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,
152 @cmd{FREQUENCIES} can also output
153 histograms and pie charts.
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.
238 @cindex Exploratory data analysis
239 @cindex normality, testing
243 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
244 [BY @var{factor1} [BY @var{subfactor1}]
245 [ @var{factor2} [BY @var{subfactor2}]]
247 [ @var{factor3} [BY @var{subfactor3}]]
249 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
250 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
252 /COMPARE=@{GROUPS,VARIABLES@}
253 /ID=@var{identity_variable}
255 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
256 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
257 [@{NOREPORT,REPORT@}]
261 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
262 In particular, it is useful for testing how closely a distribution follows a
263 normal distribution, and for finding outliers and extreme values.
265 The @subcmd{VARIABLES} subcommand is mandatory.
266 It specifies the dependent variables and optionally variables to use as
267 factors for the analysis.
268 Variables listed before the first @subcmd{BY} keyword (if any) are the
270 The dependent variables may optionally be followed by a list of
271 factors which tell @pspp{} how to break down the analysis for each
274 Following the dependent variables, factors may be specified.
275 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
276 The format for each factor is
278 @var{factorvar} [BY @var{subfactorvar}].
280 Each unique combination of the values of @var{factorvar} and
281 @var{subfactorvar} divide the dataset into @dfn{cells}.
282 Statistics will be calculated for each cell
283 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
285 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
286 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
287 non-parametrics statistics.
288 @subcmd{EXTREME} produces a table showing the extremities of each cell.
289 A number in parentheses, @var{n} determines
290 how many upper and lower extremities to show.
291 The default number is 5.
293 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
294 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
295 as well as for each cell.
296 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
297 (unless no factor variables have been given).
298 These subcommands have no effect if there have been no factor variables
304 @cindex spreadlevel plot
305 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
306 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
307 @subcmd{SPREADLEVEL}.
308 The first three can be used to visualise how closely each cell conforms to a
309 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
310 how the variance of differs between factors.
311 Boxplots will also show you the outliers and extreme values.
312 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
313 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
314 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
316 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
317 median. It takes an optional parameter @var{t}, which specifies how the data
318 should be transformed prior to plotting.
319 The given value @var{t} is a power to which the data is raised. For example, if
320 @var{t} is given as 2, then the data will be squared.
321 Zero, however is a special value. If @var{t} is 0 or
322 is omitted, then data will be transformed by taking its natural logarithm instead of
323 raising to the power of @var{t}.
325 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
326 useful there is more than one dependent variable and at least one factor.
328 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
329 each of which contain boxplots for all the cells.
330 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
331 each containing one boxplot per dependent variable.
332 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
333 @subcmd{/COMPARE=GROUPS} were given.
335 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
336 @subcmd{/STATISTICS=EXTREME} has been given.
337 If given, it should provide the name of a variable which is to be used
338 to labels extreme values and outliers.
339 Numeric or string variables are permissible.
340 If the @subcmd{ID} subcommand is not given, then the case number will be used for
343 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
344 calculation of the descriptives command. The default is 95%.
347 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
348 and which algorithm to use for calculating them. The default is to
349 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
350 @subcmd{HAVERAGE} algorithm.
352 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
353 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
354 then then statistics for the unfactored dependent variables are
355 produced in addition to the factored variables. If there are no
356 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
359 The following example will generate descriptive statistics and histograms for
360 two variables @var{score1} and @var{score2}.
361 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
362 Therefore, the descriptives and histograms will be generated for each
364 of @var{gender} @emph{and} for each distinct combination of the values
365 of @var{gender} and @var{race}.
366 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
367 @var{score1} and @var{score2} covering the whole dataset are not produced.
369 EXAMINE @var{score1} @var{score2} BY
371 @var{gender} BY @var{culture}
372 /STATISTICS = DESCRIPTIVES
377 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
379 EXAMINE @var{height} @var{weight} BY
381 /STATISTICS = EXTREME (3)
386 In this example, we look at the height and weight of a sample of individuals and
387 how they differ between male and female.
388 A table showing the 3 largest and the 3 smallest values of @var{height} and
389 @var{weight} for each gender, and for the whole dataset will be shown.
390 Boxplots will also be produced.
391 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
392 shown in the same graphic, allowing us to easily see the difference between
394 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
395 used to label the extreme values.
398 If many dependent variables are specified, or if factor variables are
400 there are many distinct values, then @cmd{EXAMINE} will produce a very
401 large quantity of output.
