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@}]
140 (These options are not currently implemented.)
146 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
148 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
149 (including median and mode) and percentiles,
150 @cmd{FREQUENCIES} can also output
151 histograms and pie charts.
153 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
154 variables to be analyzed.
156 The @subcmd{FORMAT} subcommand controls the output format. It has several
161 @subcmd{TABLE}, the default, causes a frequency table to be output for every
162 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
163 with a numeric argument causes them to be output except when there are
164 more than the specified number of values in the table.
167 Normally frequency tables are sorted in ascending order by value. This
168 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
169 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
170 respectively, by frequency count.
173 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
174 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
175 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
176 are included. System-missing values are never included in statistics,
177 but are listed in frequency tables.
179 The available @subcmd{STATISTICS} are the same as available
180 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
181 of @subcmd{MEDIAN}, the data's median
182 value, and MODE, the mode. (If there are multiple modes, the smallest
183 value is reported.) By default, the mean, standard deviation of the
184 mean, minimum, and maximum are reported for each variable.
187 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
188 The percentiles should be presented at a list of numbers between 0
190 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
191 boundaries of the data set divided into the specified number of ranges.
192 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
195 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
196 each specified numeric variable. The X axis by default ranges from
197 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
198 and @subcmd{MAXIMUM} keywords can set an explicit range. The number of
199 bins are 2IQR(x)n^-1/3 according to the Freedman-Diaconis rule. (Note that
200 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.)
201 Histograms are not created for string variables.
203 Specify @subcmd{NORMAL} to superimpose a normal curve on the
207 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
208 slice represents one value, with the size of the slice proportional to
209 the value's frequency. By default, all non-missing values are given
210 slices. The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
211 displayed slices to a given range of values. The @subcmd{MISSING} keyword adds
212 slices for missing values.
214 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and @subcmd{PIECHART} are accepted
215 but not currently honoured.
221 @cindex Exploratory data analysis
222 @cindex normality, testing
226 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
227 [BY @var{factor1} [BY @var{subfactor1}]
228 [ @var{factor2} [BY @var{subfactor2}]]
230 [ @var{factor3} [BY @var{subfactor3}]]
232 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
233 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
235 /COMPARE=@{GROUPS,VARIABLES@}
236 /ID=@var{identity_variable}
238 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
239 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
240 [@{NOREPORT,REPORT@}]
244 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
245 In particular, it is useful for testing how closely a distribution follows a
246 normal distribution, and for finding outliers and extreme values.
248 The @subcmd{VARIABLES} subcommand is mandatory.
249 It specifies the dependent variables and optionally variables to use as
250 factors for the analysis.
251 Variables listed before the first @subcmd{BY} keyword (if any) are the
253 The dependent variables may optionally be followed by a list of
254 factors which tell @pspp{} how to break down the analysis for each
257 Following the dependent variables, factors may be specified.
258 The factors (if desired) should be preceeded by a single @subcmd{BY} keyword.
259 The format for each factor is
261 @var{factorvar} [BY @var{subfactorvar}].
263 Each unique combination of the values of @var{factorvar} and
264 @var{subfactorvar} divide the dataset into @dfn{cells}.
265 Statistics will be calculated for each cell
266 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
268 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
269 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
270 non-parametrics statistics.
271 @subcmd{EXTREME} produces a table showing the extremities of each cell.
272 A number in parentheses, @var{n} determines
273 how many upper and lower extremities to show.
274 The default number is 5.
276 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
277 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
278 as well as for each cell.
279 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
280 (unless no factor variables have been given).
281 These subcommands have no effect if there have been no factor variables
287 @cindex spreadlevel plot
288 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
289 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
290 @subcmd{SPREADLEVEL}.
291 The first three can be used to visualise how closely each cell conforms to a
292 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
293 how the variance of differs between factors.
294 Boxplots will also show you the outliers and extreme values.
296 @subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
297 bins, as approximately 1 + log2(n). (Note that @cmd{FREQUENCIES} uses a
298 different algorithm to find the bin size.)
300 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
301 median. It takes an optional parameter @var{t}, which specifies how the data
302 should be transformed prior to plotting.
303 The given value @var{t} is a power to which the data is raised. For example, if
304 @var{t} is given as 2, then the data will be squared.
305 Zero, however is a special value. If @var{t} is 0 or
306 is omitted, then data will be transformed by taking its natural logarithm instead of
307 raising to the power of @var{t}.
309 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
310 useful there is more than one dependent variable and at least one factor.
312 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
313 each of which contain boxplots for all the cells.
314 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
315 each containing one boxplot per dependent variable.
316 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
317 @subcmd{/COMPARE=GROUPS} were given.
319 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
320 @subcmd{/STATISTICS=EXTREME} has been given.
321 If given, it shoule provide the name of a variable which is to be used
322 to labels extreme values and outliers.
