4 This chapter documents the statistical procedures that @pspp{} supports so
8 * DESCRIPTIVES:: Descriptive statistics.
9 * FREQUENCIES:: Frequency tables.
10 * EXAMINE:: Testing data for normality.
12 * CORRELATIONS:: Correlation tables.
13 * CROSSTABS:: Crosstabulation tables.
14 * FACTOR:: Factor analysis and Principal Components analysis.
15 * LOGISTIC REGRESSION:: Bivariate Logistic Regression.
16 * MEANS:: Average values and other statistics.
17 * NPAR TESTS:: Nonparametric tests.
18 * T-TEST:: Test hypotheses about means.
19 * ONEWAY:: One way analysis of variance.
20 * QUICK CLUSTER:: K-Means clustering.
21 * RANK:: Compute rank scores.
22 * REGRESSION:: Linear regression.
23 * RELIABILITY:: Reliability analysis.
24 * ROC:: Receiver Operating Characteristic.
33 /VARIABLES=@var{var_list}
34 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
35 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
37 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
38 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
39 SESKEWNESS,SEKURTOSIS@}
40 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
41 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
45 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
47 statistics requested by the user. In addition, it can optionally
50 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
51 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
53 All other subcommands are optional:
55 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
56 @subcmd{INCLUDE} is set, then user-missing values are included in the
57 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
58 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
59 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
60 the entire case is excluded whenever any value in that case has a
61 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
63 The @subcmd{FORMAT} subcommand affects the output format. Currently the
64 @subcmd{LABELS/NOLABELS} and @subcmd{NOINDEX/INDEX} settings are not used.
65 When @subcmd{SERIAL} is
66 set, both valid and missing number of cases are listed in the output;
67 when @subcmd{NOSERIAL} is set, only valid cases are listed.
69 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
70 the specified variables. The Z scores are saved to new variables.
71 Variable names are generated by trying first the original variable name
72 with Z prepended and truncated to a maximum of 8 characters, then the
73 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
74 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
75 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
76 list by enclosing them in parentheses after each variable.
77 When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
78 treating temporary transformations as permanent.
80 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
84 All of the statistics below.
88 Standard error of the mean.
91 @item @subcmd{VARIANCE}
93 @item @subcmd{KURTOSIS}
94 Kurtosis and standard error of the kurtosis.
95 @item @subcmd{SKEWNESS}
96 Skewness and standard error of the skewness.
106 Mean, standard deviation of the mean, minimum, maximum.
108 Standard error of the kurtosis.
110 Standard error of the skewness.
113 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
114 of the possible values should be self-explanatory. @subcmd{NAME} causes the
115 statistics to be sorted by name. By default, the statistics are listed
116 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
117 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
118 sort order, respectively.
126 /VARIABLES=@var{var_list}
127 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
128 @{AVALUE,DVALUE,AFREQ,DFREQ@}
129 /MISSING=@{EXCLUDE,INCLUDE@}
130 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
131 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
132 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
134 /PERCENTILES=percent@dots{}
135 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
136 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
137 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
138 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
139 /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
141 /ORDER=@{ANALYSIS,VARIABLE@}
144 (These options are not currently implemented.)
149 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
151 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
152 (including median and mode) and percentiles, and various graphical representations
153 of the frequency distribution.
155 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
156 variables to be analyzed.
158 The @subcmd{FORMAT} subcommand controls the output format. It has several
163 @subcmd{TABLE}, the default, causes a frequency table to be output for every
164 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
165 with a numeric argument causes them to be output except when there are
166 more than the specified number of values in the table.
169 Normally frequency tables are sorted in ascending order by value. This
170 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
171 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
172 respectively, by frequency count.
175 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
176 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
177 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
178 are included. System-missing values are never included in statistics,
179 but are listed in frequency tables.
181 The available @subcmd{STATISTICS} are the same as available
182 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
183 of @subcmd{MEDIAN}, the data's median
184 value, and MODE, the mode. (If there are multiple modes, the smallest
185 value is reported.) By default, the mean, standard deviation of the
186 mean, minimum, and maximum are reported for each variable.
189 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
190 The percentiles should be presented at a list of numbers between 0
192 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
193 boundaries of the data set divided into the specified number of ranges.
194 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
197 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
198 each specified numeric variable. The X axis by default ranges from
199 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
200 and @subcmd{MAXIMUM} keywords can set an explicit range.
201 @footnote{The number of
202 bins is chosen according to the Freedman-Diaconis rule:
203 @math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
204 and @math{n} is the number of samples. Note that
205 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
206 Histograms are not created for string variables.
208 Specify @subcmd{NORMAL} to superimpose a normal curve on the
212 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
213 slice represents one value, with the size of the slice proportional to
214 the value's frequency. By default, all non-missing values are given
216 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
217 displayed slices to a given range of values.
218 The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
219 piechart. This is the default.
220 If instead, @subcmd{MISSING} is specified, then a single slice
221 will be included representing all system missing and user-missing cases.
224 The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
225 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
226 categories whose counts which lie outside the specified limits.
227 The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
228 of each category, whereas the @subcmd{PERCENT} option will display relative
231 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
232 @subcmd{PIECHART} are accepted but not currently honoured.
