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})]
143 (These options are not currently implemented.)
148 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
150 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
151 (including median and mode) and percentiles, and various graphical representations
152 of the frequency distribution.
154 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
155 variables to be analyzed.
157 The @subcmd{FORMAT} subcommand controls the output format. It has several
162 @subcmd{TABLE}, the default, causes a frequency table to be output for every
163 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
164 with a numeric argument causes them to be output except when there are
165 more than the specified number of values in the table.
168 Normally frequency tables are sorted in ascending order by value. This
169 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
170 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
171 respectively, by frequency count.
174 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
175 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
176 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
177 are included. System-missing values are never included in statistics,
178 but are listed in frequency tables.
180 The available @subcmd{STATISTICS} are the same as available
181 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
182 of @subcmd{MEDIAN}, the data's median
183 value, and MODE, the mode. (If there are multiple modes, the smallest
184 value is reported.) By default, the mean, standard deviation of the
185 mean, minimum, and maximum are reported for each variable.
188 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
189 The percentiles should be presented at a list of numbers between 0
191 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
192 boundaries of the data set divided into the specified number of ranges.
193 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
196 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
197 each specified numeric variable. The X axis by default ranges from
198 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
199 and @subcmd{MAXIMUM} keywords can set an explicit range.
200 @footnote{The number of
201 bins is chosen according to the Freedman-Diaconis rule:
202 @math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
203 and @math{n} is the number of samples. Note that
204 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
205 Histograms are not created for string variables.
207 Specify @subcmd{NORMAL} to superimpose a normal curve on the
211 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
212 slice represents one value, with the size of the slice proportional to
213 the value's frequency. By default, all non-missing values are given
215 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
216 displayed slices to a given range of values.
217 The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
218 piechart. This is the default.
219 If instead, @subcmd{MISSING} is specified, then a single slice
220 will be included representing all system missing and user-missing cases.
223 The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
224 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
225 categories whose counts which lie outside the specified limits.
226 The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
227 of each category, whereas the @subcmd{PERCENT} option will display relative
230 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
231 @subcmd{PIECHART} are accepted but not currently honoured.
237 @cindex Exploratory data analysis
238 @cindex normality, testing
242 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
243 [BY @var{factor1} [BY @var{subfactor1}]
244 [ @var{factor2} [BY @var{subfactor2}]]
246 [ @var{factor3} [BY @var{subfactor3}]]
248 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
249 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
251 /COMPARE=@{GROUPS,VARIABLES@}
252 /ID=@var{identity_variable}
254 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
255 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
256 [@{NOREPORT,REPORT@}]
260 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
261 In particular, it is useful for testing how closely a distribution follows a
262 normal distribution, and for finding outliers and extreme values.
264 The @subcmd{VARIABLES} subcommand is mandatory.
265 It specifies the dependent variables and optionally variables to use as
266 factors for the analysis.
267 Variables listed before the first @subcmd{BY} keyword (if any) are the
269 The dependent variables may optionally be followed by a list of
270 factors which tell @pspp{} how to break down the analysis for each
273 Following the dependent variables, factors may be specified.
274 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
275 The format for each factor is
277 @var{factorvar} [BY @var{subfactorvar}].
279 Each unique combination of the values of @var{factorvar} and
280 @var{subfactorvar} divide the dataset into @dfn{cells}.
281 Statistics will be calculated for each cell
282 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
284 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
285 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
286 non-parametrics statistics.
287 @subcmd{EXTREME} produces a table showing the extremities of each cell.
288 A number in parentheses, @var{n} determines
289 how many upper and lower extremities to show.
290 The default number is 5.
292 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
293 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
294 as well as for each cell.
295 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
296 (unless no factor variables have been given).
297 These subcommands have no effect if there have been no factor variables
303 @cindex spreadlevel plot
304 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
305 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
306 @subcmd{SPREADLEVEL}.
307 The first three can be used to visualise how closely each cell conforms to a
308 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
309 how the variance of differs between factors.
310 Boxplots will also show you the outliers and extreme values.
311 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
312 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
313 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
315 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
316 median. It takes an optional parameter @var{t}, which specifies how the data
317 should be transformed prior to plotting.
318 The given value @var{t} is a power to which the data is raised. For example, if
319 @var{t} is given as 2, then the data will be squared.
320 Zero, however is a special value. If @var{t} is 0 or
321 is omitted, then data will be transformed by taking its natural logarithm instead of
322 raising to the power of @var{t}.
324 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
325 useful there is more than one dependent variable and at least one factor.
327 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
328 each of which contain boxplots for all the cells.
329 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
330 each containing one boxplot per dependent variable.
331 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
332 @subcmd{/COMPARE=GROUPS} were given.
334 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
335 @subcmd{/STATISTICS=EXTREME} has been given.
336 If given, it should provide the name of a variable which is to be used
337 to labels extreme values and outliers.