323 Numeric or string variables are permissible.
324 If the @subcmd{ID} subcommand is not given, then the casenumber will be used for
327 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
328 calculation of the descriptives command. The default is 95%.
331 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
332 and which algorithm to use for calculating them. The default is to
333 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
334 @subcmd{HAVERAGE} algorithm.
336 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
337 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
338 then then statistics for the unfactored dependent variables are
339 produced in addition to the factored variables. If there are no
340 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
343 The following example will generate descriptive statistics and histograms for
344 two variables @var{score1} and @var{score2}.
345 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
346 Therefore, the descriptives and histograms will be generated for each
348 of @var{gender} @emph{and} for each distinct combination of the values
349 of @var{gender} and @var{race}.
350 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
351 @var{score1} and @var{score2} covering the whole dataset are not produced.
353 EXAMINE @var{score1} @var{score2} BY
355 @var{gender} BY @var{culture}
356 /STATISTICS = DESCRIPTIVES
361 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
363 EXAMINE @var{height} @var{weight} BY
365 /STATISTICS = EXTREME (3)
370 In this example, we look at the height and weight of a sample of individuals and
371 how they differ between male and female.
372 A table showing the 3 largest and the 3 smallest values of @var{height} and
373 @var{weight} for each gender, and for the whole dataset will be shown.
374 Boxplots will also be produced.
375 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
376 shown in the same graphic, allowing us to easily see the difference between
378 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
379 used to label the extreme values.
382 If many dependent variables are specified, or if factor variables are
384 there are many distinct values, then @cmd{EXAMINE} will produce a very
385 large quantity of output.
391 @cindex Exploratory data analysis
392 @cindex normality, testing
396 /HISTOGRAM = @var{var}
397 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
398 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
399 [@{NOREPORT,REPORT@}]
403 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
404 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
405 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
409 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the data. The different
410 values of the optional third variable @var{var3} will result in different colours and/or
411 markers for the plot. The following is an example for producing a scatterplot.
415 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
418 This example will produce a scatterplot where height is plotted versus weight. Depending
419 on the value of the gender variable, the colour of the datapoint is different. With
420 this plot it is possible to analyze gender differences for height vs. weight relation.
424 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
425 the histogram plot. For an alternative method to produce histograms @pxref{EXAMINE}. The
426 following example produces a histogram plot for variable weigth.
430 /HISTOGRAM = @var{weight}.
434 @section CORRELATIONS
439 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
444 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
445 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
448 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
449 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
450 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
454 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
455 for a set of variables. The significance of the coefficients are also given.
457 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
458 keyword is used, then a non-square correlation table will be produced.
459 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
460 and the variables following will be the columns of the table.
461 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
464 The @cmd{MISSING} subcommand determines the handling of missing variables.
465 If @subcmd{INCLUDE} is set, then user-missing values are included in the
466 calculations, but system-missing values are not.
467 If @subcmd{EXCLUDE} is set, which is the default, user-missing
468 values are excluded as well as system-missing values.
470 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
471 whenever any variable specified in any @cmd{/VARIABLES} subcommand
472 contains a missing value.
473 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
474 values for the particular coefficient are missing.
475 The default is @subcmd{PAIRWISE}.
477 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
478 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
479 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
480 The default is @subcmd{TWOTAIL}.
482 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
483 0.05 are highlighted.
484 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
487 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
488 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
489 estimator of the standard deviation are displayed.
490 These statistics will be displayed in a separated table, for all the variables listed
491 in any @subcmd{/VARIABLES} subcommand.
492 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
493 be displayed for each pair of variables.
494 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
502 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
503 /MISSING=@{TABLE,INCLUDE,REPORT@}
504 /WRITE=@{NONE,CELLS,ALL@}
505 /FORMAT=@{TABLES,NOTABLES@}
510 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
511 ASRESIDUAL,ALL,NONE@}
512 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
513 KAPPA,ETA,CORR,ALL,NONE@}
516 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
519 The @cmd{CROSSTABS} procedure displays crosstabulation
520 tables requested by the user. It can calculate several statistics for
521 each cell in the crosstabulation tables. In addition, a number of
522 statistics can be calculated for each table itself.
524 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
525 number of dimensions is permitted, and any number of variables per
526 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
527 times as needed. This is the only required subcommand in @dfn{general
530 Occasionally, one may want to invoke a special mode called @dfn{integer
531 mode}. Normally, in general mode, @pspp{} automatically determines
532 what values occur in the data. In integer mode, the user specifies the
533 range of values that the data assumes. To invoke this mode, specify the
534 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
535 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
536 the range are truncated to the nearest integer, then assigned to that
537 value. If values occur outside this range, they are discarded. When it
538 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
541 In general mode, numeric and string variables may be specified on
542 TABLES. In integer mode, only numeric variables are allowed.
544 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
545 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
546 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
547 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
548 integer mode, user-missing values are included in tables but marked with
549 an @samp{M} (for ``missing'') and excluded from statistical
552 Currently the @subcmd{WRITE} subcommand is ignored.
554 The @subcmd{FORMAT} subcommand controls the characteristics of the
555 crosstabulation tables to be displayed. It has a number of possible
560 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
561 @subcmd{NOTABLES} suppresses them.