407 @cindex Exploratory data analysis
408 @cindex normality, testing
412 /HISTOGRAM = @var{var}
413 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
414 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
415 [@{NOREPORT,REPORT@}]
419 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
420 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
421 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
425 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the data. The different
426 values of the optional third variable @var{var3} will result in different colours and/or
427 markers for the plot. The following is an example for producing a scatterplot.
431 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
434 This example will produce a scatterplot where @var{height} is plotted versus @var{weight}. Depending
435 on the value of the @var{gender} variable, the colour of the datapoint is different. With
436 this plot it is possible to analyze gender differences for @var{height} vs.@: @var{weight} relation.
440 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
442 For an alternative method to produce histograms @pxref{EXAMINE}. The
443 following example produces a histogram plot for the variable @var{weight}.
447 /HISTOGRAM = @var{weight}.
451 @section CORRELATIONS
456 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
461 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
462 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
465 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
466 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
467 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
471 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
472 for a set of variables. The significance of the coefficients are also given.
474 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
475 keyword is used, then a non-square correlation table will be produced.
476 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
477 and the variables following will be the columns of the table.
478 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
481 The @cmd{MISSING} subcommand determines the handling of missing variables.
482 If @subcmd{INCLUDE} is set, then user-missing values are included in the
483 calculations, but system-missing values are not.
484 If @subcmd{EXCLUDE} is set, which is the default, user-missing
485 values are excluded as well as system-missing values.
487 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
488 whenever any variable specified in any @cmd{/VARIABLES} subcommand
489 contains a missing value.
490 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
491 values for the particular coefficient are missing.
492 The default is @subcmd{PAIRWISE}.
494 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
495 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
496 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
497 The default is @subcmd{TWOTAIL}.
499 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
500 0.05 are highlighted.
501 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
504 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
505 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
506 estimator of the standard deviation are displayed.
507 These statistics will be displayed in a separated table, for all the variables listed
508 in any @subcmd{/VARIABLES} subcommand.
509 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
510 be displayed for each pair of variables.
511 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
519 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
520 /MISSING=@{TABLE,INCLUDE,REPORT@}
521 /WRITE=@{NONE,CELLS,ALL@}
522 /FORMAT=@{TABLES,NOTABLES@}
527 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
528 ASRESIDUAL,ALL,NONE@}
529 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
530 KAPPA,ETA,CORR,ALL,NONE@}
534 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
537 The @cmd{CROSSTABS} procedure displays crosstabulation
538 tables requested by the user. It can calculate several statistics for
539 each cell in the crosstabulation tables. In addition, a number of
540 statistics can be calculated for each table itself.
542 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
543 number of dimensions is permitted, and any number of variables per
544 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
545 times as needed. This is the only required subcommand in @dfn{general
548 Occasionally, one may want to invoke a special mode called @dfn{integer
549 mode}. Normally, in general mode, @pspp{} automatically determines
550 what values occur in the data. In integer mode, the user specifies the
551 range of values that the data assumes. To invoke this mode, specify the
552 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
553 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
554 the range are truncated to the nearest integer, then assigned to that
555 value. If values occur outside this range, they are discarded. When it
556 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
559 In general mode, numeric and string variables may be specified on
560 TABLES. In integer mode, only numeric variables are allowed.
562 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
563 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
564 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
565 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
566 integer mode, user-missing values are included in tables but marked with
567 an @samp{M} (for ``missing'') and excluded from statistical
570 Currently the @subcmd{WRITE} subcommand is ignored.
572 The @subcmd{FORMAT} subcommand controls the characteristics of the
573 crosstabulation tables to be displayed. It has a number of possible
578 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
579 @subcmd{NOTABLES} suppresses them.
582 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
583 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
587 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
588 @subcmd{DVALUE} asserts a descending sort order.
591 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
594 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
597 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
598 crosstabulation table. The possible settings are:
614 Standardized residual.
616 Adjusted standardized residual.
620 Suppress cells entirely.
623 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
624 @subcmd{COLUMN}, and @subcmd{TOTAL}.
625 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
628 The @subcmd{STATISTICS} subcommand selects statistics for computation:
635 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
636 correction, linear-by-linear association.
640 Contingency coefficient.
644 Uncertainty coefficient.
660 Spearman correlation, Pearson's r.
667 Selected statistics are only calculated when appropriate for the
668 statistic. Certain statistics require tables of a particular size, and
669 some statistics are calculated only in integer mode.
671 @samp{/STATISTICS} without any settings selects CHISQ. If the
672 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
675 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
676 variables on each table.
677 If a table has more than two variables, the counts for the third and subsequent levels
678 will be aggregated and the chart will be produces as if there were only two variables.