338 Numeric or string variables are permissible.
339 If the @subcmd{ID} subcommand is not given, then the case number will be used for
342 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
343 calculation of the descriptives command. The default is 95%.
346 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
347 and which algorithm to use for calculating them. The default is to
348 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
349 @subcmd{HAVERAGE} algorithm.
351 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
352 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
353 then then statistics for the unfactored dependent variables are
354 produced in addition to the factored variables. If there are no
355 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
358 The following example will generate descriptive statistics and histograms for
359 two variables @var{score1} and @var{score2}.
360 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
361 Therefore, the descriptives and histograms will be generated for each
363 of @var{gender} @emph{and} for each distinct combination of the values
364 of @var{gender} and @var{race}.
365 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
366 @var{score1} and @var{score2} covering the whole dataset are not produced.
368 EXAMINE @var{score1} @var{score2} BY
370 @var{gender} BY @var{culture}
371 /STATISTICS = DESCRIPTIVES
376 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
378 EXAMINE @var{height} @var{weight} BY
380 /STATISTICS = EXTREME (3)
385 In this example, we look at the height and weight of a sample of individuals and
386 how they differ between male and female.
387 A table showing the 3 largest and the 3 smallest values of @var{height} and
388 @var{weight} for each gender, and for the whole dataset will be shown.
389 Boxplots will also be produced.
390 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
391 shown in the same graphic, allowing us to easily see the difference between
393 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
394 used to label the extreme values.
397 If many dependent variables are specified, or if factor variables are
399 there are many distinct values, then @cmd{EXAMINE} will produce a very
400 large quantity of output.
406 @cindex Exploratory data analysis
407 @cindex normality, testing
411 /HISTOGRAM = @var{var}
412 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
413 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
414 [@{NOREPORT,REPORT@}]
418 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
419 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
420 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
424 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the data. The different
425 values of the optional third variable @var{var3} will result in different colours and/or
426 markers for the plot. The following is an example for producing a scatterplot.
430 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
433 This example will produce a scatterplot where @var{height} is plotted versus @var{weight}. Depending
434 on the value of the @var{gender} variable, the colour of the datapoint is different. With
435 this plot it is possible to analyze gender differences for @var{height} vs.@: @var{weight} relation.
439 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
441 For an alternative method to produce histograms @pxref{EXAMINE}. The
442 following example produces a histogram plot for the variable @var{weight}.
446 /HISTOGRAM = @var{weight}.
450 @section CORRELATIONS
455 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
460 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
461 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
464 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
465 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
466 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
470 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
471 for a set of variables. The significance of the coefficients are also given.
473 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
474 keyword is used, then a non-square correlation table will be produced.
475 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
476 and the variables following will be the columns of the table.
477 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
480 The @cmd{MISSING} subcommand determines the handling of missing variables.
481 If @subcmd{INCLUDE} is set, then user-missing values are included in the
482 calculations, but system-missing values are not.
483 If @subcmd{EXCLUDE} is set, which is the default, user-missing
484 values are excluded as well as system-missing values.
486 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
487 whenever any variable specified in any @cmd{/VARIABLES} subcommand
488 contains a missing value.
489 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
490 values for the particular coefficient are missing.
491 The default is @subcmd{PAIRWISE}.
493 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
494 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
495 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
496 The default is @subcmd{TWOTAIL}.
498 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
499 0.05 are highlighted.
500 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
503 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
504 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
505 estimator of the standard deviation are displayed.
506 These statistics will be displayed in a separated table, for all the variables listed
507 in any @subcmd{/VARIABLES} subcommand.
508 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
509 be displayed for each pair of variables.
510 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
518 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
519 /MISSING=@{TABLE,INCLUDE,REPORT@}
520 /WRITE=@{NONE,CELLS,ALL@}
521 /FORMAT=@{TABLES,NOTABLES@}
526 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
527 ASRESIDUAL,ALL,NONE@}
528 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
529 KAPPA,ETA,CORR,ALL,NONE@}
533 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
536 The @cmd{CROSSTABS} procedure displays crosstabulation
537 tables requested by the user. It can calculate several statistics for
538 each cell in the crosstabulation tables. In addition, a number of
539 statistics can be calculated for each table itself.
541 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
542 number of dimensions is permitted, and any number of variables per
543 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
544 times as needed. This is the only required subcommand in @dfn{general
547 Occasionally, one may want to invoke a special mode called @dfn{integer
548 mode}. Normally, in general mode, @pspp{} automatically determines
549 what values occur in the data. In integer mode, the user specifies the
550 range of values that the data assumes. To invoke this mode, specify the
551 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
552 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
553 the range are truncated to the nearest integer, then assigned to that
554 value. If values occur outside this range, they are discarded. When it
555 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
558 In general mode, numeric and string variables may be specified on
559 TABLES. In integer mode, only numeric variables are allowed.
561 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
562 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
563 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
564 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
565 integer mode, user-missing values are included in tables but marked with
566 an @samp{M} (for ``missing'') and excluded from statistical
569 Currently the @subcmd{WRITE} subcommand is ignored.
571 The @subcmd{FORMAT} subcommand controls the characteristics of the
572 crosstabulation tables to be displayed. It has a number of possible
577 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
578 @subcmd{NOTABLES} suppresses them.