564 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
565 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
569 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
570 @subcmd{DVALUE} asserts a descending sort order.
573 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
576 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
579 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
580 crosstabulation table. The possible settings are:
596 Standardized residual.
598 Adjusted standardized residual.
602 Suppress cells entirely.
605 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
606 @subcmd{COLUMN}, and @subcmd{TOTAL}.
607 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
610 The @subcmd{STATISTICS} subcommand selects statistics for computation:
617 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
618 correction, linear-by-linear association.
622 Contingency coefficient.
626 Uncertainty coefficient.
642 Spearman correlation, Pearson's r.
649 Selected statistics are only calculated when appropriate for the
650 statistic. Certain statistics require tables of a particular size, and
651 some statistics are calculated only in integer mode.
653 @samp{/STATISTICS} without any settings selects CHISQ. If the
654 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
656 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
661 Significance of some symmetric and directional measures is not calculated.
663 Asymptotic standard error is not calculated for
664 Goodman and Kruskal's tau or symmetric Somers' d.
666 Approximate T is not calculated for symmetric uncertainty coefficient.
669 Fixes for any of these deficiencies would be welcomed.
675 @cindex factor analysis
676 @cindex principal components analysis
677 @cindex principal axis factoring
678 @cindex data reduction
681 FACTOR VARIABLES=@var{var_list}
683 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
685 [ /EXTRACTION=@{PC, PAF@}]
687 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
689 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
693 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
695 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
697 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
700 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
701 common factors in the data or for data reduction purposes.
703 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
705 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
706 If @subcmd{PC} is specified, then Principal Components Analysis is used.
707 If @subcmd{PAF} is specified, then Principal Axis Factoring is
708 used. By default Principal Components Analysis will be used.
710 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
711 Three orthogonal rotation methods are available:
712 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
713 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
714 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
715 The default value of @var{k} is 5.
716 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
717 rotation on the data.
719 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
720 to be analysed. By default, the correlation matrix is analysed.
722 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
725 @item @subcmd{UNIVARIATE}
726 A table of mean values, standard deviations and total weights are printed.
727 @item @subcmd{INITIAL}
728 Initial communalities and eigenvalues are printed.
729 @item @subcmd{EXTRACTION}
730 Extracted communalities and eigenvalues are printed.
731 @item @subcmd{ROTATION}
732 Rotated communalities and eigenvalues are printed.
733 @item @subcmd{CORRELATION}
734 The correlation matrix is printed.
735 @item @subcmd{COVARIANCE}
736 The covariance matrix is printed.
738 The determinant of the correlation or covariance matrix is printed.
740 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
742 The significance of the elements of correlation matrix is printed.
744 All of the above are printed.
745 @item @subcmd{DEFAULT}
746 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
749 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
750 which factors (components) should be retained.
752 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
753 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
754 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
755 performed, and all coefficients will be printed.
757 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
758 If @subcmd{FACTORS(@var{n})} is
759 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
761 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
762 The default value of @var{l} is 1.
763 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
764 extraction (such as Principal Axis Factoring) are used.
765 @subcmd{ECONVERGE(@var{delta})} specifies that
766 iteration should cease when
767 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
768 default value of @var{delta} is 0.001.
769 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
770 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
772 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
773 If @subcmd{EXTRACTION} follows, it affects convergence.
774 If @subcmd{ROTATION} follows, it affects rotation.
775 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
776 The default value of @var{m} is 25.
778 The @cmd{MISSING} subcommand determines the handling of missing variables.
779 If @subcmd{INCLUDE} is set, then user-missing values are included in the
780 calculations, but system-missing values are not.
781 If @subcmd{EXCLUDE} is set, which is the default, user-missing
782 values are excluded as well as system-missing values.
784 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
785 whenever any variable specified in the @cmd{VARIABLES} subcommand
786 contains a missing value.
787 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
788 values for the particular coefficient are missing.
789 The default is @subcmd{LISTWISE}.
791 @node LOGISTIC REGRESSION
792 @section LOGISTIC REGRESSION
794 @vindex LOGISTIC REGRESSION
795 @cindex logistic regression
796 @cindex bivariate logistic regression
799 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
801 [/CATEGORICAL = @var{categorical_predictors}]
803 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
805 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
807 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
808 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
809 [CUT(@var{cut_point})]]
811 [/MISSING = @{INCLUDE|EXCLUDE@}]
814 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
815 variable in terms of one or more predictor variables.