234 The @subcmd{ORDER} subcommand is accepted but ignored.
240 @cindex Exploratory data analysis
241 @cindex normality, testing
245 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
246 [BY @var{factor1} [BY @var{subfactor1}]
247 [ @var{factor2} [BY @var{subfactor2}]]
249 [ @var{factor3} [BY @var{subfactor3}]]
251 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
252 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
254 /COMPARE=@{GROUPS,VARIABLES@}
255 /ID=@var{identity_variable}
257 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
258 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
259 [@{NOREPORT,REPORT@}]
263 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
264 In particular, it is useful for testing how closely a distribution follows a
265 normal distribution, and for finding outliers and extreme values.
267 The @subcmd{VARIABLES} subcommand is mandatory.
268 It specifies the dependent variables and optionally variables to use as
269 factors for the analysis.
270 Variables listed before the first @subcmd{BY} keyword (if any) are the
272 The dependent variables may optionally be followed by a list of
273 factors which tell @pspp{} how to break down the analysis for each
276 Following the dependent variables, factors may be specified.
277 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
278 The format for each factor is
280 @var{factorvar} [BY @var{subfactorvar}].
282 Each unique combination of the values of @var{factorvar} and
283 @var{subfactorvar} divide the dataset into @dfn{cells}.
284 Statistics will be calculated for each cell
285 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
287 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
288 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
289 non-parametrics statistics.
290 @subcmd{EXTREME} produces a table showing the extremities of each cell.
291 A number in parentheses, @var{n} determines
292 how many upper and lower extremities to show.
293 The default number is 5.
295 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
296 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
297 as well as for each cell.
298 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
299 (unless no factor variables have been given).
300 These subcommands have no effect if there have been no factor variables
306 @cindex spreadlevel plot
307 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
308 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
309 @subcmd{SPREADLEVEL}.
310 The first three can be used to visualise how closely each cell conforms to a
311 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
312 how the variance of differs between factors.
313 Boxplots will also show you the outliers and extreme values.
314 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
315 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
316 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
318 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
319 median. It takes an optional parameter @var{t}, which specifies how the data
320 should be transformed prior to plotting.
321 The given value @var{t} is a power to which the data is raised. For example, if
322 @var{t} is given as 2, then the data will be squared.
323 Zero, however is a special value. If @var{t} is 0 or
324 is omitted, then data will be transformed by taking its natural logarithm instead of
325 raising to the power of @var{t}.
327 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
328 useful there is more than one dependent variable and at least one factor.
330 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
331 each of which contain boxplots for all the cells.
332 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
333 each containing one boxplot per dependent variable.
334 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
335 @subcmd{/COMPARE=GROUPS} were given.
337 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
338 @subcmd{/STATISTICS=EXTREME} has been given.
339 If given, it should provide the name of a variable which is to be used
340 to labels extreme values and outliers.
341 Numeric or string variables are permissible.
342 If the @subcmd{ID} subcommand is not given, then the case number will be used for
345 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
346 calculation of the descriptives command. The default is 95%.
349 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
350 and which algorithm to use for calculating them. The default is to
351 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
352 @subcmd{HAVERAGE} algorithm.
354 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
355 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
356 then then statistics for the unfactored dependent variables are
357 produced in addition to the factored variables. If there are no
358 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
361 The following example will generate descriptive statistics and histograms for
362 two variables @var{score1} and @var{score2}.
363 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
364 Therefore, the descriptives and histograms will be generated for each
366 of @var{gender} @emph{and} for each distinct combination of the values
367 of @var{gender} and @var{race}.
368 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
369 @var{score1} and @var{score2} covering the whole dataset are not produced.
371 EXAMINE @var{score1} @var{score2} BY
373 @var{gender} BY @var{culture}
374 /STATISTICS = DESCRIPTIVES
379 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
381 EXAMINE @var{height} @var{weight} BY
383 /STATISTICS = EXTREME (3)
388 In this example, we look at the height and weight of a sample of individuals and
389 how they differ between male and female.
390 A table showing the 3 largest and the 3 smallest values of @var{height} and
391 @var{weight} for each gender, and for the whole dataset will be shown.
392 Boxplots will also be produced.
393 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
394 shown in the same graphic, allowing us to easily see the difference between
396 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
397 used to label the extreme values.
400 If many dependent variables are specified, or if factor variables are
402 there are many distinct values, then @cmd{EXAMINE} will produce a very
403 large quantity of output.
409 @cindex Exploratory data analysis
410 @cindex normality, testing
414 /HISTOGRAM = @var{var}
415 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
416 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
417 [@{NOREPORT,REPORT@}]
421 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
422 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
423 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
427 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the data. The different
428 values of the optional third variable @var{var3} will result in different colours and/or
429 markers for the plot. The following is an example for producing a scatterplot.
433 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
436 This example will produce a scatterplot where @var{height} is plotted versus @var{weight}. Depending
437 on the value of the @var{gender} variable, the colour of the datapoint is different. With
438 this plot it is possible to analyze gender differences for @var{height} vs.@: @var{weight} relation.
442 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
444 For an alternative method to produce histograms @pxref{EXAMINE}. The
445 following example produces a histogram plot for the variable @var{weight}.
449 /HISTOGRAM = @var{weight}.
