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, 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 methods are available: @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
712 If don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
713 rotation on the data. Oblique rotations are not supported.
715 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
716 to be analysed. By default, the correlation matrix is analysed.
718 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
721 @item @subcmd{UNIVARIATE}
722 A table of mean values, standard deviations and total weights are printed.
723 @item @subcmd{INITIAL}
724 Initial communalities and eigenvalues are printed.
725 @item @subcmd{EXTRACTION}
726 Extracted communalities and eigenvalues are printed.
727 @item @subcmd{ROTATION}
728 Rotated communalities and eigenvalues are printed.
729 @item @subcmd{CORRELATION}
730 The correlation matrix is printed.
731 @item @subcmd{COVARIANCE}
732 The covariance matrix is printed.
734 The determinant of the correlation or covariance matrix is printed.
736 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
738 The significance of the elements of correlation matrix is printed.
740 All of the above are printed.
741 @item @subcmd{DEFAULT}
742 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
745 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
746 which factors (components) should be retained.
748 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
749 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
750 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
751 performed, and all coefficients will be printed.
753 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
754 If @subcmd{FACTORS(@var{n})} is
755 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
757 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
758 The default value of @var{l} is 1.
759 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
760 extraction (such as Principal Axis Factoring) are used.
761 @subcmd{ECONVERGE(@var{delta})} specifies that
762 iteration should cease when
763 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
764 default value of @var{delta} is 0.001.
765 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
766 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
768 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
769 If @subcmd{EXTRACTION} follows, it affects convergence.
770 If @subcmd{ROTATION} follows, it affects rotation.
771 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
772 The default value of @var{m} is 25.
774 The @cmd{MISSING} subcommand determines the handling of missing variables.
775 If @subcmd{INCLUDE} is set, then user-missing values are included in the
776 calculations, but system-missing values are not.
777 If @subcmd{EXCLUDE} is set, which is the default, user-missing
778 values are excluded as well as system-missing values.
780 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
781 whenever any variable specified in the @cmd{VARIABLES} subcommand
782 contains a missing value.
783 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
784 values for the particular coefficient are missing.
785 The default is @subcmd{LISTWISE}.
787 @node LOGISTIC REGRESSION
788 @section LOGISTIC REGRESSION
790 @vindex LOGISTIC REGRESSION
791 @cindex logistic regression
792 @cindex bivariate logistic regression
795 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
797 [/CATEGORICAL = @var{categorical_predictors}]
799 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
801 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
803 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
804 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
805 [CUT(@var{cut_point})]]
807 [/MISSING = @{INCLUDE|EXCLUDE@}]
810 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
811 variable in terms of one or more predictor variables.
813 The minimum command is
815 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
817 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
818 are the predictor variables whose coefficients the procedure estimates.
820 By default, a constant term is included in the model.
821 Hence, the full model is
824 = b_0 + b_1 {\bf x_1}
830 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
831 Simple variables as well as interactions between variables may be listed here.
833 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
834 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
836 An iterative Newton-Raphson procedure is used to fit the model.
837 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
838 and other parameters.
839 The value of @var{cut_point} is used in the classification table. It is the
840 threshold above which predicted values are considered to be 1. Values
841 of @var{cut_point} must lie in the range [0,1].
842 During iterations, if any one of the stopping criteria are satisfied, the procedure is
844 The stopping criteria are:
846 @item The number of iterations exceeds @var{max_iterations}.
847 The default value of @var{max_iterations} is 20.
848 @item The change in the all coefficient estimates are less than @var{min_delta}.
849 The default value of @var{min_delta} is 0.001.
850 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
851 The default value of @var{min_delta} is zero.
852 This means that this criterion is disabled.
853 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
854 In other words, the probabilities are close to zero or one.
855 The default value of @var{min_epsilon} is 0.00000001.
859 The @subcmd{PRINT} subcommand controls the display of optional statistics.
860 Currently there is one such option, @subcmd{CI}, which indicates that the
861 confidence interval of the odds ratio should be displayed as well as its value.