681 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
682 following limitations:
686 Significance of some symmetric and directional measures is not calculated.
688 Asymptotic standard error is not calculated for
689 Goodman and Kruskal's tau or symmetric Somers' d.
691 Approximate T is not calculated for symmetric uncertainty coefficient.
694 Fixes for any of these deficiencies would be welcomed.
700 @cindex factor analysis
701 @cindex principal components analysis
702 @cindex principal axis factoring
703 @cindex data reduction
706 FACTOR VARIABLES=@var{var_list}
708 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
710 [ /EXTRACTION=@{PC, PAF@}]
712 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
714 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
718 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
720 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
722 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
725 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
726 common factors in the data or for data reduction purposes.
728 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
730 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
731 If @subcmd{PC} is specified, then Principal Components Analysis is used.
732 If @subcmd{PAF} is specified, then Principal Axis Factoring is
733 used. By default Principal Components Analysis will be used.
735 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
736 Three orthogonal rotation methods are available:
737 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
738 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
739 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
740 The default value of @var{k} is 5.
741 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
742 rotation on the data.
744 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
745 to be analysed. By default, the correlation matrix is analysed.
747 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
750 @item @subcmd{UNIVARIATE}
751 A table of mean values, standard deviations and total weights are printed.
752 @item @subcmd{INITIAL}
753 Initial communalities and eigenvalues are printed.
754 @item @subcmd{EXTRACTION}
755 Extracted communalities and eigenvalues are printed.
756 @item @subcmd{ROTATION}
757 Rotated communalities and eigenvalues are printed.
758 @item @subcmd{CORRELATION}
759 The correlation matrix is printed.
760 @item @subcmd{COVARIANCE}
761 The covariance matrix is printed.
763 The determinant of the correlation or covariance matrix is printed.
765 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
767 The significance of the elements of correlation matrix is printed.
769 All of the above are printed.
770 @item @subcmd{DEFAULT}
771 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
774 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
775 which factors (components) should be retained.
777 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
778 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
779 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
780 performed, and all coefficients will be printed.
782 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
783 If @subcmd{FACTORS(@var{n})} is
784 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
786 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
787 The default value of @var{l} is 1.
788 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
789 extraction (such as Principal Axis Factoring) are used.
790 @subcmd{ECONVERGE(@var{delta})} specifies that
791 iteration should cease when
792 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
793 default value of @var{delta} is 0.001.
794 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
795 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
797 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
798 If @subcmd{EXTRACTION} follows, it affects convergence.
799 If @subcmd{ROTATION} follows, it affects rotation.
800 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
801 The default value of @var{m} is 25.
803 The @cmd{MISSING} subcommand determines the handling of missing variables.
804 If @subcmd{INCLUDE} is set, then user-missing values are included in the
805 calculations, but system-missing values are not.
806 If @subcmd{EXCLUDE} is set, which is the default, user-missing
807 values are excluded as well as system-missing values.
809 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
810 whenever any variable specified in the @cmd{VARIABLES} subcommand
811 contains a missing value.
812 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
813 values for the particular coefficient are missing.
814 The default is @subcmd{LISTWISE}.
816 @node LOGISTIC REGRESSION
817 @section LOGISTIC REGRESSION
819 @vindex LOGISTIC REGRESSION
820 @cindex logistic regression
821 @cindex bivariate logistic regression
824 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
826 [/CATEGORICAL = @var{categorical_predictors}]
828 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
830 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
832 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
833 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
834 [CUT(@var{cut_point})]]
836 [/MISSING = @{INCLUDE|EXCLUDE@}]
839 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
840 variable in terms of one or more predictor variables.
842 The minimum command is
844 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
846 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
847 are the predictor variables whose coefficients the procedure estimates.
849 By default, a constant term is included in the model.
850 Hence, the full model is
853 = b_0 + b_1 {\bf x_1}
859 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
860 Simple variables as well as interactions between variables may be listed here.
862 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
863 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
865 An iterative Newton-Raphson procedure is used to fit the model.
866 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
867 and other parameters.
868 The value of @var{cut_point} is used in the classification table. It is the
869 threshold above which predicted values are considered to be 1. Values
870 of @var{cut_point} must lie in the range [0,1].
871 During iterations, if any one of the stopping criteria are satisfied, the procedure is
873 The stopping criteria are:
875 @item The number of iterations exceeds @var{max_iterations}.
876 The default value of @var{max_iterations} is 20.
877 @item The change in the all coefficient estimates are less than @var{min_delta}.