453 @section CORRELATIONS
458 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
463 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
464 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
467 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
468 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
469 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
473 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
474 for a set of variables. The significance of the coefficients are also given.
476 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
477 keyword is used, then a non-square correlation table will be produced.
478 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
479 and the variables following will be the columns of the table.
480 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
483 The @cmd{MISSING} subcommand determines the handling of missing variables.
484 If @subcmd{INCLUDE} is set, then user-missing values are included in the
485 calculations, but system-missing values are not.
486 If @subcmd{EXCLUDE} is set, which is the default, user-missing
487 values are excluded as well as system-missing values.
489 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
490 whenever any variable specified in any @cmd{/VARIABLES} subcommand
491 contains a missing value.
492 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
493 values for the particular coefficient are missing.
494 The default is @subcmd{PAIRWISE}.
496 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
497 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
498 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
499 The default is @subcmd{TWOTAIL}.
501 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
502 0.05 are highlighted.
503 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
506 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
507 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
508 estimator of the standard deviation are displayed.
509 These statistics will be displayed in a separated table, for all the variables listed
510 in any @subcmd{/VARIABLES} subcommand.
511 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
512 be displayed for each pair of variables.
513 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
521 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
522 /MISSING=@{TABLE,INCLUDE,REPORT@}
523 /WRITE=@{NONE,CELLS,ALL@}
524 /FORMAT=@{TABLES,NOTABLES@}
529 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
530 ASRESIDUAL,ALL,NONE@}
531 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
532 KAPPA,ETA,CORR,ALL,NONE@}
536 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
539 The @cmd{CROSSTABS} procedure displays crosstabulation
540 tables requested by the user. It can calculate several statistics for
541 each cell in the crosstabulation tables. In addition, a number of
542 statistics can be calculated for each table itself.
544 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
545 number of dimensions is permitted, and any number of variables per
546 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
547 times as needed. This is the only required subcommand in @dfn{general
550 Occasionally, one may want to invoke a special mode called @dfn{integer
551 mode}. Normally, in general mode, @pspp{} automatically determines
552 what values occur in the data. In integer mode, the user specifies the
553 range of values that the data assumes. To invoke this mode, specify the
554 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
555 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
556 the range are truncated to the nearest integer, then assigned to that
557 value. If values occur outside this range, they are discarded. When it
558 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
561 In general mode, numeric and string variables may be specified on
562 TABLES. In integer mode, only numeric variables are allowed.
564 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
565 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
566 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
567 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
568 integer mode, user-missing values are included in tables but marked with
569 an @samp{M} (for ``missing'') and excluded from statistical
572 Currently the @subcmd{WRITE} subcommand is ignored.
574 The @subcmd{FORMAT} subcommand controls the characteristics of the
575 crosstabulation tables to be displayed. It has a number of possible
580 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
581 @subcmd{NOTABLES} suppresses them.
584 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
585 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
589 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
590 @subcmd{DVALUE} asserts a descending sort order.
593 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
596 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
599 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
600 crosstabulation table. The possible settings are:
616 Standardized residual.
618 Adjusted standardized residual.
622 Suppress cells entirely.
625 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
626 @subcmd{COLUMN}, and @subcmd{TOTAL}.
627 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
630 The @subcmd{STATISTICS} subcommand selects statistics for computation:
637 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
638 correction, linear-by-linear association.
642 Contingency coefficient.
646 Uncertainty coefficient.
662 Spearman correlation, Pearson's r.
669 Selected statistics are only calculated when appropriate for the
670 statistic. Certain statistics require tables of a particular size, and
671 some statistics are calculated only in integer mode.
673 @samp{/STATISTICS} without any settings selects CHISQ. If the
674 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
677 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
678 variables on each table.
679 If a table has more than two variables, the counts for the third and subsequent levels
680 will be aggregated and the chart will be produces as if there were only two variables.
683 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
684 following limitations:
688 Significance of some symmetric and directional measures is not calculated.
690 Asymptotic standard error is not calculated for
691 Goodman and Kruskal's tau or symmetric Somers' d.
693 Approximate T is not calculated for symmetric uncertainty coefficient.
696 Fixes for any of these deficiencies would be welcomed.
702 @cindex factor analysis
703 @cindex principal components analysis
704 @cindex principal axis factoring
705 @cindex data reduction
708 FACTOR VARIABLES=@var{var_list}
710 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
712 [ /EXTRACTION=@{PC, PAF@}]
714 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
716 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
720 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
722 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
724 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
727 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
728 common factors in the data or for data reduction purposes.
730 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
732 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
733 If @subcmd{PC} is specified, then Principal Components Analysis is used.
734 If @subcmd{PAF} is specified, then Principal Axis Factoring is
735 used. By default Principal Components Analysis will be used.
737 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
738 Three orthogonal rotation methods are available:
739 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
740 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
741 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
742 The default value of @var{k} is 5.
743 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
744 rotation on the data.
746 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
747 to be analysed. By default, the correlation matrix is analysed.