862 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
863 confidence level of the desired confidence interval.
865 The @subcmd{MISSING} subcommand determines the handling of missing
867 If @subcmd{INCLUDE} is set, then user-missing values are included in the
868 calculations, but system-missing values are not.
869 If @subcmd{EXCLUDE} is set, which is the default, user-missing
870 values are excluded as well as system-missing values.
882 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
884 [ /@{@var{var_list}@}
885 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
887 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
888 [VARIANCE] [KURT] [SEKURT]
889 [SKEW] [SESKEW] [FIRST] [LAST]
890 [HARMONIC] [GEOMETRIC]
895 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
898 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
899 statistics, either for the dataset as a whole or for categories of data.
901 The simplest form of the command is
905 @noindent which calculates the mean, count and standard deviation for @var{v}.
906 If you specify a grouping variable, for example
908 MEANS @var{v} BY @var{g}.
910 @noindent then the means, counts and standard deviations for @var{v} after having
911 been grouped by @var{g} will be calculated.
912 Instead of the mean, count and standard deviation, you could specify the statistics
913 in which you are interested:
915 MEANS @var{x} @var{y} BY @var{g}
916 /CELLS = HARMONIC SUM MIN.
918 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
921 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
925 @cindex arithmetic mean
928 The count of the values.
929 @item @subcmd{STDDEV}
930 The standard deviation.
931 @item @subcmd{SEMEAN}
932 The standard error of the mean.
934 The sum of the values.
940 The difference between the maximum and minimum values.
941 @item @subcmd{VARIANCE}
944 The first value in the category.
946 The last value in the category.
949 @item @subcmd{SESKEW}
950 The standard error of the skewness.
953 @item @subcmd{SEKURT}
954 The standard error of the kurtosis.
955 @item @subcmd{HARMONIC}
956 @cindex harmonic mean
958 @item @subcmd{GEOMETRIC}
959 @cindex geometric mean
963 In addition, three special keywords are recognized:
965 @item @subcmd{DEFAULT}
966 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
968 All of the above statistics will be calculated.
970 No statistics will be calculated (only a summary will be shown).
974 More than one @dfn{table} can be specified in a single command.
975 Each table is separated by a @samp{/}. For
979 @var{c} @var{d} @var{e} BY @var{x}
980 /@var{a} @var{b} BY @var{x} @var{y}
981 /@var{f} BY @var{y} BY @var{z}.
983 has three tables (the @samp{TABLE =} is optional).
984 The first table has three dependent variables @var{c}, @var{d} and @var{e}
985 and a single categorical variable @var{x}.
986 The second table has two dependent variables @var{a} and @var{b},
987 and two categorical variables @var{x} and @var{y}.
988 The third table has a single dependent variables @var{f}
989 and a categorical variable formed by the combination of @var{y} and @var{z}.
992 By default values are omitted from the analysis only if missing values
993 (either system missing or user missing)
994 for any of the variables directly involved in their calculation are
996 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
997 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
999 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1000 in the table specification currently being processed, regardless of
1001 whether it is needed to calculate the statistic.
1003 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1004 variables or in the categorical variables should be taken at their face
1005 value, and not excluded.
1007 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1008 variables should be taken at their face value, however cases which
1009 have user missing values for the categorical variables should be omitted
1010 from the calculation.
1016 @cindex nonparametric tests
1021 nonparametric test subcommands
1026 [ /STATISTICS=@{DESCRIPTIVES@} ]
1028 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1030 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1033 @cmd{NPAR TESTS} performs nonparametric tests.
1034 Non parametric tests make very few assumptions about the distribution of the
1036 One or more tests may be specified by using the corresponding subcommand.
1037 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1038 produces for each variable that is the subject of any test.
1040 Certain tests may take a long time to execute, if an exact figure is required.
1041 Therefore, by default asymptotic approximations are used unless the
1042 subcommand @subcmd{/METHOD=EXACT} is specified.