878 The default value of @var{min_delta} is 0.001.
879 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
880 The default value of @var{min_delta} is zero.
881 This means that this criterion is disabled.
882 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
883 In other words, the probabilities are close to zero or one.
884 The default value of @var{min_epsilon} is 0.00000001.
888 The @subcmd{PRINT} subcommand controls the display of optional statistics.
889 Currently there is one such option, @subcmd{CI}, which indicates that the
890 confidence interval of the odds ratio should be displayed as well as its value.
891 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
892 confidence level of the desired confidence interval.
894 The @subcmd{MISSING} subcommand determines the handling of missing
896 If @subcmd{INCLUDE} is set, then user-missing values are included in the
897 calculations, but system-missing values are not.
898 If @subcmd{EXCLUDE} is set, which is the default, user-missing
899 values are excluded as well as system-missing values.
911 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
913 [ /@{@var{var_list}@}
914 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
916 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
917 [VARIANCE] [KURT] [SEKURT]
918 [SKEW] [SESKEW] [FIRST] [LAST]
919 [HARMONIC] [GEOMETRIC]
924 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
927 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
928 statistics, either for the dataset as a whole or for categories of data.
930 The simplest form of the command is
934 @noindent which calculates the mean, count and standard deviation for @var{v}.
935 If you specify a grouping variable, for example
937 MEANS @var{v} BY @var{g}.
939 @noindent then the means, counts and standard deviations for @var{v} after having
940 been grouped by @var{g} will be calculated.
941 Instead of the mean, count and standard deviation, you could specify the statistics
942 in which you are interested:
944 MEANS @var{x} @var{y} BY @var{g}
945 /CELLS = HARMONIC SUM MIN.
947 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
950 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
954 @cindex arithmetic mean
957 The count of the values.
958 @item @subcmd{STDDEV}
959 The standard deviation.
960 @item @subcmd{SEMEAN}
961 The standard error of the mean.
963 The sum of the values.
969 The difference between the maximum and minimum values.
970 @item @subcmd{VARIANCE}
973 The first value in the category.
975 The last value in the category.
978 @item @subcmd{SESKEW}
979 The standard error of the skewness.
982 @item @subcmd{SEKURT}
983 The standard error of the kurtosis.
984 @item @subcmd{HARMONIC}
985 @cindex harmonic mean
987 @item @subcmd{GEOMETRIC}
988 @cindex geometric mean
992 In addition, three special keywords are recognized:
994 @item @subcmd{DEFAULT}
995 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
997 All of the above statistics will be calculated.
999 No statistics will be calculated (only a summary will be shown).
1003 More than one @dfn{table} can be specified in a single command.
1004 Each table is separated by a @samp{/}. For
1008 @var{c} @var{d} @var{e} BY @var{x}
1009 /@var{a} @var{b} BY @var{x} @var{y}
1010 /@var{f} BY @var{y} BY @var{z}.
1012 has three tables (the @samp{TABLE =} is optional).
1013 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1014 and a single categorical variable @var{x}.
1015 The second table has two dependent variables @var{a} and @var{b},
1016 and two categorical variables @var{x} and @var{y}.
1017 The third table has a single dependent variables @var{f}
1018 and a categorical variable formed by the combination of @var{y} and @var{z}.
1021 By default values are omitted from the analysis only if missing values
1022 (either system missing or user missing)
1023 for any of the variables directly involved in their calculation are
1025 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1026 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1028 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1029 in the table specification currently being processed, regardless of
1030 whether it is needed to calculate the statistic.
1032 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1033 variables or in the categorical variables should be taken at their face
1034 value, and not excluded.
1036 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1037 variables should be taken at their face value, however cases which
1038 have user missing values for the categorical variables should be omitted
1039 from the calculation.
1045 @cindex nonparametric tests
1050 nonparametric test subcommands
1055 [ /STATISTICS=@{DESCRIPTIVES@} ]
1057 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1059 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1062 @cmd{NPAR TESTS} performs nonparametric tests.
1063 Non parametric tests make very few assumptions about the distribution of the
1065 One or more tests may be specified by using the corresponding subcommand.
1066 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1067 produces for each variable that is the subject of any test.
1069 Certain tests may take a long time to execute, if an exact figure is required.
1070 Therefore, by default asymptotic approximations are used unless the
1071 subcommand @subcmd{/METHOD=EXACT} is specified.
1072 Exact tests give more accurate results, but may take an unacceptably long
1073 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1074 after which the test will be abandoned, and a warning message printed.