749 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
752 @item @subcmd{UNIVARIATE}
753 A table of mean values, standard deviations and total weights are printed.
754 @item @subcmd{INITIAL}
755 Initial communalities and eigenvalues are printed.
756 @item @subcmd{EXTRACTION}
757 Extracted communalities and eigenvalues are printed.
758 @item @subcmd{ROTATION}
759 Rotated communalities and eigenvalues are printed.
760 @item @subcmd{CORRELATION}
761 The correlation matrix is printed.
762 @item @subcmd{COVARIANCE}
763 The covariance matrix is printed.
765 The determinant of the correlation or covariance matrix is printed.
767 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
769 The significance of the elements of correlation matrix is printed.
771 All of the above are printed.
772 @item @subcmd{DEFAULT}
773 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
776 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
777 which factors (components) should be retained.
779 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
780 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
781 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
782 performed, and all coefficients will be printed.
784 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
785 If @subcmd{FACTORS(@var{n})} is
786 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
788 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
789 The default value of @var{l} is 1.
790 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
791 extraction (such as Principal Axis Factoring) are used.
792 @subcmd{ECONVERGE(@var{delta})} specifies that
793 iteration should cease when
794 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
795 default value of @var{delta} is 0.001.
796 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
797 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
799 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
800 If @subcmd{EXTRACTION} follows, it affects convergence.
801 If @subcmd{ROTATION} follows, it affects rotation.
802 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
803 The default value of @var{m} is 25.
805 The @cmd{MISSING} subcommand determines the handling of missing variables.
806 If @subcmd{INCLUDE} is set, then user-missing values are included in the
807 calculations, but system-missing values are not.
808 If @subcmd{EXCLUDE} is set, which is the default, user-missing
809 values are excluded as well as system-missing values.
811 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
812 whenever any variable specified in the @cmd{VARIABLES} subcommand
813 contains a missing value.
814 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
815 values for the particular coefficient are missing.
816 The default is @subcmd{LISTWISE}.
818 @node LOGISTIC REGRESSION
819 @section LOGISTIC REGRESSION
821 @vindex LOGISTIC REGRESSION
822 @cindex logistic regression
823 @cindex bivariate logistic regression
826 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
828 [/CATEGORICAL = @var{categorical_predictors}]
830 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
832 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
834 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
835 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
836 [CUT(@var{cut_point})]]
838 [/MISSING = @{INCLUDE|EXCLUDE@}]
841 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
842 variable in terms of one or more predictor variables.
844 The minimum command is
846 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
848 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
849 are the predictor variables whose coefficients the procedure estimates.
851 By default, a constant term is included in the model.
852 Hence, the full model is
855 = b_0 + b_1 {\bf x_1}
861 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
862 Simple variables as well as interactions between variables may be listed here.
864 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
865 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
867 An iterative Newton-Raphson procedure is used to fit the model.
868 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
869 and other parameters.
870 The value of @var{cut_point} is used in the classification table. It is the
871 threshold above which predicted values are considered to be 1. Values
872 of @var{cut_point} must lie in the range [0,1].
873 During iterations, if any one of the stopping criteria are satisfied, the procedure is
875 The stopping criteria are:
877 @item The number of iterations exceeds @var{max_iterations}.
878 The default value of @var{max_iterations} is 20.
879 @item The change in the all coefficient estimates are less than @var{min_delta}.
880 The default value of @var{min_delta} is 0.001.
881 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
882 The default value of @var{min_delta} is zero.
883 This means that this criterion is disabled.
884 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
885 In other words, the probabilities are close to zero or one.
886 The default value of @var{min_epsilon} is 0.00000001.
890 The @subcmd{PRINT} subcommand controls the display of optional statistics.
891 Currently there is one such option, @subcmd{CI}, which indicates that the
892 confidence interval of the odds ratio should be displayed as well as its value.
893 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
894 confidence level of the desired confidence interval.
896 The @subcmd{MISSING} subcommand determines the handling of missing
898 If @subcmd{INCLUDE} is set, then user-missing values are included in the
899 calculations, but system-missing values are not.
900 If @subcmd{EXCLUDE} is set, which is the default, user-missing
901 values are excluded as well as system-missing values.
913 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
915 [ /@{@var{var_list}@}
916 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
918 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
919 [VARIANCE] [KURT] [SEKURT]
920 [SKEW] [SESKEW] [FIRST] [LAST]
921 [HARMONIC] [GEOMETRIC]
926 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
929 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
930 statistics, either for the dataset as a whole or for categories of data.
932 The simplest form of the command is
936 @noindent which calculates the mean, count and standard deviation for @var{v}.
937 If you specify a grouping variable, for example
939 MEANS @var{v} BY @var{g}.
941 @noindent then the means, counts and standard deviations for @var{v} after having
942 been grouped by @var{g} will be calculated.
943 Instead of the mean, count and standard deviation, you could specify the statistics
944 in which you are interested:
946 MEANS @var{x} @var{y} BY @var{g}
947 /CELLS = HARMONIC SUM MIN.