1043 Exact tests give more accurate results, but may take an unacceptably long
1044 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1045 after which the test will be abandoned, and a warning message printed.
1046 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1047 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1052 * BINOMIAL:: Binomial Test
1053 * CHISQUARE:: Chisquare Test
1054 * COCHRAN:: Cochran Q Test
1055 * FRIEDMAN:: Friedman Test
1056 * KENDALL:: Kendall's W Test
1057 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1058 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1059 * MANN-WHITNEY:: Mann Whitney U Test
1060 * MCNEMAR:: McNemar Test
1061 * MEDIAN:: Median Test
1063 * SIGN:: The Sign Test
1064 * WILCOXON:: Wilcoxon Signed Ranks Test
1069 @subsection Binomial test
1071 @cindex binomial test
1074 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1077 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1078 variable with that of a binomial distribution.
1079 The variable @var{p} specifies the test proportion of the binomial
1081 The default value of 0.5 is assumed if @var{p} is omitted.
1083 If a single value appears after the variable list, then that value is
1084 used as the threshold to partition the observed values. Values less
1085 than or equal to the threshold value form the first category. Values
1086 greater than the threshold form the second category.
1088 If two values appear after the variable list, then they will be used
1089 as the values which a variable must take to be in the respective
1091 Cases for which a variable takes a value equal to neither of the specified
1092 values, take no part in the test for that variable.
1094 If no values appear, then the variable must assume dichotomous
1096 If more than two distinct, non-missing values for a variable
1097 under test are encountered then an error occurs.
1099 If the test proportion is equal to 0.5, then a two tailed test is
1100 reported. For any other test proportion, a one tailed test is
1102 For one tailed tests, if the test proportion is less than
1103 or equal to the observed proportion, then the significance of
1104 observing the observed proportion or more is reported.
1105 If the test proportion is more than the observed proportion, then the
1106 significance of observing the observed proportion or less is reported.
1107 That is to say, the test is always performed in the observed
1110 @pspp{} uses a very precise approximation to the gamma function to
1111 compute the binomial significance. Thus, exact results are reported
1112 even for very large sample sizes.
1117 @subsection Chisquare Test
1119 @cindex chisquare test
1123 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1127 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1128 between the expected and observed frequencies of the categories of a variable.
1129 Optionally, a range of values may appear after the variable list.
1130 If a range is given, then non integer values are truncated, and values
1131 outside the specified range are excluded from the analysis.
1133 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1135 There must be exactly one non-zero expected value, for each observed
1136 category, or the @subcmd{EQUAL} keywork must be specified.
1137 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1138 consecutive expected categories all taking a frequency of @var{f}.
1139 The frequencies given are proportions, not absolute frequencies. The
1140 sum of the frequencies need not be 1.
1141 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1146 @subsection Cochran Q Test
1148 @cindex Cochran Q test
1149 @cindex Q, Cochran Q
1152 [ /COCHRAN = @var{var_list} ]
1155 The Cochran Q test is used to test for differences between three or more groups.
1156 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1158 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1161 @subsection Friedman Test
1163 @cindex Friedman test
1166 [ /FRIEDMAN = @var{var_list} ]
1169 The Friedman test is used to test for differences between repeated measures when
1170 there is no indication that the distributions are normally distributed.
1172 A list of variables which contain the measured data must be given. The procedure
1173 prints the sum of ranks for each variable, the test statistic and its significance.
1176 @subsection Kendall's W Test
1178 @cindex Kendall's W test
1179 @cindex coefficient of concordance
1182 [ /KENDALL = @var{var_list} ]
1185 The Kendall test investigates whether an arbitrary number of related samples come from the
1187 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1188 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1189 unity indicates complete agreement.
1192 @node KOLMOGOROV-SMIRNOV
1193 @subsection Kolmogorov-Smirnov Test
1194 @vindex KOLMOGOROV-SMIRNOV
1196 @cindex Kolmogorov-Smirnov test
1199 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1202 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1203 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1204 Normal, Uniform, Poisson and Exponential.