817 The minimum command is
819 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
821 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
822 are the predictor variables whose coefficients the procedure estimates.
824 By default, a constant term is included in the model.
825 Hence, the full model is
828 = b_0 + b_1 {\bf x_1}
834 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
835 Simple variables as well as interactions between variables may be listed here.
837 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
838 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
840 An iterative Newton-Raphson procedure is used to fit the model.
841 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
842 and other parameters.
843 The value of @var{cut_point} is used in the classification table. It is the
844 threshold above which predicted values are considered to be 1. Values
845 of @var{cut_point} must lie in the range [0,1].
846 During iterations, if any one of the stopping criteria are satisfied, the procedure is
848 The stopping criteria are:
850 @item The number of iterations exceeds @var{max_iterations}.
851 The default value of @var{max_iterations} is 20.
852 @item The change in the all coefficient estimates are less than @var{min_delta}.
853 The default value of @var{min_delta} is 0.001.
854 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
855 The default value of @var{min_delta} is zero.
856 This means that this criterion is disabled.
857 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
858 In other words, the probabilities are close to zero or one.
859 The default value of @var{min_epsilon} is 0.00000001.
863 The @subcmd{PRINT} subcommand controls the display of optional statistics.
864 Currently there is one such option, @subcmd{CI}, which indicates that the
865 confidence interval of the odds ratio should be displayed as well as its value.
866 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
867 confidence level of the desired confidence interval.
869 The @subcmd{MISSING} subcommand determines the handling of missing
871 If @subcmd{INCLUDE} is set, then user-missing values are included in the
872 calculations, but system-missing values are not.
873 If @subcmd{EXCLUDE} is set, which is the default, user-missing
874 values are excluded as well as system-missing values.
886 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
888 [ /@{@var{var_list}@}
889 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
891 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
892 [VARIANCE] [KURT] [SEKURT]
893 [SKEW] [SESKEW] [FIRST] [LAST]
894 [HARMONIC] [GEOMETRIC]
899 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
902 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
903 statistics, either for the dataset as a whole or for categories of data.
905 The simplest form of the command is
909 @noindent which calculates the mean, count and standard deviation for @var{v}.
910 If you specify a grouping variable, for example
912 MEANS @var{v} BY @var{g}.
914 @noindent then the means, counts and standard deviations for @var{v} after having
915 been grouped by @var{g} will be calculated.
916 Instead of the mean, count and standard deviation, you could specify the statistics
917 in which you are interested:
919 MEANS @var{x} @var{y} BY @var{g}
920 /CELLS = HARMONIC SUM MIN.
922 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
925 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
929 @cindex arithmetic mean
932 The count of the values.
933 @item @subcmd{STDDEV}
934 The standard deviation.
935 @item @subcmd{SEMEAN}
936 The standard error of the mean.
938 The sum of the values.
944 The difference between the maximum and minimum values.
945 @item @subcmd{VARIANCE}
948 The first value in the category.
950 The last value in the category.
953 @item @subcmd{SESKEW}
954 The standard error of the skewness.
957 @item @subcmd{SEKURT}
958 The standard error of the kurtosis.
959 @item @subcmd{HARMONIC}
960 @cindex harmonic mean
962 @item @subcmd{GEOMETRIC}
963 @cindex geometric mean
967 In addition, three special keywords are recognized:
969 @item @subcmd{DEFAULT}
970 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
972 All of the above statistics will be calculated.
974 No statistics will be calculated (only a summary will be shown).
978 More than one @dfn{table} can be specified in a single command.
979 Each table is separated by a @samp{/}. For
983 @var{c} @var{d} @var{e} BY @var{x}
984 /@var{a} @var{b} BY @var{x} @var{y}
985 /@var{f} BY @var{y} BY @var{z}.
987 has three tables (the @samp{TABLE =} is optional).
988 The first table has three dependent variables @var{c}, @var{d} and @var{e}
989 and a single categorical variable @var{x}.
990 The second table has two dependent variables @var{a} and @var{b},
991 and two categorical variables @var{x} and @var{y}.
992 The third table has a single dependent variables @var{f}
993 and a categorical variable formed by the combination of @var{y} and @var{z}.
996 By default values are omitted from the analysis only if missing values
997 (either system missing or user missing)
998 for any of the variables directly involved in their calculation are
1000 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1001 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1003 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1004 in the table specification currently being processed, regardless of
1005 whether it is needed to calculate the statistic.
1007 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1008 variables or in the categorical variables should be taken at their face
1009 value, and not excluded.
1011 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1012 variables should be taken at their face value, however cases which
1013 have user missing values for the categorical variables should be omitted
1014 from the calculation.