949 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
952 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
956 @cindex arithmetic mean
959 The count of the values.
960 @item @subcmd{STDDEV}
961 The standard deviation.
962 @item @subcmd{SEMEAN}
963 The standard error of the mean.
965 The sum of the values.
971 The difference between the maximum and minimum values.
972 @item @subcmd{VARIANCE}
975 The first value in the category.
977 The last value in the category.
980 @item @subcmd{SESKEW}
981 The standard error of the skewness.
984 @item @subcmd{SEKURT}
985 The standard error of the kurtosis.
986 @item @subcmd{HARMONIC}
987 @cindex harmonic mean
989 @item @subcmd{GEOMETRIC}
990 @cindex geometric mean
994 In addition, three special keywords are recognized:
996 @item @subcmd{DEFAULT}
997 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
999 All of the above statistics will be calculated.
1001 No statistics will be calculated (only a summary will be shown).
1005 More than one @dfn{table} can be specified in a single command.
1006 Each table is separated by a @samp{/}. For
1010 @var{c} @var{d} @var{e} BY @var{x}
1011 /@var{a} @var{b} BY @var{x} @var{y}
1012 /@var{f} BY @var{y} BY @var{z}.
1014 has three tables (the @samp{TABLE =} is optional).
1015 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1016 and a single categorical variable @var{x}.
1017 The second table has two dependent variables @var{a} and @var{b},
1018 and two categorical variables @var{x} and @var{y}.
1019 The third table has a single dependent variables @var{f}
1020 and a categorical variable formed by the combination of @var{y} and @var{z}.
1023 By default values are omitted from the analysis only if missing values
1024 (either system missing or user missing)
1025 for any of the variables directly involved in their calculation are
1027 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1028 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1030 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1031 in the table specification currently being processed, regardless of
1032 whether it is needed to calculate the statistic.
1034 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1035 variables or in the categorical variables should be taken at their face
1036 value, and not excluded.
1038 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1039 variables should be taken at their face value, however cases which
1040 have user missing values for the categorical variables should be omitted
1041 from the calculation.
1047 @cindex nonparametric tests
1052 nonparametric test subcommands
1057 [ /STATISTICS=@{DESCRIPTIVES@} ]
1059 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1061 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1064 @cmd{NPAR TESTS} performs nonparametric tests.
1065 Non parametric tests make very few assumptions about the distribution of the
1067 One or more tests may be specified by using the corresponding subcommand.
1068 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1069 produces for each variable that is the subject of any test.
1071 Certain tests may take a long time to execute, if an exact figure is required.
1072 Therefore, by default asymptotic approximations are used unless the
1073 subcommand @subcmd{/METHOD=EXACT} is specified.
1074 Exact tests give more accurate results, but may take an unacceptably long
1075 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1076 after which the test will be abandoned, and a warning message printed.
1077 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1078 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1083 * BINOMIAL:: Binomial Test
1084 * CHISQUARE:: Chisquare Test
1085 * COCHRAN:: Cochran Q Test
1086 * FRIEDMAN:: Friedman Test
1087 * KENDALL:: Kendall's W Test
1088 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1089 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1090 * MANN-WHITNEY:: Mann Whitney U Test
1091 * MCNEMAR:: McNemar Test
1092 * MEDIAN:: Median Test
1094 * SIGN:: The Sign Test
1095 * WILCOXON:: Wilcoxon Signed Ranks Test
1100 @subsection Binomial test
1102 @cindex binomial test
1105 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1108 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1109 variable with that of a binomial distribution.
1110 The variable @var{p} specifies the test proportion of the binomial
1112 The default value of 0.5 is assumed if @var{p} is omitted.
1114 If a single value appears after the variable list, then that value is
1115 used as the threshold to partition the observed values. Values less
1116 than or equal to the threshold value form the first category. Values
1117 greater than the threshold form the second category.
1119 If two values appear after the variable list, then they will be used
1120 as the values which a variable must take to be in the respective
1122 Cases for which a variable takes a value equal to neither of the specified
1123 values, take no part in the test for that variable.
1125 If no values appear, then the variable must assume dichotomous
1127 If more than two distinct, non-missing values for a variable
1128 under test are encountered then an error occurs.
1130 If the test proportion is equal to 0.5, then a two tailed test is
1131 reported. For any other test proportion, a one tailed test is
1133 For one tailed tests, if the test proportion is less than
1134 or equal to the observed proportion, then the significance of
1135 observing the observed proportion or more is reported.
1136 If the test proportion is more than the observed proportion, then the
1137 significance of observing the observed proportion or less is reported.
1138 That is to say, the test is always performed in the observed
1141 @pspp{} uses a very precise approximation to the gamma function to
1142 compute the binomial significance. Thus, exact results are reported
1143 even for very large sample sizes.
1148 @subsection Chisquare Test
1150 @cindex chisquare test
1154 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1158 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1159 between the expected and observed frequencies of the categories of a variable.
1160 Optionally, a range of values may appear after the variable list.
1161 If a range is given, then non integer values are truncated, and values
1162 outside the specified range are excluded from the analysis.
1164 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1166 There must be exactly one non-zero expected value, for each observed
1167 category, or the @subcmd{EQUAL} keyword must be specified.
1168 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1169 consecutive expected categories all taking a frequency of @var{f}.
1170 The frequencies given are proportions, not absolute frequencies. The
1171 sum of the frequencies need not be 1.
