized
1562 The value given to the @subcmd{TESTVAL} subcommand is the value against
1563 which you wish to test.
1564 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1565 tell @pspp{} which variables you wish to test.
1567 @node Independent Samples Mode
1568 @subsection Independent Samples Mode
1570 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1572 This mode is used to test whether two groups of values have the
1573 same population mean.
1574 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1575 tell @pspp{} the dependent variables you wish to test.
1577 The variable given in the @subcmd{GROUPS} subcommand is the independent
1578 variable which determines to which group the samples belong.
1579 The values in parentheses are the specific values of the independent
1580 variable for each group.
1581 If the parentheses are omitted and no values are given, the default values
1582 of 1.0 and 2.0 are assumed.
1584 If the independent variable is numeric,
1585 it is acceptable to specify only one value inside the parentheses.
1586 If you do this, cases where the independent variable is
1587 greater than or equal to this value belong to the first group, and cases
1588 less than this value belong to the second group.
1589 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1590 the independent variable are excluded on a listwise basis, regardless
1591 of whether @subcmd{/MISSING=LISTWISE} was specified.
1594 @node Paired Samples Mode
1595 @subsection Paired Samples Mode
1597 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1598 Use this mode when repeated measures have been taken from the same
1600 If the @subcmd{WITH} keyword is omitted, then tables for all
1601 combinations of variables given in the @cmd{PAIRS} subcommand are
1603 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1604 is also given, then the number of variables preceding @subcmd{WITH}
1605 must be the same as the number following it.
1606 In this case, tables for each respective pair of variables are
1608 In the event that the @subcmd{WITH} keyword is given, but the
1609 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1610 of variable preceding @subcmd{WITH} against variable following
1611 @subcmd{WITH} are generated.
1618 @cindex analysis of variance
1623 [/VARIABLES = ] @var{var_list} BY @var{var}
1624 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1625 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1626 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1627 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1630 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1631 variables factored by a single independent variable.
1632 It is used to compare the means of a population
1633 divided into more than two groups.
1635 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1637 The list of variables must be followed by the @subcmd{BY} keyword and
1638 the name of the independent (or factor) variable.
1640 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1641 ancillary information. The options accepted are:
1644 Displays descriptive statistics about the groups factored by the independent
1647 Displays the Levene test of Homogeneity of Variance for the
1648 variables and their groups.
1651 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1652 differences between the groups.
1653 The subcommand must be followed by a list of numerals which are the
1654 coefficients of the groups to be tested.
1655 The number of coefficients must correspond to the number of distinct
1656 groups (or values of the independent variable).
1657 If the total sum of the coefficients are not zero, then @pspp{} will
1658 display a warning, but will proceed with the analysis.
1659 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1660 to specify different contrast tests.
1661 The @subcmd{MISSING} subcommand defines how missing values are handled.
1662 If @subcmd{LISTWISE} is specified then cases which have missing values for
1663 the independent variable or any dependent variable will be ignored.
1664 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1665 variable is missing or if the dependent variable currently being
1666 analysed is missing. The default is @subcmd{ANALYSIS}.
1667 A setting of @subcmd{EXCLUDE} means that variables whose values are
1668 user-missing are to be excluded from the analysis. A setting of
1669 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1671 Using the @code{POSTHOC} subcommand you can perform multiple
1672 pairwise comparisons on the data. The following comparison methods
1676 Least Significant Difference.
1677 @item @subcmd{TUKEY}
1678 Tukey Honestly Significant Difference.
1679 @item @subcmd{BONFERRONI}
1681 @item @subcmd{SCHEFFE}
1683 @item @subcmd{SIDAK}
1686 The Games-Howell test.
1690 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1691 that @var{value} should be used as the
1692 confidence level for which the posthoc tests will be performed.
1693 The default is 0.05.
1696 @section QUICK CLUSTER
1697 @vindex QUICK CLUSTER
1699 @cindex K-means clustering
1703 QUICK CLUSTER @var{var_list}
1704 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
1705 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1706 [/PRINT=@{INITIAL@} @{CLUSTERS@}]
1709 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1710 dataset. This is useful when you wish to allocate cases into clusters
1711 of similar values and you already know the number of clusters.
1713 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1714 of the variables which contain the cluster data. Normally you will also
1715 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1716 number of clusters. If this is not specified, then @var{k} defaults to 2.
1718 If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
1719 the initial clusters is used. This will provide for faster execution but
1720 less well separated initial clusters and hence possibly an inferior final
1724 @cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
1725 The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
1726 During classification, @pspp{} will continue iterating until until @var{max_iter}
1727 iterations have been done or the convergence criterion (see below) is fulfilled.
1728 The default value of @var{max_iter} is 2.
1730 If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
1731 no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
1734 The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
1735 to set the convergence criterion. The value of convergence criterion is @var{epsilon}
1736 times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
1737 the mean cluster distance between one iteration and the next
1738 is less than the convergence criterion. The default value of @var{epsilon} is zero.