1020 @cindex nonparametric tests
1025 nonparametric test subcommands
1030 [ /STATISTICS=@{DESCRIPTIVES@} ]
1032 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1034 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1037 @cmd{NPAR TESTS} performs nonparametric tests.
1038 Non parametric tests make very few assumptions about the distribution of the
1040 One or more tests may be specified by using the corresponding subcommand.
1041 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1042 produces for each variable that is the subject of any test.
1044 Certain tests may take a long time to execute, if an exact figure is required.
1045 Therefore, by default asymptotic approximations are used unless the
1046 subcommand @subcmd{/METHOD=EXACT} is specified.
1047 Exact tests give more accurate results, but may take an unacceptably long
1048 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1049 after which the test will be abandoned, and a warning message printed.
1050 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1051 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1056 * BINOMIAL:: Binomial Test
1057 * CHISQUARE:: Chisquare Test
1058 * COCHRAN:: Cochran Q Test
1059 * FRIEDMAN:: Friedman Test
1060 * KENDALL:: Kendall's W Test
1061 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1062 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1063 * MANN-WHITNEY:: Mann Whitney U Test
1064 * MCNEMAR:: McNemar Test
1065 * MEDIAN:: Median Test
1067 * SIGN:: The Sign Test
1068 * WILCOXON:: Wilcoxon Signed Ranks Test
1073 @subsection Binomial test
1075 @cindex binomial test
1078 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1081 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1082 variable with that of a binomial distribution.
1083 The variable @var{p} specifies the test proportion of the binomial
1085 The default value of 0.5 is assumed if @var{p} is omitted.
1087 If a single value appears after the variable list, then that value is
1088 used as the threshold to partition the observed values. Values less
1089 than or equal to the threshold value form the first category. Values
1090 greater than the threshold form the second category.
1092 If two values appear after the variable list, then they will be used
1093 as the values which a variable must take to be in the respective
1095 Cases for which a variable takes a value equal to neither of the specified
1096 values, take no part in the test for that variable.
1098 If no values appear, then the variable must assume dichotomous
1100 If more than two distinct, non-missing values for a variable
1101 under test are encountered then an error occurs.
1103 If the test proportion is equal to 0.5, then a two tailed test is
1104 reported. For any other test proportion, a one tailed test is
1106 For one tailed tests, if the test proportion is less than
1107 or equal to the observed proportion, then the significance of
1108 observing the observed proportion or more is reported.
1109 If the test proportion is more than the observed proportion, then the
1110 significance of observing the observed proportion or less is reported.
1111 That is to say, the test is always performed in the observed
1114 @pspp{} uses a very precise approximation to the gamma function to
1115 compute the binomial significance. Thus, exact results are reported
1116 even for very large sample sizes.
1121 @subsection Chisquare Test
1123 @cindex chisquare test
1127 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1131 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1132 between the expected and observed frequencies of the categories of a variable.
1133 Optionally, a range of values may appear after the variable list.
1134 If a range is given, then non integer values are truncated, and values
1135 outside the specified range are excluded from the analysis.
1137 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1139 There must be exactly one non-zero expected value, for each observed
1140 category, or the @subcmd{EQUAL} keywork must be specified.
1141 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1142 consecutive expected categories all taking a frequency of @var{f}.
1143 The frequencies given are proportions, not absolute frequencies. The
1144 sum of the frequencies need not be 1.
1145 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1150 @subsection Cochran Q Test
1152 @cindex Cochran Q test
1153 @cindex Q, Cochran Q
1156 [ /COCHRAN = @var{var_list} ]
1159 The Cochran Q test is used to test for differences between three or more groups.
1160 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1162 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1165 @subsection Friedman Test
1167 @cindex Friedman test
1170 [ /FRIEDMAN = @var{var_list} ]
1173 The Friedman test is used to test for differences between repeated measures when
1174 there is no indication that the distributions are normally distributed.
1176 A list of variables which contain the measured data must be given. The procedure
1177 prints the sum of ranks for each variable, the test statistic and its significance.
1180 @subsection Kendall's W Test
1182 @cindex Kendall's W test
1183 @cindex coefficient of concordance
1186 [ /KENDALL = @var{var_list} ]
1189 The Kendall test investigates whether an arbitrary number of related samples come from the
1191 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1192 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1193 unity indicates complete agreement.
1196 @node KOLMOGOROV-SMIRNOV
1197 @subsection Kolmogorov-Smirnov Test
1198 @vindex KOLMOGOROV-SMIRNOV
1200 @cindex Kolmogorov-Smirnov test
1203 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1206 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1207 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1208 Normal, Uniform, Poisson and Exponential.
1210 Ideally you should provide the parameters of the distribution against which you wish to test
1211 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1212 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1214 However, if the parameters are omitted they will be imputed from the data. Imputing the
1215 parameters reduces the power of the test so should be avoided if possible.