1206 Ideally you should provide the parameters of the distribution against which you wish to test
1207 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1208 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1210 However, if the parameters are omitted they will be imputed from the data. Imputing the
1211 parameters reduces the power of the test so should be avoided if possible.
1213 In the following example, two variables @var{score} and @var{age} are tested to see if
1214 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1217 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1219 If the variables need to be tested against different distributions, then a separate
1220 subcommand must be used. For example the following syntax tests @var{score} against
1221 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1222 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1225 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1226 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1229 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1231 @node KRUSKAL-WALLIS
1232 @subsection Kruskal-Wallis Test
1233 @vindex KRUSKAL-WALLIS
1235 @cindex Kruskal-Wallis test
1238 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1241 The Kruskal-Wallis test is used to compare data from an
1242 arbitrary number of populations. It does not assume normality.
1243 The data to be compared are specified by @var{var_list}.
1244 The categorical variable determining the groups to which the
1245 data belongs is given by @var{var}. The limits @var{lower} and
1246 @var{upper} specify the valid range of @var{var}. Any cases for
1247 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1250 The mean rank of each group as well as the chi-squared value and significance
1251 of the test will be printed.
1252 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1256 @subsection Mann-Whitney U Test
1257 @vindex MANN-WHITNEY
1259 @cindex Mann-Whitney U test
1260 @cindex U, Mann-Whitney U
1263 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1266 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1267 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}.
1268 @var{Var} may be either a string or an alpha variable.
1269 @var{Group1} and @var{group2} specify the
1270 two values of @var{var} which determine the groups of the test data.
1271 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1273 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1274 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1277 @subsection McNemar Test
1279 @cindex McNemar test
1282 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1285 Use McNemar's test to analyse the significance of the difference between
1286 pairs of correlated proportions.
1288 If the @code{WITH} keyword is omitted, then tests for all
1289 combinations of the listed variables are performed.
1290 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1291 is also given, then the number of variables preceding @code{WITH}
1292 must be the same as the number following it.
1293 In this case, tests for each respective pair of variables are
1295 If the @code{WITH} keyword is given, but the
1296 @code{(PAIRED)} keyword is omitted, then tests for each combination
1297 of variable preceding @code{WITH} against variable following
1298 @code{WITH} are performed.
1300 The data in each variable must be dichotomous. If there are more
1301 than two distinct variables an error will occur and the test will
1305 @subsection Median Test
1310 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1313 The median test is used to test whether independent samples come from
1314 populations with a common median.
1315 The median of the populations against which the samples are to be tested
1316 may be given in parentheses immediately after the
1317 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1318 union of all the samples.
1320 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1321 keyword @code{BY} must come next, and then the grouping variable. Two values
1322 in parentheses should follow. If the first value is greater than the second,
1323 then a 2 sample test is performed using these two values to determine the groups.
1324 If however, the first variable is less than the second, then a @i{k} sample test is
1325 conducted and the group values used are all values encountered which lie in the
1326 range [@var{value1},@var{value2}].
1330 @subsection Runs Test
1335 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1338 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1340 It works by examining the number of times a variable's value crosses a given threshold.
1341 The desired threshold must be specified within parentheses.
1342 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1343 Following the threshold specification comes the list of variables whose values are to be
1346 The subcommand shows the number of runs, the asymptotic significance based on the
1350 @subsection Sign Test
1355 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1358 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1360 The test does not make any assumptions about the
1361 distribution of the data.
1363 If the @code{WITH} keyword is omitted, then tests for all
1364 combinations of the listed variables are performed.
1365 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1366 is also given, then the number of variables preceding @code{WITH}
1367 must be the same as the number following it.
1368 In this case, tests for each respective pair of variables are
1370 If the @code{WITH} keyword is given, but the
1371 @code{(PAIRED)} keyword is omitted, then tests for each combination
1372 of variable preceding @code{WITH} against variable following
1373 @code{WITH} are performed.