1172 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1177 @subsection Cochran Q Test
1179 @cindex Cochran Q test
1180 @cindex Q, Cochran Q
1183 [ /COCHRAN = @var{var_list} ]
1186 The Cochran Q test is used to test for differences between three or more groups.
1187 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1189 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1192 @subsection Friedman Test
1194 @cindex Friedman test
1197 [ /FRIEDMAN = @var{var_list} ]
1200 The Friedman test is used to test for differences between repeated measures when
1201 there is no indication that the distributions are normally distributed.
1203 A list of variables which contain the measured data must be given. The procedure
1204 prints the sum of ranks for each variable, the test statistic and its significance.
1207 @subsection Kendall's W Test
1209 @cindex Kendall's W test
1210 @cindex coefficient of concordance
1213 [ /KENDALL = @var{var_list} ]
1216 The Kendall test investigates whether an arbitrary number of related samples come from the
1218 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1219 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1220 unity indicates complete agreement.
1223 @node KOLMOGOROV-SMIRNOV
1224 @subsection Kolmogorov-Smirnov Test
1225 @vindex KOLMOGOROV-SMIRNOV
1227 @cindex Kolmogorov-Smirnov test
1230 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1233 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1234 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1235 Normal, Uniform, Poisson and Exponential.
1237 Ideally you should provide the parameters of the distribution against which you wish to test
1238 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1239 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1241 However, if the parameters are omitted they will be imputed from the data. Imputing the
1242 parameters reduces the power of the test so should be avoided if possible.
1244 In the following example, two variables @var{score} and @var{age} are tested to see if
1245 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1248 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1250 If the variables need to be tested against different distributions, then a separate
1251 subcommand must be used. For example the following syntax tests @var{score} against
1252 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1253 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1256 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1257 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1260 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1262 @node KRUSKAL-WALLIS
1263 @subsection Kruskal-Wallis Test
1264 @vindex KRUSKAL-WALLIS
1266 @cindex Kruskal-Wallis test
1269 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1272 The Kruskal-Wallis test is used to compare data from an
1273 arbitrary number of populations. It does not assume normality.
1274 The data to be compared are specified by @var{var_list}.
1275 The categorical variable determining the groups to which the
1276 data belongs is given by @var{var}. The limits @var{lower} and
1277 @var{upper} specify the valid range of @var{var}. Any cases for
1278 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1281 The mean rank of each group as well as the chi-squared value and significance
1282 of the test will be printed.
1283 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1287 @subsection Mann-Whitney U Test
1288 @vindex MANN-WHITNEY
1290 @cindex Mann-Whitney U test
1291 @cindex U, Mann-Whitney U
1294 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1297 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1298 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}.
1299 @var{Var} may be either a string or an alpha variable.
1300 @var{Group1} and @var{group2} specify the
1301 two values of @var{var} which determine the groups of the test data.
1302 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1304 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1305 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1308 @subsection McNemar Test
1310 @cindex McNemar test
1313 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1316 Use McNemar's test to analyse the significance of the difference between
1317 pairs of correlated proportions.
1319 If the @code{WITH} keyword is omitted, then tests for all
1320 combinations of the listed variables are performed.
1321 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1322 is also given, then the number of variables preceding @code{WITH}
1323 must be the same as the number following it.
1324 In this case, tests for each respective pair of variables are
1326 If the @code{WITH} keyword is given, but the
1327 @code{(PAIRED)} keyword is omitted, then tests for each combination
1328 of variable preceding @code{WITH} against variable following
1329 @code{WITH} are performed.
1331 The data in each variable must be dichotomous. If there are more
1332 than two distinct variables an error will occur and the test will
1336 @subsection Median Test
1341 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1344 The median test is used to test whether independent samples come from
1345 populations with a common median.
1346 The median of the populations against which the samples are to be tested
1347 may be given in parentheses immediately after the
1348 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1349 union of all the samples.
1351 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1352 keyword @code{BY} must come next, and then the grouping variable. Two values
1353 in parentheses should follow. If the first value is greater than the second,
1354 then a 2 sample test is performed using these two values to determine the groups.
1355 If however, the first variable is less than the second, then a @i{k} sample test is
1356 conducted and the group values used are all values encountered which lie in the
1357 range [@var{value1},@var{value2}].
1361 @subsection Runs Test
1366 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1369 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1371 It works by examining the number of times a variable's value crosses a given threshold.
1372 The desired threshold must be specified within parentheses.
1373 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1374 Following the threshold specification comes the list of variables whose values are to be
1377 The subcommand shows the number of runs, the asymptotic significance based on the
1381 @subsection Sign Test
1386 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1389 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1391 The test does not make any assumptions about the
1392 distribution of the data.
1394 If the @code{WITH} keyword is omitted, then tests for all
1395 combinations of the listed variables are performed.
1396 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1397 is also given, then the number of variables preceding @code{WITH}
1398 must be the same as the number following it.
1399 In this case, tests for each respective pair of variables are
1401 If the @code{WITH} keyword is given, but the
1402 @code{(PAIRED)} keyword is omitted, then tests for each combination
1403 of variable preceding @code{WITH} against variable following
1404 @code{WITH} are performed.
1407 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1409 @cindex wilcoxon matched pairs signed ranks test
1412 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1415 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1417 The test does not make any assumptions about the variances of the samples.
1418 It does however assume that the distribution is symmetrical.
1420 If the @subcmd{WITH} keyword is omitted, then tests for all
1421 combinations of the listed variables are performed.