1217 In the following example, two variables @var{score} and @var{age} are tested to see if
1218 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1221 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1223 If the variables need to be tested against different distributions, then a separate
1224 subcommand must be used. For example the following syntax tests @var{score} against
1225 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1226 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1229 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1230 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1233 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1235 @node KRUSKAL-WALLIS
1236 @subsection Kruskal-Wallis Test
1237 @vindex KRUSKAL-WALLIS
1239 @cindex Kruskal-Wallis test
1242 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1245 The Kruskal-Wallis test is used to compare data from an
1246 arbitrary number of populations. It does not assume normality.
1247 The data to be compared are specified by @var{var_list}.
1248 The categorical variable determining the groups to which the
1249 data belongs is given by @var{var}. The limits @var{lower} and
1250 @var{upper} specify the valid range of @var{var}. Any cases for
1251 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1254 The mean rank of each group as well as the chi-squared value and significance
1255 of the test will be printed.
1256 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1260 @subsection Mann-Whitney U Test
1261 @vindex MANN-WHITNEY
1263 @cindex Mann-Whitney U test
1264 @cindex U, Mann-Whitney U
1267 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1270 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1271 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}.
1272 @var{Var} may be either a string or an alpha variable.
1273 @var{Group1} and @var{group2} specify the
1274 two values of @var{var} which determine the groups of the test data.
1275 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1277 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1278 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1281 @subsection McNemar Test
1283 @cindex McNemar test
1286 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1289 Use McNemar's test to analyse the significance of the difference between
1290 pairs of correlated proportions.
1292 If the @code{WITH} keyword is omitted, then tests for all
1293 combinations of the listed variables are performed.
1294 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1295 is also given, then the number of variables preceding @code{WITH}
1296 must be the same as the number following it.
1297 In this case, tests for each respective pair of variables are
1299 If the @code{WITH} keyword is given, but the
1300 @code{(PAIRED)} keyword is omitted, then tests for each combination
1301 of variable preceding @code{WITH} against variable following
1302 @code{WITH} are performed.
1304 The data in each variable must be dichotomous. If there are more
1305 than two distinct variables an error will occur and the test will
1309 @subsection Median Test
1314 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1317 The median test is used to test whether independent samples come from
1318 populations with a common median.
1319 The median of the populations against which the samples are to be tested
1320 may be given in parentheses immediately after the
1321 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1322 union of all the samples.
1324 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1325 keyword @code{BY} must come next, and then the grouping variable. Two values
1326 in parentheses should follow. If the first value is greater than the second,
1327 then a 2 sample test is performed using these two values to determine the groups.
1328 If however, the first variable is less than the second, then a @i{k} sample test is
1329 conducted and the group values used are all values encountered which lie in the
1330 range [@var{value1},@var{value2}].
1334 @subsection Runs Test
1339 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1342 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1344 It works by examining the number of times a variable's value crosses a given threshold.
1345 The desired threshold must be specified within parentheses.
1346 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1347 Following the threshold specification comes the list of variables whose values are to be
1350 The subcommand shows the number of runs, the asymptotic significance based on the
1354 @subsection Sign Test
1359 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1362 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1364 The test does not make any assumptions about the
1365 distribution of the data.
1367 If the @code{WITH} keyword is omitted, then tests for all
1368 combinations of the listed variables are performed.
1369 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1370 is also given, then the number of variables preceding @code{WITH}
1371 must be the same as the number following it.
1372 In this case, tests for each respective pair of variables are
1374 If the @code{WITH} keyword is given, but the
1375 @code{(PAIRED)} keyword is omitted, then tests for each combination
1376 of variable preceding @code{WITH} against variable following
1377 @code{WITH} are performed.
1380 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1382 @cindex wilcoxon matched pairs signed ranks test
1385 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1388 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1390 The test does not make any assumptions about the variances of the samples.
1391 It does however assume that the distribution is symetrical.
1393 If the @subcmd{WITH} keyword is omitted, then tests for all
1394 combinations of the listed variables are performed.
1395 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1396 is also given, then the number of variables preceding @subcmd{WITH}
1397 must be the same as the number following it.
1398 In this case, tests for each respective pair of variables are
1400 If the @subcmd{WITH} keyword is given, but the
1401 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1402 of variable preceding @subcmd{WITH} against variable following
1403 @subcmd{WITH} are performed.
1412 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1413 /CRITERIA=CIN(@var{confidence})
1417 TESTVAL=@var{test_value}
1418 /VARIABLES=@var{var_list}
1421 (Independent Samples mode.)
1422 GROUPS=var(@var{value1} [, @var{value2}])
1423 /VARIABLES=@var{var_list}
1426 (Paired Samples mode.)
1427 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1432 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1434 It operates in one of three modes:
1436 @item One Sample mode.
1437 @item Independent Groups mode.