1075 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1076 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1081 * BINOMIAL:: Binomial Test
1082 * CHISQUARE:: Chisquare Test
1083 * COCHRAN:: Cochran Q Test
1084 * FRIEDMAN:: Friedman Test
1085 * KENDALL:: Kendall's W Test
1086 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1087 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1088 * MANN-WHITNEY:: Mann Whitney U Test
1089 * MCNEMAR:: McNemar Test
1090 * MEDIAN:: Median Test
1092 * SIGN:: The Sign Test
1093 * WILCOXON:: Wilcoxon Signed Ranks Test
1098 @subsection Binomial test
1100 @cindex binomial test
1103 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1106 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1107 variable with that of a binomial distribution.
1108 The variable @var{p} specifies the test proportion of the binomial
1110 The default value of 0.5 is assumed if @var{p} is omitted.
1112 If a single value appears after the variable list, then that value is
1113 used as the threshold to partition the observed values. Values less
1114 than or equal to the threshold value form the first category. Values
1115 greater than the threshold form the second category.
1117 If two values appear after the variable list, then they will be used
1118 as the values which a variable must take to be in the respective
1120 Cases for which a variable takes a value equal to neither of the specified
1121 values, take no part in the test for that variable.
1123 If no values appear, then the variable must assume dichotomous
1125 If more than two distinct, non-missing values for a variable
1126 under test are encountered then an error occurs.
1128 If the test proportion is equal to 0.5, then a two tailed test is
1129 reported. For any other test proportion, a one tailed test is
1131 For one tailed tests, if the test proportion is less than
1132 or equal to the observed proportion, then the significance of
1133 observing the observed proportion or more is reported.
1134 If the test proportion is more than the observed proportion, then the
1135 significance of observing the observed proportion or less is reported.
1136 That is to say, the test is always performed in the observed
1139 @pspp{} uses a very precise approximation to the gamma function to
1140 compute the binomial significance. Thus, exact results are reported
1141 even for very large sample sizes.
1146 @subsection Chisquare Test
1148 @cindex chisquare test
1152 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1156 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1157 between the expected and observed frequencies of the categories of a variable.
1158 Optionally, a range of values may appear after the variable list.
1159 If a range is given, then non integer values are truncated, and values
1160 outside the specified range are excluded from the analysis.
1162 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1164 There must be exactly one non-zero expected value, for each observed
1165 category, or the @subcmd{EQUAL} keyword must be specified.
1166 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1167 consecutive expected categories all taking a frequency of @var{f}.
1168 The frequencies given are proportions, not absolute frequencies. The
1169 sum of the frequencies need not be 1.
1170 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1175 @subsection Cochran Q Test
1177 @cindex Cochran Q test
1178 @cindex Q, Cochran Q
1181 [ /COCHRAN = @var{var_list} ]
1184 The Cochran Q test is used to test for differences between three or more groups.
1185 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1187 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1190 @subsection Friedman Test
1192 @cindex Friedman test
1195 [ /FRIEDMAN = @var{var_list} ]
1198 The Friedman test is used to test for differences between repeated measures when
1199 there is no indication that the distributions are normally distributed.
1201 A list of variables which contain the measured data must be given. The procedure
1202 prints the sum of ranks for each variable, the test statistic and its significance.
1205 @subsection Kendall's W Test
1207 @cindex Kendall's W test
1208 @cindex coefficient of concordance
1211 [ /KENDALL = @var{var_list} ]
1214 The Kendall test investigates whether an arbitrary number of related samples come from the
1216 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1217 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1218 unity indicates complete agreement.
1221 @node KOLMOGOROV-SMIRNOV
1222 @subsection Kolmogorov-Smirnov Test
1223 @vindex KOLMOGOROV-SMIRNOV
1225 @cindex Kolmogorov-Smirnov test
1228 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1231 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1232 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1233 Normal, Uniform, Poisson and Exponential.
1235 Ideally you should provide the parameters of the distribution against which you wish to test
1236 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1237 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1239 However, if the parameters are omitted they will be imputed from the data. Imputing the
1240 parameters reduces the power of the test so should be avoided if possible.
1242 In the following example, two variables @var{score} and @var{age} are tested to see if
1243 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1246 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1248 If the variables need to be tested against different distributions, then a separate
1249 subcommand must be used. For example the following syntax tests @var{score} against
1250 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1251 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1254 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1255 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1258 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1260 @node KRUSKAL-WALLIS
1261 @subsection Kruskal-Wallis Test
1262 @vindex KRUSKAL-WALLIS
1264 @cindex Kruskal-Wallis test
1267 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1270 The Kruskal-Wallis test is used to compare data from an
1271 arbitrary number of populations. It does not assume normality.