1422 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1423 is also given, then the number of variables preceding @subcmd{WITH}
1424 must be the same as the number following it.
1425 In this case, tests for each respective pair of variables are
1427 If the @subcmd{WITH} keyword is given, but the
1428 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1429 of variable preceding @subcmd{WITH} against variable following
1430 @subcmd{WITH} are performed.
1439 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1440 /CRITERIA=CIN(@var{confidence})
1444 TESTVAL=@var{test_value}
1445 /VARIABLES=@var{var_list}
1448 (Independent Samples mode.)
1449 GROUPS=var(@var{value1} [, @var{value2}])
1450 /VARIABLES=@var{var_list}
1453 (Paired Samples mode.)
1454 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1459 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1461 It operates in one of three modes:
1463 @item One Sample mode.
1464 @item Independent Groups mode.
1469 Each of these modes are described in more detail below.
1470 There are two optional subcommands which are common to all modes.
1472 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1473 in the tests. The default value is 0.95.
1476 The @cmd{MISSING} subcommand determines the handling of missing
1478 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1479 calculations, but system-missing values are not.
1480 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1481 values are excluded as well as system-missing values.
1482 This is the default.
1484 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1485 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1486 @subcmd{/GROUPS} subcommands contains a missing value.
1487 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1488 which they would be needed. This is the default.
1492 * One Sample Mode:: Testing against a hypothesized mean
1493 * Independent Samples Mode:: Testing two independent groups for equal mean
1494 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1497 @node One Sample Mode
1498 @subsection One Sample Mode
1500 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1501 This mode is used to test a population mean against a hypothesized
1503 The value given to the @subcmd{TESTVAL} subcommand is the value against
1504 which you wish to test.
1505 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1506 tell @pspp{} which variables you wish to test.
1508 @node Independent Samples Mode
1509 @subsection Independent Samples Mode
1511 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1513 This mode is used to test whether two groups of values have the
1514 same population mean.
1515 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1516 tell @pspp{} the dependent variables you wish to test.
1518 The variable given in the @subcmd{GROUPS} subcommand is the independent
1519 variable which determines to which group the samples belong.
1520 The values in parentheses are the specific values of the independent
1521 variable for each group.
1522 If the parentheses are omitted and no values are given, the default values
1523 of 1.0 and 2.0 are assumed.
1525 If the independent variable is numeric,
1526 it is acceptable to specify only one value inside the parentheses.
1527 If you do this, cases where the independent variable is
1528 greater than or equal to this value belong to the first group, and cases
1529 less than this value belong to the second group.
1530 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1531 the independent variable are excluded on a listwise basis, regardless
1532 of whether @subcmd{/MISSING=LISTWISE} was specified.
1535 @node Paired Samples Mode
1536 @subsection Paired Samples Mode
1538 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1539 Use this mode when repeated measures have been taken from the same
1541 If the @subcmd{WITH} keyword is omitted, then tables for all
1542 combinations of variables given in the @cmd{PAIRS} subcommand are
1544 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1545 is also given, then the number of variables preceding @subcmd{WITH}
1546 must be the same as the number following it.
1547 In this case, tables for each respective pair of variables are
1549 In the event that the @subcmd{WITH} keyword is given, but the
1550 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1551 of variable preceding @subcmd{WITH} against variable following
1552 @subcmd{WITH} are generated.
1559 @cindex analysis of variance
1564 [/VARIABLES = ] @var{var_list} BY @var{var}
1565 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1566 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1567 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1568 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1571 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1572 variables factored by a single independent variable.
1573 It is used to compare the means of a population
1574 divided into more than two groups.
1576 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1578 The list of variables must be followed by the @subcmd{BY} keyword and
1579 the name of the independent (or factor) variable.
1581 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1582 ancillary information. The options accepted are:
1585 Displays descriptive statistics about the groups factored by the independent
1588 Displays the Levene test of Homogeneity of Variance for the
1589 variables and their groups.
1592 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1593 differences between the groups.
1594 The subcommand must be followed by a list of numerals which are the
1595 coefficients of the groups to be tested.
1596 The number of coefficients must correspond to the number of distinct
1597 groups (or values of the independent variable).
1598 If the total sum of the coefficients are not zero, then @pspp{} will
1599 display a warning, but will proceed with the analysis.
1600 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1601 to specify different contrast tests.
1602 The @subcmd{MISSING} subcommand defines how missing values are handled.
1603 If @subcmd{LISTWISE} is specified then cases which have missing values for
1604 the independent variable or any dependent variable will be ignored.
1605 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1606 variable is missing or if the dependent variable currently being
1607 analysed is missing. The default is @subcmd{ANALYSIS}.
1608 A setting of @subcmd{EXCLUDE} means that variables whose values are
1609 user-missing are to be excluded from the analysis. A setting of
1610 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1612 Using the @code{POSTHOC} subcommand you can perform multiple
1613 pairwise comparisons on the data. The following comparison methods
1617 Least Significant Difference.
1618 @item @subcmd{TUKEY}
1619 Tukey Honestly Significant Difference.
1620 @item @subcmd{BONFERRONI}
1622 @item @subcmd{SCHEFFE}
1624 @item @subcmd{SIDAK}
1627 The Games-Howell test.
1631 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1632 that @var{value} should be used as the
1633 confidence level for which the posthoc tests will be performed.