1442 Each of these modes are described in more detail below.
1443 There are two optional subcommands which are common to all modes.
1445 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1446 in the tests. The default value is 0.95.
1449 The @cmd{MISSING} subcommand determines the handling of missing
1451 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1452 calculations, but system-missing values are not.
1453 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1454 values are excluded as well as system-missing values.
1455 This is the default.
1457 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1458 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1459 @subcmd{/GROUPS} subcommands contains a missing value.
1460 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1461 which they would be needed. This is the default.
1465 * One Sample Mode:: Testing against a hypothesized mean
1466 * Independent Samples Mode:: Testing two independent groups for equal mean
1467 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1470 @node One Sample Mode
1471 @subsection One Sample Mode
1473 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1474 This mode is used to test a population mean against a hypothesized
1476 The value given to the @subcmd{TESTVAL} subcommand is the value against
1477 which you wish to test.
1478 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1479 tell @pspp{} which variables you wish to test.
1481 @node Independent Samples Mode
1482 @subsection Independent Samples Mode
1484 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1486 This mode is used to test whether two groups of values have the
1487 same population mean.
1488 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1489 tell @pspp{} the dependent variables you wish to test.
1491 The variable given in the @subcmd{GROUPS} subcommand is the independent
1492 variable which determines to which group the samples belong.
1493 The values in parentheses are the specific values of the independent
1494 variable for each group.
1495 If the parentheses are omitted and no values are given, the default values
1496 of 1.0 and 2.0 are assumed.
1498 If the independent variable is numeric,
1499 it is acceptable to specify only one value inside the parentheses.
1500 If you do this, cases where the independent variable is
1501 greater than or equal to this value belong to the first group, and cases
1502 less than this value belong to the second group.
1503 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1504 the independent variable are excluded on a listwise basis, regardless
1505 of whether @subcmd{/MISSING=LISTWISE} was specified.
1508 @node Paired Samples Mode
1509 @subsection Paired Samples Mode
1511 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1512 Use this mode when repeated measures have been taken from the same
1514 If the @subcmd{WITH} keyword is omitted, then tables for all
1515 combinations of variables given in the @cmd{PAIRS} subcommand are
1517 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1518 is also given, then the number of variables preceding @subcmd{WITH}
1519 must be the same as the number following it.
1520 In this case, tables for each respective pair of variables are
1522 In the event that the @subcmd{WITH} keyword is given, but the
1523 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1524 of variable preceding @subcmd{WITH} against variable following
1525 @subcmd{WITH} are generated.
1532 @cindex analysis of variance
1537 [/VARIABLES = ] @var{var_list} BY @var{var}
1538 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1539 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1540 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1541 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1544 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1545 variables factored by a single independent variable.
1546 It is used to compare the means of a population
1547 divided into more than two groups.
1549 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1551 The list of variables must be followed by the @subcmd{BY} keyword and
1552 the name of the independent (or factor) variable.
1554 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1555 ancilliary information. The options accepted are:
1558 Displays descriptive statistics about the groups factored by the independent
1561 Displays the Levene test of Homogeneity of Variance for the
1562 variables and their groups.
1565 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1566 differences between the groups.
1567 The subcommand must be followed by a list of numerals which are the
1568 coefficients of the groups to be tested.
1569 The number of coefficients must correspond to the number of distinct
1570 groups (or values of the independent variable).
1571 If the total sum of the coefficients are not zero, then @pspp{} will
1572 display a warning, but will proceed with the analysis.
1573 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1574 to specify different contrast tests.
1575 The @subcmd{MISSING} subcommand defines how missing values are handled.
1576 If @subcmd{LISTWISE} is specified then cases which have missing values for
1577 the independent variable or any dependent variable will be ignored.
1578 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1579 variable is missing or if the dependent variable currently being
1580 analysed is missing. The default is @subcmd{ANALYSIS}.
1581 A setting of @subcmd{EXCLUDE} means that variables whose values are
1582 user-missing are to be excluded from the analysis. A setting of
1583 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1585 Using the @code{POSTHOC} subcommand you can perform multiple
1586 pairwise comparisons on the data. The following comparison methods
1590 Least Significant Difference.
1591 @item @subcmd{TUKEY}
1592 Tukey Honestly Significant Difference.
1593 @item @subcmd{BONFERRONI}
1595 @item @subcmd{SCHEFFE}
1597 @item @subcmd{SIDAK}
1600 The Games-Howell test.
1604 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1605 that @var{value} should be used as the
1606 confidence level for which the posthoc tests will be performed.
1607 The default is 0.05.
1610 @section QUICK CLUSTER
1611 @vindex QUICK CLUSTER
1613 @cindex K-means clustering
1617 QUICK CLUSTER @var{var_list}
1618 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1619 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1622 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1623 dataset. This is useful when you wish to allocate cases into clusters
1624 of similar values and you already know the number of clusters.