581 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
582 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
586 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
587 @subcmd{DVALUE} asserts a descending sort order.
590 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
593 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
596 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
597 crosstabulation table. The possible settings are:
613 Standardized residual.
615 Adjusted standardized residual.
619 Suppress cells entirely.
622 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
623 @subcmd{COLUMN}, and @subcmd{TOTAL}.
624 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
627 The @subcmd{STATISTICS} subcommand selects statistics for computation:
634 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
635 correction, linear-by-linear association.
639 Contingency coefficient.
643 Uncertainty coefficient.
659 Spearman correlation, Pearson's r.
666 Selected statistics are only calculated when appropriate for the
667 statistic. Certain statistics require tables of a particular size, and
668 some statistics are calculated only in integer mode.
670 @samp{/STATISTICS} without any settings selects CHISQ. If the
671 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
674 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
675 variables on each table.
676 If a table has more than two variables, the counts for the third and subsequent levels
677 will be aggregated and the chart will be produces as if there were only two variables.
680 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
681 following limitations:
685 Significance of some symmetric and directional measures is not calculated.
687 Asymptotic standard error is not calculated for
688 Goodman and Kruskal's tau or symmetric Somers' d.
690 Approximate T is not calculated for symmetric uncertainty coefficient.
693 Fixes for any of these deficiencies would be welcomed.
699 @cindex factor analysis
700 @cindex principal components analysis
701 @cindex principal axis factoring
702 @cindex data reduction
705 FACTOR VARIABLES=@var{var_list}
707 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
709 [ /EXTRACTION=@{PC, PAF@}]
711 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
713 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
717 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
719 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
721 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
724 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
725 common factors in the data or for data reduction purposes.
727 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
729 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
730 If @subcmd{PC} is specified, then Principal Components Analysis is used.
731 If @subcmd{PAF} is specified, then Principal Axis Factoring is
732 used. By default Principal Components Analysis will be used.
734 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
735 Three orthogonal rotation methods are available:
736 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
737 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
738 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
739 The default value of @var{k} is 5.
740 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
741 rotation on the data.
743 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
744 to be analysed. By default, the correlation matrix is analysed.
746 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
749 @item @subcmd{UNIVARIATE}
750 A table of mean values, standard deviations and total weights are printed.
751 @item @subcmd{INITIAL}
752 Initial communalities and eigenvalues are printed.
753 @item @subcmd{EXTRACTION}
754 Extracted communalities and eigenvalues are printed.
755 @item @subcmd{ROTATION}
756 Rotated communalities and eigenvalues are printed.
757 @item @subcmd{CORRELATION}
758 The correlation matrix is printed.
759 @item @subcmd{COVARIANCE}
760 The covariance matrix is printed.
762 The determinant of the correlation or covariance matrix is printed.
764 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
766 The significance of the elements of correlation matrix is printed.
768 All of the above are printed.
769 @item @subcmd{DEFAULT}
770 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
773 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
774 which factors (components) should be retained.
776 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
777 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
778 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
779 performed, and all coefficients will be printed.
781 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
782 If @subcmd{FACTORS(@var{n})} is
783 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
785 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
786 The default value of @var{l} is 1.
787 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
788 extraction (such as Principal Axis Factoring) are used.
789 @subcmd{ECONVERGE(@var{delta})} specifies that
790 iteration should cease when
791 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
792 default value of @var{delta} is 0.001.
793 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
794 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
796 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
797 If @subcmd{EXTRACTION} follows, it affects convergence.
798 If @subcmd{ROTATION} follows, it affects rotation.
799 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
800 The default value of @var{m} is 25.
802 The @cmd{MISSING} subcommand determines the handling of missing variables.
803 If @subcmd{INCLUDE} is set, then user-missing values are included in the
804 calculations, but system-missing values are not.
805 If @subcmd{EXCLUDE} is set, which is the default, user-missing
806 values are excluded as well as system-missing values.
808 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
809 whenever any variable specified in the @cmd{VARIABLES} subcommand
810 contains a missing value.
811 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
812 values for the particular coefficient are missing.
813 The default is @subcmd{LISTWISE}.
815 @node LOGISTIC REGRESSION
816 @section LOGISTIC REGRESSION
818 @vindex LOGISTIC REGRESSION
819 @cindex logistic regression
820 @cindex bivariate logistic regression
823 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
825 [/CATEGORICAL = @var{categorical_predictors}]
827 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
829 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
831 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
832 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
833 [CUT(@var{cut_point})]]
835 [/MISSING = @{INCLUDE|EXCLUDE@}]
838 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
839 variable in terms of one or more predictor variables.