1272 The data to be compared are specified by @var{var_list}.
1273 The categorical variable determining the groups to which the
1274 data belongs is given by @var{var}. The limits @var{lower} and
1275 @var{upper} specify the valid range of @var{var}. Any cases for
1276 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1279 The mean rank of each group as well as the chi-squared value and significance
1280 of the test will be printed.
1281 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1285 @subsection Mann-Whitney U Test
1286 @vindex MANN-WHITNEY
1288 @cindex Mann-Whitney U test
1289 @cindex U, Mann-Whitney U
1292 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1295 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1296 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}.
1297 @var{Var} may be either a string or an alpha variable.
1298 @var{Group1} and @var{group2} specify the
1299 two values of @var{var} which determine the groups of the test data.
1300 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1302 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1303 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1306 @subsection McNemar Test
1308 @cindex McNemar test
1311 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1314 Use McNemar's test to analyse the significance of the difference between
1315 pairs of correlated proportions.
1317 If the @code{WITH} keyword is omitted, then tests for all
1318 combinations of the listed variables are performed.
1319 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1320 is also given, then the number of variables preceding @code{WITH}
1321 must be the same as the number following it.
1322 In this case, tests for each respective pair of variables are
1324 If the @code{WITH} keyword is given, but the
1325 @code{(PAIRED)} keyword is omitted, then tests for each combination
1326 of variable preceding @code{WITH} against variable following
1327 @code{WITH} are performed.
1329 The data in each variable must be dichotomous. If there are more
1330 than two distinct variables an error will occur and the test will
1334 @subsection Median Test
1339 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1342 The median test is used to test whether independent samples come from
1343 populations with a common median.
1344 The median of the populations against which the samples are to be tested
1345 may be given in parentheses immediately after the
1346 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1347 union of all the samples.
1349 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1350 keyword @code{BY} must come next, and then the grouping variable. Two values
1351 in parentheses should follow. If the first value is greater than the second,
1352 then a 2 sample test is performed using these two values to determine the groups.
1353 If however, the first variable is less than the second, then a @i{k} sample test is
1354 conducted and the group values used are all values encountered which lie in the
1355 range [@var{value1},@var{value2}].
1359 @subsection Runs Test
1364 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1367 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1369 It works by examining the number of times a variable's value crosses a given threshold.
1370 The desired threshold must be specified within parentheses.
1371 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1372 Following the threshold specification comes the list of variables whose values are to be
1375 The subcommand shows the number of runs, the asymptotic significance based on the
1379 @subsection Sign Test
1384 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1387 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1389 The test does not make any assumptions about the
1390 distribution of the data.
1392 If the @code{WITH} keyword is omitted, then tests for all
1393 combinations of the listed variables are performed.
1394 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1395 is also given, then the number of variables preceding @code{WITH}
1396 must be the same as the number following it.
1397 In this case, tests for each respective pair of variables are
1399 If the @code{WITH} keyword is given, but the
1400 @code{(PAIRED)} keyword is omitted, then tests for each combination
1401 of variable preceding @code{WITH} against variable following
1402 @code{WITH} are performed.
1405 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1407 @cindex wilcoxon matched pairs signed ranks test
1410 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1413 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1415 The test does not make any assumptions about the variances of the samples.
1416 It does however assume that the distribution is symmetrical.
1418 If the @subcmd{WITH} keyword is omitted, then tests for all
1419 combinations of the listed variables are performed.
1420 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1421 is also given, then the number of variables preceding @subcmd{WITH}
1422 must be the same as the number following it.
1423 In this case, tests for each respective pair of variables are
1425 If the @subcmd{WITH} keyword is given, but the
1426 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1427 of variable preceding @subcmd{WITH} against variable following
1428 @subcmd{WITH} are performed.
1437 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1438 /CRITERIA=CIN(@var{confidence})
1442 TESTVAL=@var{test_value}
1443 /VARIABLES=@var{var_list}
1446 (Independent Samples mode.)
1447 GROUPS=var(@var{value1} [, @var{value2}])
1448 /VARIABLES=@var{var_list}
1451 (Paired Samples mode.)
1452 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1457 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1459 It operates in one of three modes:
1461 @item One Sample mode.
1462 @item Independent Groups mode.
1467 Each of these modes are described in more detail below.
1468 There are two optional subcommands which are common to all modes.
1470 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1471 in the tests. The default value is 0.95.
1474 The @cmd{MISSING} subcommand determines the handling of missing
1476 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1477 calculations, but system-missing values are not.
1478 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1479 values are excluded as well as system-missing values.
1480 This is the default.
1482 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1483 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1484 @subcmd{/GROUPS} subcommands contains a missing value.