1740 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1741 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1742 value and not as missing values.
1743 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1744 values are excluded as well as system-missing values.
1746 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1747 whenever any of the clustering variables contains a missing value.
1748 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1749 clustering variables contain missing values. Otherwise it is clustered
1750 on the basis of the non-missing values.
1751 The default is @subcmd{LISTWISE}.
1753 The @subcmd{PRINT} subcommand requests additional output to be printed.
1754 If @subcmd{INITIAL} is set, then the initial cluster memberships will
1756 If @subcmd{CLUSTERS} is set, the cluster memberships of the individual
1757 cases will be displayed (potentially generating lengthy output).
1766 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1767 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1768 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1770 /MISSING=@{EXCLUDE,INCLUDE@}
1772 /RANK [INTO @var{var_list}]
1773 /NTILES(k) [INTO @var{var_list}]
1774 /NORMAL [INTO @var{var_list}]
1775 /PERCENT [INTO @var{var_list}]
1776 /RFRACTION [INTO @var{var_list}]
1777 /PROPORTION [INTO @var{var_list}]
1778 /N [INTO @var{var_list}]
1779 /SAVAGE [INTO @var{var_list}]
1782 The @cmd{RANK} command ranks variables and stores the results into new
1785 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1786 more variables whose values are to be ranked.
1787 After each variable, @samp{A} or @samp{D} may appear, indicating that
1788 the variable is to be ranked in ascending or descending order.
1789 Ascending is the default.
1790 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1791 which are to serve as group variables.
1792 In this case, the cases are gathered into groups, and ranks calculated
1795 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1796 default is to take the mean value of all the tied cases.
1798 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1799 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1800 functions are requested.
1802 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1803 variables created should appear in the output.
1805 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1806 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1807 If none are given, then the default is RANK.
1808 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1809 partitions into which values should be ranked.
1810 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1811 variables which are the variables to be created and receive the rank
1812 scores. There may be as many variables specified as there are
1813 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1814 then the variable names are automatically created.
1816 The @subcmd{MISSING} subcommand determines how user missing values are to be
1817 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1818 user-missing are to be excluded from the rank scores. A setting of
1819 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1821 @include regression.texi
1825 @section RELIABILITY
1830 /VARIABLES=@var{var_list}
1831 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1832 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1833 /SUMMARY=@{TOTAL,ALL@}
1834 /MISSING=@{EXCLUDE,INCLUDE@}
1837 @cindex Cronbach's Alpha
1838 The @cmd{RELIABILITY} command performs reliability analysis on the data.
1840 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1841 upon which analysis is to be performed.
1843 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1844 calculated for. If it is omitted, then analysis for all variables named
1845 in the @subcmd{VARIABLES} subcommand will be used.
1846 Optionally, the @var{name} parameter may be specified to set a string name
1849 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1850 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1851 then the variables are divided into 2 subsets. An optional parameter
1852 @var{n} may be given, to specify how many variables to be in the first subset.
1853 If @var{n} is omitted, then it defaults to one half of the variables in the
1854 scale, or one half minus one if there are an odd number of variables.
1855 The default model is @subcmd{ALPHA}.
1857 By default, any cases with user missing, or system missing values for
1859 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1860 The @subcmd{MISSING} subcommand determines whether user missing values are to
1861 be included or excluded in the analysis.
1863 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1864 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1865 analysis tested against the totals.
1873 @cindex Receiver Operating Characteristic
1874 @cindex Area under curve
1877 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1878 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1879 /PRINT = [ SE ] [ COORDINATES ]
1880 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1881 [ TESTPOS (@{LARGE,SMALL@}) ]
1882 [ CI (@var{confidence}) ]
1883 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1884 /MISSING=@{EXCLUDE,INCLUDE@}
1888 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1889 of a dataset, and to estimate the area under the curve.
1890 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1892 The mandatory @var{var_list} is the list of predictor variables.
1893 The variable @var{state_var} is the variable whose values represent the actual states,
1894 and @var{state_value} is the value of this variable which represents the positive state.
1896 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1897 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1898 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1899 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1900 By default, the curve is drawn with no reference line.
1902 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1903 Two additional tables are available.
1904 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1906 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1908 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1910 The @subcmd{CRITERIA} subcommand has four optional parameters:
1912 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1913 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1914 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1916 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1917 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1919 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1921 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1922 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1923 exponential distribution estimate.
1924 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1925 equal to the number of negative actual states.
1926 The default is @subcmd{FREE}.
1928 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1931 The @subcmd{MISSING} subcommand determines whether user missing values are to
1932 be included or excluded in the analysis. The default behaviour is to
1934 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1935 or if the variable @var{state_var} is missing, then the entire case will be