1376 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1378 @cindex wilcoxon matched pairs signed ranks test
1381 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1384 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1386 The test does not make any assumptions about the variances of the samples.
1387 It does however assume that the distribution is symetrical.
1389 If the @subcmd{WITH} keyword is omitted, then tests for all
1390 combinations of the listed variables are performed.
1391 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1392 is also given, then the number of variables preceding @subcmd{WITH}
1393 must be the same as the number following it.
1394 In this case, tests for each respective pair of variables are
1396 If the @subcmd{WITH} keyword is given, but the
1397 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1398 of variable preceding @subcmd{WITH} against variable following
1399 @subcmd{WITH} are performed.
1408 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1409 /CRITERIA=CIN(@var{confidence})
1413 TESTVAL=@var{test_value}
1414 /VARIABLES=@var{var_list}
1417 (Independent Samples mode.)
1418 GROUPS=var(@var{value1} [, @var{value2}])
1419 /VARIABLES=@var{var_list}
1422 (Paired Samples mode.)
1423 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1428 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1430 It operates in one of three modes:
1432 @item One Sample mode.
1433 @item Independent Groups mode.
1438 Each of these modes are described in more detail below.
1439 There are two optional subcommands which are common to all modes.
1441 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1442 in the tests. The default value is 0.95.
1445 The @cmd{MISSING} subcommand determines the handling of missing
1447 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1448 calculations, but system-missing values are not.
1449 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1450 values are excluded as well as system-missing values.
1451 This is the default.
1453 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1454 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1455 @subcmd{/GROUPS} subcommands contains a missing value.
1456 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1457 which they would be needed. This is the default.
1461 * One Sample Mode:: Testing against a hypothesized mean
1462 * Independent Samples Mode:: Testing two independent groups for equal mean
1463 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1466 @node One Sample Mode
1467 @subsection One Sample Mode
1469 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1470 This mode is used to test a population mean against a hypothesized
1472 The value given to the @subcmd{TESTVAL} subcommand is the value against
1473 which you wish to test.
1474 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1475 tell @pspp{} which variables you wish to test.
1477 @node Independent Samples Mode
1478 @subsection Independent Samples Mode
1480 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1482 This mode is used to test whether two groups of values have the
1483 same population mean.
1484 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1485 tell @pspp{} the dependent variables you wish to test.
1487 The variable given in the @subcmd{GROUPS} subcommand is the independent
1488 variable which determines to which group the samples belong.
1489 The values in parentheses are the specific values of the independent
1490 variable for each group.
1491 If the parentheses are omitted and no values are given, the default values
1492 of 1.0 and 2.0 are assumed.
1494 If the independent variable is numeric,
1495 it is acceptable to specify only one value inside the parentheses.
1496 If you do this, cases where the independent variable is
1497 greater than or equal to this value belong to the first group, and cases
1498 less than this value belong to the second group.
1499 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1500 the independent variable are excluded on a listwise basis, regardless
1501 of whether @subcmd{/MISSING=LISTWISE} was specified.
1504 @node Paired Samples Mode
1505 @subsection Paired Samples Mode
1507 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1508 Use this mode when repeated measures have been taken from the same
1510 If the @subcmd{WITH} keyword is omitted, then tables for all
1511 combinations of variables given in the @cmd{PAIRS} subcommand are
1513 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1514 is also given, then the number of variables preceding @subcmd{WITH}
1515 must be the same as the number following it.
1516 In this case, tables for each respective pair of variables are
1518 In the event that the @subcmd{WITH} keyword is given, but the
1519 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1520 of variable preceding @subcmd{WITH} against variable following
1521 @subcmd{WITH} are generated.
1528 @cindex analysis of variance
1533 [/VARIABLES = ] @var{var_list} BY @var{var}
1534 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1535 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1536 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1537 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1540 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1541 variables factored by a single independent variable.
1542 It is used to compare the means of a population
1543 divided into more than two groups.
1545 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1547 The list of variables must be followed by the @subcmd{BY} keyword and
1548 the name of the independent (or factor) variable.