841 The minimum command is
843 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
845 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
846 are the predictor variables whose coefficients the procedure estimates.
848 By default, a constant term is included in the model.
849 Hence, the full model is
852 = b_0 + b_1 {\bf x_1}
858 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
859 Simple variables as well as interactions between variables may be listed here.
861 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
862 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
864 An iterative Newton-Raphson procedure is used to fit the model.
865 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
866 and other parameters.
867 The value of @var{cut_point} is used in the classification table. It is the
868 threshold above which predicted values are considered to be 1. Values
869 of @var{cut_point} must lie in the range [0,1].
870 During iterations, if any one of the stopping criteria are satisfied, the procedure is
872 The stopping criteria are:
874 @item The number of iterations exceeds @var{max_iterations}.
875 The default value of @var{max_iterations} is 20.
876 @item The change in the all coefficient estimates are less than @var{min_delta}.
877 The default value of @var{min_delta} is 0.001.
878 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
879 The default value of @var{min_delta} is zero.
880 This means that this criterion is disabled.
881 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
882 In other words, the probabilities are close to zero or one.
883 The default value of @var{min_epsilon} is 0.00000001.
887 The @subcmd{PRINT} subcommand controls the display of optional statistics.
888 Currently there is one such option, @subcmd{CI}, which indicates that the
889 confidence interval of the odds ratio should be displayed as well as its value.
890 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
891 confidence level of the desired confidence interval.
893 The @subcmd{MISSING} subcommand determines the handling of missing
895 If @subcmd{INCLUDE} is set, then user-missing values are included in the
896 calculations, but system-missing values are not.
897 If @subcmd{EXCLUDE} is set, which is the default, user-missing
898 values are excluded as well as system-missing values.
910 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
912 [ /@{@var{var_list}@}
913 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
915 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
916 [VARIANCE] [KURT] [SEKURT]
917 [SKEW] [SESKEW] [FIRST] [LAST]
918 [HARMONIC] [GEOMETRIC]
923 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
926 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
927 statistics, either for the dataset as a whole or for categories of data.
929 The simplest form of the command is
933 @noindent which calculates the mean, count and standard deviation for @var{v}.
934 If you specify a grouping variable, for example
936 MEANS @var{v} BY @var{g}.
938 @noindent then the means, counts and standard deviations for @var{v} after having
939 been grouped by @var{g} will be calculated.
940 Instead of the mean, count and standard deviation, you could specify the statistics
941 in which you are interested:
943 MEANS @var{x} @var{y} BY @var{g}
944 /CELLS = HARMONIC SUM MIN.
946 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
949 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
953 @cindex arithmetic mean
956 The count of the values.
957 @item @subcmd{STDDEV}
958 The standard deviation.
959 @item @subcmd{SEMEAN}
960 The standard error of the mean.
962 The sum of the values.
968 The difference between the maximum and minimum values.
969 @item @subcmd{VARIANCE}
972 The first value in the category.
974 The last value in the category.
977 @item @subcmd{SESKEW}
978 The standard error of the skewness.
981 @item @subcmd{SEKURT}
982 The standard error of the kurtosis.
983 @item @subcmd{HARMONIC}
984 @cindex harmonic mean
986 @item @subcmd{GEOMETRIC}
987 @cindex geometric mean
991 In addition, three special keywords are recognized:
993 @item @subcmd{DEFAULT}
994 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
996 All of the above statistics will be calculated.
998 No statistics will be calculated (only a summary will be shown).
1002 More than one @dfn{table} can be specified in a single command.
1003 Each table is separated by a @samp{/}. For
1007 @var{c} @var{d} @var{e} BY @var{x}
1008 /@var{a} @var{b} BY @var{x} @var{y}
1009 /@var{f} BY @var{y} BY @var{z}.
1011 has three tables (the @samp{TABLE =} is optional).
1012 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1013 and a single categorical variable @var{x}.
1014 The second table has two dependent variables @var{a} and @var{b},
1015 and two categorical variables @var{x} and @var{y}.
1016 The third table has a single dependent variables @var{f}
1017 and a categorical variable formed by the combination of @var{y} and @var{z}.
1020 By default values are omitted from the analysis only if missing values
1021 (either system missing or user missing)
1022 for any of the variables directly involved in their calculation are
1024 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1025 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1027 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1028 in the table specification currently being processed, regardless of
1029 whether it is needed to calculate the statistic.
1031 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1032 variables or in the categorical variables should be taken at their face
1033 value, and not excluded.
1035 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1036 variables should be taken at their face value, however cases which
1037 have user missing values for the categorical variables should be omitted
1038 from the calculation.