1626 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1627 of the variables which contain the cluster data. Normally you will also
1628 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1629 number of clusters. If this is not given, then @var{k} defaults to 2.
1631 The command uses an iterative algorithm to determine the clusters for
1632 each case. It will continue iterating until convergence, or until @var{max_iter}
1633 iterations have been done. The default value of @var{max_iter} is 2.
1635 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1636 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1637 value and not as missing values.
1638 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1639 values are excluded as well as system-missing values.
1641 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1642 whenever any of the clustering variables contains a missing value.
1643 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1644 clustering variables contain missing values. Otherwise it is clustered
1645 on the basis of the non-missing values.
1646 The default is @subcmd{LISTWISE}.
1655 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1656 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1657 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1659 /MISSING=@{EXCLUDE,INCLUDE@}
1661 /RANK [INTO @var{var_list}]
1662 /NTILES(k) [INTO @var{var_list}]
1663 /NORMAL [INTO @var{var_list}]
1664 /PERCENT [INTO @var{var_list}]
1665 /RFRACTION [INTO @var{var_list}]
1666 /PROPORTION [INTO @var{var_list}]
1667 /N [INTO @var{var_list}]
1668 /SAVAGE [INTO @var{var_list}]
1671 The @cmd{RANK} command ranks variables and stores the results into new
1674 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1675 more variables whose values are to be ranked.
1676 After each variable, @samp{A} or @samp{D} may appear, indicating that
1677 the variable is to be ranked in ascending or descending order.
1678 Ascending is the default.
1679 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1680 which are to serve as group variables.
1681 In this case, the cases are gathered into groups, and ranks calculated
1684 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1685 default is to take the mean value of all the tied cases.
1687 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1688 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1689 functions are requested.
1691 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1692 variables created should appear in the output.
1694 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1695 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1696 If none are given, then the default is RANK.
1697 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1698 partitions into which values should be ranked.
1699 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1700 variables which are the variables to be created and receive the rank
1701 scores. There may be as many variables specified as there are
1702 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1703 then the variable names are automatically created.
1705 The @subcmd{MISSING} subcommand determines how user missing values are to be
1706 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1707 user-missing are to be excluded from the rank scores. A setting of
1708 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1710 @include regression.texi
1714 @section RELIABILITY
1719 /VARIABLES=@var{var_list}
1720 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1721 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1722 /SUMMARY=@{TOTAL,ALL@}
1723 /MISSING=@{EXCLUDE,INCLUDE@}
1726 @cindex Cronbach's Alpha
1727 The @cmd{RELIABILTY} command performs reliability analysis on the data.
1729 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1730 upon which analysis is to be performed.
1732 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1733 calculated for. If it is omitted, then analysis for all variables named
1734 in the @subcmd{VARIABLES} subcommand will be used.
1735 Optionally, the @var{name} parameter may be specified to set a string name
1738 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1739 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1740 then the variables are divided into 2 subsets. An optional parameter
1741 @var{n} may be given, to specify how many variables to be in the first subset.
1742 If @var{n} is omitted, then it defaults to one half of the variables in the
1743 scale, or one half minus one if there are an odd number of variables.
1744 The default model is @subcmd{ALPHA}.
1746 By default, any cases with user missing, or system missing values for
1748 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1749 The @subcmd{MISSING} subcommand determines whether user missing values are to
1750 be included or excluded in the analysis.
1752 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1753 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1754 analysis tested against the totals.
1762 @cindex Receiver Operating Characteristic
1763 @cindex Area under curve
1766 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1767 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1768 /PRINT = [ SE ] [ COORDINATES ]
1769 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1770 [ TESTPOS (@{LARGE,SMALL@}) ]
1771 [ CI (@var{confidence}) ]
1772 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1773 /MISSING=@{EXCLUDE,INCLUDE@}
1777 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1778 of a dataset, and to estimate the area under the curve.
1779 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1781 The mandatory @var{var_list} is the list of predictor variables.
1782 The variable @var{state_var} is the variable whose values represent the actual states,
1783 and @var{state_value} is the value of this variable which represents the positive state.
1785 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1786 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1787 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1788 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1789 By default, the curve is drawn with no reference line.
1791 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1792 Two additional tables are available.
1793 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1795 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1797 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1799 The @subcmd{CRITERIA} subcommand has four optional parameters:
1801 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1802 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1803 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1805 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1806 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1808 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1810 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1811 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1812 exponential distribution estimate.
1813 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1814 equal to the number of negative actual states.
1815 The default is @subcmd{FREE}.
1817 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1820 The @subcmd{MISSING} subcommand determines whether user missing values are to
1821 be included or excluded in the analysis. The default behaviour is to
1823 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1824 or if the variable @var{state_var} is missing, then the entire case will be