1485 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1486 which they would be needed. This is the default.
1490 * One Sample Mode:: Testing against a hypothesized mean
1491 * Independent Samples Mode:: Testing two independent groups for equal mean
1492 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1495 @node One Sample Mode
1496 @subsection One Sample Mode
1498 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1499 This mode is used to test a population mean against a hypothesized
1501 The value given to the @subcmd{TESTVAL} subcommand is the value against
1502 which you wish to test.
1503 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1504 tell @pspp{} which variables you wish to test.
1506 @node Independent Samples Mode
1507 @subsection Independent Samples Mode
1509 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1511 This mode is used to test whether two groups of values have the
1512 same population mean.
1513 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1514 tell @pspp{} the dependent variables you wish to test.
1516 The variable given in the @subcmd{GROUPS} subcommand is the independent
1517 variable which determines to which group the samples belong.
1518 The values in parentheses are the specific values of the independent
1519 variable for each group.
1520 If the parentheses are omitted and no values are given, the default values
1521 of 1.0 and 2.0 are assumed.
1523 If the independent variable is numeric,
1524 it is acceptable to specify only one value inside the parentheses.
1525 If you do this, cases where the independent variable is
1526 greater than or equal to this value belong to the first group, and cases
1527 less than this value belong to the second group.
1528 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1529 the independent variable are excluded on a listwise basis, regardless
1530 of whether @subcmd{/MISSING=LISTWISE} was specified.
1533 @node Paired Samples Mode
1534 @subsection Paired Samples Mode
1536 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1537 Use this mode when repeated measures have been taken from the same
1539 If the @subcmd{WITH} keyword is omitted, then tables for all
1540 combinations of variables given in the @cmd{PAIRS} subcommand are
1542 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1543 is also given, then the number of variables preceding @subcmd{WITH}
1544 must be the same as the number following it.
1545 In this case, tables for each respective pair of variables are
1547 In the event that the @subcmd{WITH} keyword is given, but the
1548 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1549 of variable preceding @subcmd{WITH} against variable following
1550 @subcmd{WITH} are generated.
1557 @cindex analysis of variance
1562 [/VARIABLES = ] @var{var_list} BY @var{var}
1563 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1564 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1565 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1566 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1569 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1570 variables factored by a single independent variable.
1571 It is used to compare the means of a population
1572 divided into more than two groups.
1574 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1576 The list of variables must be followed by the @subcmd{BY} keyword and
1577 the name of the independent (or factor) variable.
1579 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1580 ancillary information. The options accepted are:
1583 Displays descriptive statistics about the groups factored by the independent
1586 Displays the Levene test of Homogeneity of Variance for the
1587 variables and their groups.
1590 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1591 differences between the groups.
1592 The subcommand must be followed by a list of numerals which are the
1593 coefficients of the groups to be tested.
1594 The number of coefficients must correspond to the number of distinct
1595 groups (or values of the independent variable).
1596 If the total sum of the coefficients are not zero, then @pspp{} will
1597 display a warning, but will proceed with the analysis.
1598 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1599 to specify different contrast tests.
1600 The @subcmd{MISSING} subcommand defines how missing values are handled.
1601 If @subcmd{LISTWISE} is specified then cases which have missing values for
1602 the independent variable or any dependent variable will be ignored.
1603 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1604 variable is missing or if the dependent variable currently being
1605 analysed is missing. The default is @subcmd{ANALYSIS}.
1606 A setting of @subcmd{EXCLUDE} means that variables whose values are
1607 user-missing are to be excluded from the analysis. A setting of
1608 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1610 Using the @code{POSTHOC} subcommand you can perform multiple
1611 pairwise comparisons on the data. The following comparison methods
1615 Least Significant Difference.
1616 @item @subcmd{TUKEY}
1617 Tukey Honestly Significant Difference.
1618 @item @subcmd{BONFERRONI}
1620 @item @subcmd{SCHEFFE}
1622 @item @subcmd{SIDAK}
1625 The Games-Howell test.
1629 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1630 that @var{value} should be used as the
1631 confidence level for which the posthoc tests will be performed.
1632 The default is 0.05.
1635 @section QUICK CLUSTER
1636 @vindex QUICK CLUSTER
1638 @cindex K-means clustering
1642 QUICK CLUSTER @var{var_list}
1643 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1644 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1647 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1648 dataset. This is useful when you wish to allocate cases into clusters
1649 of similar values and you already know the number of clusters.
1651 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1652 of the variables which contain the cluster data. Normally you will also
1653 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1654 number of clusters. If this is not given, then @var{k} defaults to 2.