1044 @cindex nonparametric tests
1049 nonparametric test subcommands
1054 [ /STATISTICS=@{DESCRIPTIVES@} ]
1056 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1058 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1061 @cmd{NPAR TESTS} performs nonparametric tests.
1062 Non parametric tests make very few assumptions about the distribution of the
1064 One or more tests may be specified by using the corresponding subcommand.
1065 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1066 produces for each variable that is the subject of any test.
1068 Certain tests may take a long time to execute, if an exact figure is required.
1069 Therefore, by default asymptotic approximations are used unless the
1070 subcommand @subcmd{/METHOD=EXACT} is specified.
1071 Exact tests give more accurate results, but may take an unacceptably long
1072 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1073 after which the test will be abandoned, and a warning message printed.
1074 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1075 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1080 * BINOMIAL:: Binomial Test
1081 * CHISQUARE:: Chisquare Test
1082 * COCHRAN:: Cochran Q Test
1083 * FRIEDMAN:: Friedman Test
1084 * KENDALL:: Kendall's W Test
1085 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1086 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1087 * MANN-WHITNEY:: Mann Whitney U Test
1088 * MCNEMAR:: McNemar Test
1089 * MEDIAN:: Median Test
1091 * SIGN:: The Sign Test
1092 * WILCOXON:: Wilcoxon Signed Ranks Test
1097 @subsection Binomial test
1099 @cindex binomial test
1102 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1105 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1106 variable with that of a binomial distribution.
1107 The variable @var{p} specifies the test proportion of the binomial
1109 The default value of 0.5 is assumed if @var{p} is omitted.
1111 If a single value appears after the variable list, then that value is
1112 used as the threshold to partition the observed values. Values less
1113 than or equal to the threshold value form the first category. Values
1114 greater than the threshold form the second category.
1116 If two values appear after the variable list, then they will be used
1117 as the values which a variable must take to be in the respective
1119 Cases for which a variable takes a value equal to neither of the specified
1120 values, take no part in the test for that variable.
1122 If no values appear, then the variable must assume dichotomous
1124 If more than two distinct, non-missing values for a variable
1125 under test are encountered then an error occurs.
1127 If the test proportion is equal to 0.5, then a two tailed test is
1128 reported. For any other test proportion, a one tailed test is
1130 For one tailed tests, if the test proportion is less than
1131 or equal to the observed proportion, then the significance of
1132 observing the observed proportion or more is reported.
1133 If the test proportion is more than the observed proportion, then the
1134 significance of observing the observed proportion or less is reported.
1135 That is to say, the test is always performed in the observed
1138 @pspp{} uses a very precise approximation to the gamma function to
1139 compute the binomial significance. Thus, exact results are reported
1140 even for very large sample sizes.
1145 @subsection Chisquare Test
1147 @cindex chisquare test
1151 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1155 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1156 between the expected and observed frequencies of the categories of a variable.
1157 Optionally, a range of values may appear after the variable list.
1158 If a range is given, then non integer values are truncated, and values
1159 outside the specified range are excluded from the analysis.
1161 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1163 There must be exactly one non-zero expected value, for each observed
1164 category, or the @subcmd{EQUAL} keyword must be specified.
1165 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1166 consecutive expected categories all taking a frequency of @var{f}.
1167 The frequencies given are proportions, not absolute frequencies. The
1168 sum of the frequencies need not be 1.
1169 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1174 @subsection Cochran Q Test
1176 @cindex Cochran Q test
1177 @cindex Q, Cochran Q
1180 [ /COCHRAN = @var{var_list} ]
1183 The Cochran Q test is used to test for differences between three or more groups.
1184 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1186 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1189 @subsection Friedman Test
1191 @cindex Friedman test
1194 [ /FRIEDMAN = @var{var_list} ]
1197 The Friedman test is used to test for differences between repeated measures when
1198 there is no indication that the distributions are normally distributed.
1200 A list of variables which contain the measured data must be given. The procedure
1201 prints the sum of ranks for each variable, the test statistic and its significance.
1204 @subsection Kendall's W Test
1206 @cindex Kendall's W test
1207 @cindex coefficient of concordance
1210 [ /KENDALL = @var{var_list} ]
1213 The Kendall test investigates whether an arbitrary number of related samples come from the
1215 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1216 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1217 unity indicates complete agreement.
1220 @node KOLMOGOROV-SMIRNOV
1221 @subsection Kolmogorov-Smirnov Test
1222 @vindex KOLMOGOROV-SMIRNOV
1224 @cindex Kolmogorov-Smirnov test
1227 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1230 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1231 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1232 Normal, Uniform, Poisson and Exponential.
1234 Ideally you should provide the parameters of the distribution against which you wish to test
1235 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1236 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1238 However, if the parameters are omitted they will be imputed from the data. Imputing the
1239 parameters reduces the power of the test so should be avoided if possible.