1634 The default is 0.05.
1637 @section QUICK CLUSTER
1638 @vindex QUICK CLUSTER
1640 @cindex K-means clustering
1644 QUICK CLUSTER @var{var_list}
1645 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1646 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1649 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1650 dataset. This is useful when you wish to allocate cases into clusters
1651 of similar values and you already know the number of clusters.
1653 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1654 of the variables which contain the cluster data. Normally you will also
1655 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1656 number of clusters. If this is not given, then @var{k} defaults to 2.
1658 The command uses an iterative algorithm to determine the clusters for
1659 each case. It will continue iterating until convergence, or until @var{max_iter}
1660 iterations have been done. The default value of @var{max_iter} is 2.
1662 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1663 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1664 value and not as missing values.
1665 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1666 values are excluded as well as system-missing values.
1668 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1669 whenever any of the clustering variables contains a missing value.
1670 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1671 clustering variables contain missing values. Otherwise it is clustered
1672 on the basis of the non-missing values.
1673 The default is @subcmd{LISTWISE}.
1682 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1683 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1684 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1686 /MISSING=@{EXCLUDE,INCLUDE@}
1688 /RANK [INTO @var{var_list}]
1689 /NTILES(k) [INTO @var{var_list}]
1690 /NORMAL [INTO @var{var_list}]
1691 /PERCENT [INTO @var{var_list}]
1692 /RFRACTION [INTO @var{var_list}]
1693 /PROPORTION [INTO @var{var_list}]
1694 /N [INTO @var{var_list}]
1695 /SAVAGE [INTO @var{var_list}]
1698 The @cmd{RANK} command ranks variables and stores the results into new
1701 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1702 more variables whose values are to be ranked.
1703 After each variable, @samp{A} or @samp{D} may appear, indicating that
1704 the variable is to be ranked in ascending or descending order.
1705 Ascending is the default.
1706 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1707 which are to serve as group variables.
1708 In this case, the cases are gathered into groups, and ranks calculated
1711 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1712 default is to take the mean value of all the tied cases.
1714 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1715 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1716 functions are requested.
1718 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1719 variables created should appear in the output.
1721 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1722 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1723 If none are given, then the default is RANK.
1724 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1725 partitions into which values should be ranked.
1726 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1727 variables which are the variables to be created and receive the rank
1728 scores. There may be as many variables specified as there are
1729 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1730 then the variable names are automatically created.
1732 The @subcmd{MISSING} subcommand determines how user missing values are to be
1733 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1734 user-missing are to be excluded from the rank scores. A setting of
1735 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1737 @include regression.texi
1741 @section RELIABILITY
1746 /VARIABLES=@var{var_list}
1747 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1748 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1749 /SUMMARY=@{TOTAL,ALL@}
1750 /MISSING=@{EXCLUDE,INCLUDE@}
1753 @cindex Cronbach's Alpha
1754 The @cmd{RELIABILITY} command performs reliability analysis on the data.
1756 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1757 upon which analysis is to be performed.
1759 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1760 calculated for. If it is omitted, then analysis for all variables named
1761 in the @subcmd{VARIABLES} subcommand will be used.
1762 Optionally, the @var{name} parameter may be specified to set a string name
1765 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1766 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1767 then the variables are divided into 2 subsets. An optional parameter
1768 @var{n} may be given, to specify how many variables to be in the first subset.
1769 If @var{n} is omitted, then it defaults to one half of the variables in the
1770 scale, or one half minus one if there are an odd number of variables.
1771 The default model is @subcmd{ALPHA}.
1773 By default, any cases with user missing, or system missing values for
1775 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1776 The @subcmd{MISSING} subcommand determines whether user missing values are to
1777 be included or excluded in the analysis.
1779 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1780 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1781 analysis tested against the totals.
1789 @cindex Receiver Operating Characteristic
1790 @cindex Area under curve
1793 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1794 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1795 /PRINT = [ SE ] [ COORDINATES ]
1796 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1797 [ TESTPOS (@{LARGE,SMALL@}) ]
1798 [ CI (@var{confidence}) ]
1799 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1800 /MISSING=@{EXCLUDE,INCLUDE@}
1804 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1805 of a dataset, and to estimate the area under the curve.
1806 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1808 The mandatory @var{var_list} is the list of predictor variables.
1809 The variable @var{state_var} is the variable whose values represent the actual states,
1810 and @var{state_value} is the value of this variable which represents the positive state.
1812 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1813 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1814 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1815 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1816 By default, the curve is drawn with no reference line.
1818 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1819 Two additional tables are available.
1820 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1822 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1824 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1826 The @subcmd{CRITERIA} subcommand has four optional parameters:
1828 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1829 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1830 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1832 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1833 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1835 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1837 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1838 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1839 exponential distribution estimate.
1840 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1841 equal to the number of negative actual states.
1842 The default is @subcmd{FREE}.
1844 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1847 The @subcmd{MISSING} subcommand determines whether user missing values are to
1848 be included or excluded in the analysis. The default behaviour is to
1850 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1851 or if the variable @var{state_var} is missing, then the entire case will be