1656 The command uses an iterative algorithm to determine the clusters for
1657 each case. It will continue iterating until convergence, or until @var{max_iter}
1658 iterations have been done. The default value of @var{max_iter} is 2.
1660 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1661 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1662 value and not as missing values.
1663 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1664 values are excluded as well as system-missing values.
1666 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1667 whenever any of the clustering variables contains a missing value.
1668 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1669 clustering variables contain missing values. Otherwise it is clustered
1670 on the basis of the non-missing values.
1671 The default is @subcmd{LISTWISE}.
1680 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1681 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1682 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1684 /MISSING=@{EXCLUDE,INCLUDE@}
1686 /RANK [INTO @var{var_list}]
1687 /NTILES(k) [INTO @var{var_list}]
1688 /NORMAL [INTO @var{var_list}]
1689 /PERCENT [INTO @var{var_list}]
1690 /RFRACTION [INTO @var{var_list}]
1691 /PROPORTION [INTO @var{var_list}]
1692 /N [INTO @var{var_list}]
1693 /SAVAGE [INTO @var{var_list}]
1696 The @cmd{RANK} command ranks variables and stores the results into new
1699 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1700 more variables whose values are to be ranked.
1701 After each variable, @samp{A} or @samp{D} may appear, indicating that
1702 the variable is to be ranked in ascending or descending order.
1703 Ascending is the default.
1704 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1705 which are to serve as group variables.
1706 In this case, the cases are gathered into groups, and ranks calculated
1709 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1710 default is to take the mean value of all the tied cases.
1712 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1713 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1714 functions are requested.
1716 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1717 variables created should appear in the output.
1719 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1720 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1721 If none are given, then the default is RANK.
1722 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1723 partitions into which values should be ranked.
1724 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1725 variables which are the variables to be created and receive the rank
1726 scores. There may be as many variables specified as there are
1727 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1728 then the variable names are automatically created.
1730 The @subcmd{MISSING} subcommand determines how user missing values are to be
1731 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1732 user-missing are to be excluded from the rank scores. A setting of
1733 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1735 @include regression.texi
1739 @section RELIABILITY
1744 /VARIABLES=@var{var_list}
1745 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1746 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1747 /SUMMARY=@{TOTAL,ALL@}
1748 /MISSING=@{EXCLUDE,INCLUDE@}
1751 @cindex Cronbach's Alpha
1752 The @cmd{RELIABILITY} command performs reliability analysis on the data.
1754 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1755 upon which analysis is to be performed.
1757 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1758 calculated for. If it is omitted, then analysis for all variables named
1759 in the @subcmd{VARIABLES} subcommand will be used.
1760 Optionally, the @var{name} parameter may be specified to set a string name
1763 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1764 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1765 then the variables are divided into 2 subsets. An optional parameter
1766 @var{n} may be given, to specify how many variables to be in the first subset.
1767 If @var{n} is omitted, then it defaults to one half of the variables in the
1768 scale, or one half minus one if there are an odd number of variables.
1769 The default model is @subcmd{ALPHA}.
1771 By default, any cases with user missing, or system missing values for
1773 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1774 The @subcmd{MISSING} subcommand determines whether user missing values are to
1775 be included or excluded in the analysis.
1777 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1778 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1779 analysis tested against the totals.
1787 @cindex Receiver Operating Characteristic
1788 @cindex Area under curve
1791 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1792 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1793 /PRINT = [ SE ] [ COORDINATES ]
1794 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1795 [ TESTPOS (@{LARGE,SMALL@}) ]
1796 [ CI (@var{confidence}) ]
1797 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1798 /MISSING=@{EXCLUDE,INCLUDE@}
1802 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1803 of a dataset, and to estimate the area under the curve.
1804 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1806 The mandatory @var{var_list} is the list of predictor variables.
1807 The variable @var{state_var} is the variable whose values represent the actual states,
1808 and @var{state_value} is the value of this variable which represents the positive state.
1810 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1811 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1812 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1813 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1814 By default, the curve is drawn with no reference line.
1816 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1817 Two additional tables are available.
1818 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1820 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1822 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1824 The @subcmd{CRITERIA} subcommand has four optional parameters:
1826 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1827 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1828 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1830 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1831 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1833 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1835 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1836 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1837 exponential distribution estimate.
1838 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1839 equal to the number of negative actual states.
1840 The default is @subcmd{FREE}.
1842 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1845 The @subcmd{MISSING} subcommand determines whether user missing values are to
1846 be included or excluded in the analysis. The default behaviour is to
1848 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1849 or if the variable @var{state_var} is missing, then the entire case will be