1241 In the following example, two variables @var{score} and @var{age} are tested to see if
1242 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1245 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1247 If the variables need to be tested against different distributions, then a separate
1248 subcommand must be used. For example the following syntax tests @var{score} against
1249 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1250 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1253 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1254 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1257 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1259 @node KRUSKAL-WALLIS
1260 @subsection Kruskal-Wallis Test
1261 @vindex KRUSKAL-WALLIS
1263 @cindex Kruskal-Wallis test
1266 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1269 The Kruskal-Wallis test is used to compare data from an
1270 arbitrary number of populations. It does not assume normality.
1271 The data to be compared are specified by @var{var_list}.
1272 The categorical variable determining the groups to which the
1273 data belongs is given by @var{var}. The limits @var{lower} and
1274 @var{upper} specify the valid range of @var{var}. Any cases for
1275 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1278 The mean rank of each group as well as the chi-squared value and significance
1279 of the test will be printed.
1280 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1284 @subsection Mann-Whitney U Test
1285 @vindex MANN-WHITNEY
1287 @cindex Mann-Whitney U test
1288 @cindex U, Mann-Whitney U
1291 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1294 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1295 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}.
1296 @var{Var} may be either a string or an alpha variable.
1297 @var{Group1} and @var{group2} specify the
1298 two values of @var{var} which determine the groups of the test data.
1299 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1301 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1302 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1305 @subsection McNemar Test
1307 @cindex McNemar test
1310 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1313 Use McNemar's test to analyse the significance of the difference between
1314 pairs of correlated proportions.
1316 If the @code{WITH} keyword is omitted, then tests for all
1317 combinations of the listed variables are performed.
1318 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1319 is also given, then the number of variables preceding @code{WITH}
1320 must be the same as the number following it.
1321 In this case, tests for each respective pair of variables are
1323 If the @code{WITH} keyword is given, but the
1324 @code{(PAIRED)} keyword is omitted, then tests for each combination
1325 of variable preceding @code{WITH} against variable following
1326 @code{WITH} are performed.
1328 The data in each variable must be dichotomous. If there are more
1329 than two distinct variables an error will occur and the test will
1333 @subsection Median Test
1338 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1341 The median test is used to test whether independent samples come from
1342 populations with a common median.
1343 The median of the populations against which the samples are to be tested
1344 may be given in parentheses immediately after the
1345 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1346 union of all the samples.
1348 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1349 keyword @code{BY} must come next, and then the grouping variable. Two values
1350 in parentheses should follow. If the first value is greater than the second,
1351 then a 2 sample test is performed using these two values to determine the groups.
1352 If however, the first variable is less than the second, then a @i{k} sample test is
1353 conducted and the group values used are all values encountered which lie in the
1354 range [@var{value1},@var{value2}].
1358 @subsection Runs Test
1363 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1366 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1368 It works by examining the number of times a variable's value crosses a given threshold.
1369 The desired threshold must be specified within parentheses.
1370 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1371 Following the threshold specification comes the list of variables whose values are to be
1374 The subcommand shows the number of runs, the asymptotic significance based on the
1378 @subsection Sign Test
1383 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1386 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1388 The test does not make any assumptions about the
1389 distribution of the data.
1391 If the @code{WITH} keyword is omitted, then tests for all
1392 combinations of the listed variables are performed.
1393 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1394 is also given, then the number of variables preceding @code{WITH}
1395 must be the same as the number following it.
1396 In this case, tests for each respective pair of variables are
1398 If the @code{WITH} keyword is given, but the
1399 @code{(PAIRED)} keyword is omitted, then tests for each combination
1400 of variable preceding @code{WITH} against variable following
1401 @code{WITH} are performed.
1404 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1406 @cindex wilcoxon matched pairs signed ranks test
1409 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1412 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1414 The test does not make any assumptions about the variances of the samples.
1415 It does however assume that the distribution is symmetrical.
1417 If the @subcmd{WITH} keyword is omitted, then tests for all
1418 combinations of the listed variables are performed.
1419 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1420 is also given, then the number of variables preceding @subcmd{WITH}
1421 must be the same as the number following it.
1422 In this case, tests for each respective pair of variables are
1424 If the @subcmd{WITH} keyword is given, but the
1425 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1426 of variable preceding @subcmd{WITH} against variable following
1427 @subcmd{WITH} are performed.
1436 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1437 /CRITERIA=CIN(@var{confidence})
1441 TESTVAL=@var{test_value}
1442 /VARIABLES=@var{var_list}
1445 (Independent Samples mode.)
1446 GROUPS=var(@var{value1} [, @var{value2}])
1447 /VARIABLES=@var{var_list}
1450 (Paired Samples mode.)
1451 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1456 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1458 It operates in one of three modes:
1460 @item One Sample mode.
1461 @item Independent Groups mode.
1466 Each of these modes are described in more detail below.
1467 There are two optional subcommands which are common to all modes.
1469 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1470 in the tests. The default value is 0.95.
1473 The @cmd{MISSING} subcommand determines the handling of missing
1475 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1476 calculations, but system-missing values are not.
1477 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1478 values are excluded as well as system-missing values.
1479 This is the default.
1481 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1482 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1483 @subcmd{/GROUPS} subcommands contains a missing value.
1484 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1485 which they would be needed. This is the default.
1489 * One Sample Mode:: Testing against a hypothesized mean
1490 * Independent Samples Mode:: Testing two independent groups for equal mean
1491 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1494 @node One Sample Mode
1495 @subsection One Sample Mode
1497 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1498 This mode is used to test a population mean against a hypothesized
1500 The value given to the @subcmd{TESTVAL} subcommand is the value against
1501 which you wish to test.
1502 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1503 tell @pspp{} which variables you wish to test.
1505 @node Independent Samples Mode
1506 @subsection Independent Samples Mode
1508 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1510 This mode is used to test whether two groups of values have the
1511 same population mean.
1512 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1513 tell @pspp{} the dependent variables you wish to test.
1515 The variable given in the @subcmd{GROUPS} subcommand is the independent
1516 variable which determines to which group the samples belong.
1517 The values in parentheses are the specific values of the independent
1518 variable for each group.
1519 If the parentheses are omitted and no values are given, the default values
1520 of 1.0 and 2.0 are assumed.
1522 If the independent variable is numeric,
1523 it is acceptable to specify only one value inside the parentheses.
1524 If you do this, cases where the independent variable is
1525 greater than or equal to this value belong to the first group, and cases
1526 less than this value belong to the second group.
1527 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1528 the independent variable are excluded on a listwise basis, regardless
1529 of whether @subcmd{/MISSING=LISTWISE} was specified.
1532 @node Paired Samples Mode
1533 @subsection Paired Samples Mode
1535 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1536 Use this mode when repeated measures have been taken from the same
1538 If the @subcmd{WITH} keyword is omitted, then tables for all
1539 combinations of variables given in the @cmd{PAIRS} subcommand are
1541 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1542 is also given, then the number of variables preceding @subcmd{WITH}
1543 must be the same as the number following it.
1544 In this case, tables for each respective pair of variables are
1546 In the event that the @subcmd{WITH} keyword is given, but the
1547 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1548 of variable preceding @subcmd{WITH} against variable following
1549 @subcmd{WITH} are generated.
1556 @cindex analysis of variance
1561 [/VARIABLES = ] @var{var_list} BY @var{var}
1562 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1563 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1564 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1565 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1568 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1569 variables factored by a single independent variable.
1570 It is used to compare the means of a population
1571 divided into more than two groups.
1573 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1575 The list of variables must be followed by the @subcmd{BY} keyword and
1576 the name of the independent (or factor) variable.
1578 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1579 ancillary information. The options accepted are:
1582 Displays descriptive statistics about the groups factored by the independent
1585 Displays the Levene test of Homogeneity of Variance for the
1586 variables and their groups.
1589 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1590 differences between the groups.
1591 The subcommand must be followed by a list of numerals which are the
1592 coefficients of the groups to be tested.
1593 The number of coefficients must correspond to the number of distinct
1594 groups (or values of the independent variable).
1595 If the total sum of the coefficients are not zero, then @pspp{} will
1596 display a warning, but will proceed with the analysis.
1597 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1598 to specify different contrast tests.
1599 The @subcmd{MISSING} subcommand defines how missing values are handled.
1600 If @subcmd{LISTWISE} is specified then cases which have missing values for
1601 the independent variable or any dependent variable will be ignored.
1602 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1603 variable is missing or if the dependent variable currently being
1604 analysed is missing. The default is @subcmd{ANALYSIS}.
1605 A setting of @subcmd{EXCLUDE} means that variables whose values are
1606 user-missing are to be excluded from the analysis. A setting of
1607 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1609 Using the @code{POSTHOC} subcommand you can perform multiple
1610 pairwise comparisons on the data. The following comparison methods
1614 Least Significant Difference.
1615 @item @subcmd{TUKEY}
1616 Tukey Honestly Significant Difference.
1617 @item @subcmd{BONFERRONI}
1619 @item @subcmd{SCHEFFE}
1621 @item @subcmd{SIDAK}
1624 The Games-Howell test.
1628 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1629 that @var{value} should be used as the
1630 confidence level for which the posthoc tests will be performed.
1631 The default is 0.05.
1634 @section QUICK CLUSTER
1635 @vindex QUICK CLUSTER
1637 @cindex K-means clustering
1641 QUICK CLUSTER @var{var_list}
1642 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1643 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1646 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1647 dataset. This is useful when you wish to allocate cases into clusters
1648 of similar values and you already know the number of clusters.
1650 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1651 of the variables which contain the cluster data. Normally you will also
1652 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1653 number of clusters. If this is not given, then @var{k} defaults to 2.
1655 The command uses an iterative algorithm to determine the clusters for
1656 each case. It will continue iterating until convergence, or until @var{max_iter}
1657 iterations have been done. The default value of @var{max_iter} is 2.
1659 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1660 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1661 value and not as missing values.
1662 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1663 values are excluded as well as system-missing values.
1665 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1666 whenever any of the clustering variables contains a missing value.
1667 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1668 clustering variables contain missing values. Otherwise it is clustered
1669 on the basis of the non-missing values.
1670 The default is @subcmd{LISTWISE}.
1679 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1680 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1681 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1683 /MISSING=@{EXCLUDE,INCLUDE@}
1685 /RANK [INTO @var{var_list}]
1686 /NTILES(k) [INTO @var{var_list}]
1687 /NORMAL [INTO @var{var_list}]
1688 /PERCENT [INTO @var{var_list}]
1689 /RFRACTION [INTO @var{var_list}]
1690 /PROPORTION [INTO @var{var_list}]
1691 /N [INTO @var{var_list}]
1692 /SAVAGE [INTO @var{var_list}]
1695 The @cmd{RANK} command ranks variables and stores the results into new
1698 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1699 more variables whose values are to be ranked.
1700 After each variable, @samp{A} or @samp{D} may appear, indicating that
1701 the variable is to be ranked in ascending or descending order.
1702 Ascending is the default.
1703 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1704 which are to serve as group variables.
1705 In this case, the cases are gathered into groups, and ranks calculated
1708 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1709 default is to take the mean value of all the tied cases.
1711 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1712 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1713 functions are requested.
1715 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1716 variables created should appear in the output.
1718 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1719 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1720 If none are given, then the default is RANK.
1721 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1722 partitions into which values should be ranked.
1723 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1724 variables which are the variables to be created and receive the rank
1725 scores. There may be as many variables specified as there are
1726 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1727 then the variable names are automatically created.
1729 The @subcmd{MISSING} subcommand determines how user missing values are to be
1730 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1731 user-missing are to be excluded from the rank scores. A setting of
1732 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1734 @include regression.texi
1738 @section RELIABILITY
1743 /VARIABLES=@var{var_list}
1744 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1745 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1746 /SUMMARY=@{TOTAL,ALL@}
1747 /MISSING=@{EXCLUDE,INCLUDE@}
1750 @cindex Cronbach's Alpha
1751 The @cmd{RELIABILITY} command performs reliability analysis on the data.
1753 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1754 upon which analysis is to be performed.
1756 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1757 calculated for. If it is omitted, then analysis for all variables named
1758 in the @subcmd{VARIABLES} subcommand will be used.
1759 Optionally, the @var{name} parameter may be specified to set a string name
1762 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1763 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1764 then the variables are divided into 2 subsets. An optional parameter
1765 @var{n} may be given, to specify how many variables to be in the first subset.
1766 If @var{n} is omitted, then it defaults to one half of the variables in the
1767 scale, or one half minus one if there are an odd number of variables.
1768 The default model is @subcmd{ALPHA}.
1770 By default, any cases with user missing, or system missing values for
1772 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1773 The @subcmd{MISSING} subcommand determines whether user missing values are to
1774 be included or excluded in the analysis.
1776 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1777 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1778 analysis tested against the totals.
1786 @cindex Receiver Operating Characteristic
1787 @cindex Area under curve
1790 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1791 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1792 /PRINT = [ SE ] [ COORDINATES ]
1793 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1794 [ TESTPOS (@{LARGE,SMALL@}) ]
1795 [ CI (@var{confidence}) ]
1796 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1797 /MISSING=@{EXCLUDE,INCLUDE@}
1801 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1802 of a dataset, and to estimate the area under the curve.
1803 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1805 The mandatory @var{var_list} is the list of predictor variables.
1806 The variable @var{state_var} is the variable whose values represent the actual states,
1807 and @var{state_value} is the value of this variable which represents the positive state.
1809 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1810 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1811 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1812 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1813 By default, the curve is drawn with no reference line.
1815 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1816 Two additional tables are available.
1817 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1819 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1821 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1823 The @subcmd{CRITERIA} subcommand has four optional parameters:
1825 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1826 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1827 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1829 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1830 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1832 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1834 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1835 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1836 exponential distribution estimate.
1837 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1838 equal to the number of negative actual states.
1839 The default is @subcmd{FREE}.
1841 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1844 The @subcmd{MISSING} subcommand determines whether user missing values are to
1845 be included or excluded in the analysis. The default behaviour is to
1847 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1848 or if the variable @var{state_var} is missing, then the entire case will be