1550 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1551 ancilliary information. The options accepted are:
1554 Displays descriptive statistics about the groups factored by the independent
1557 Displays the Levene test of Homogeneity of Variance for the
1558 variables and their groups.
1561 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1562 differences between the groups.
1563 The subcommand must be followed by a list of numerals which are the
1564 coefficients of the groups to be tested.
1565 The number of coefficients must correspond to the number of distinct
1566 groups (or values of the independent variable).
1567 If the total sum of the coefficients are not zero, then @pspp{} will
1568 display a warning, but will proceed with the analysis.
1569 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1570 to specify different contrast tests.
1571 The @subcmd{MISSING} subcommand defines how missing values are handled.
1572 If @subcmd{LISTWISE} is specified then cases which have missing values for
1573 the independent variable or any dependent variable will be ignored.
1574 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1575 variable is missing or if the dependent variable currently being
1576 analysed is missing. The default is @subcmd{ANALYSIS}.
1577 A setting of @subcmd{EXCLUDE} means that variables whose values are
1578 user-missing are to be excluded from the analysis. A setting of
1579 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1581 Using the @code{POSTHOC} subcommand you can perform multiple
1582 pairwise comparisons on the data. The following comparison methods
1586 Least Significant Difference.
1587 @item @subcmd{TUKEY}
1588 Tukey Honestly Significant Difference.
1589 @item @subcmd{BONFERRONI}
1591 @item @subcmd{SCHEFFE}
1593 @item @subcmd{SIDAK}
1596 The Games-Howell test.
1600 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1601 that @var{value} should be used as the
1602 confidence level for which the posthoc tests will be performed.
1603 The default is 0.05.
1606 @section QUICK CLUSTER
1607 @vindex QUICK CLUSTER
1609 @cindex K-means clustering
1613 QUICK CLUSTER @var{var_list}
1614 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1615 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1618 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1619 dataset. This is useful when you wish to allocate cases into clusters
1620 of similar values and you already know the number of clusters.
1622 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1623 of the variables which contain the cluster data. Normally you will also
1624 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1625 number of clusters. If this is not given, then @var{k} defaults to 2.
1627 The command uses an iterative algorithm to determine the clusters for
1628 each case. It will continue iterating until convergence, or until @var{max_iter}
1629 iterations have been done. The default value of @var{max_iter} is 2.
1631 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1632 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1633 value and not as missing values.
1634 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1635 values are excluded as well as system-missing values.
1637 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1638 whenever any of the clustering variables contains a missing value.
1639 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1640 clustering variables contain missing values. Otherwise it is clustered
1641 on the basis of the non-missing values.
1642 The default is @subcmd{LISTWISE}.
1651 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1652 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1653 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1655 /MISSING=@{EXCLUDE,INCLUDE@}
1657 /RANK [INTO @var{var_list}]
1658 /NTILES(k) [INTO @var{var_list}]
1659 /NORMAL [INTO @var{var_list}]
1660 /PERCENT [INTO @var{var_list}]
1661 /RFRACTION [INTO @var{var_list}]
1662 /PROPORTION [INTO @var{var_list}]
1663 /N [INTO @var{var_list}]
1664 /SAVAGE [INTO @var{var_list}]
1667 The @cmd{RANK} command ranks variables and stores the results into new
1670 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1671 more variables whose values are to be ranked.
1672 After each variable, @samp{A} or @samp{D} may appear, indicating that
1673 the variable is to be ranked in ascending or descending order.
1674 Ascending is the default.
1675 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1676 which are to serve as group variables.
1677 In this case, the cases are gathered into groups, and ranks calculated
1680 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1681 default is to take the mean value of all the tied cases.
1683 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1684 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1685 functions are requested.
1687 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1688 variables created should appear in the output.
1690 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1691 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1692 If none are given, then the default is RANK.
1693 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1694 partitions into which values should be ranked.
1695 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1696 variables which are the variables to be created and receive the rank
1697 scores. There may be as many variables specified as there are
1698 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1699 then the variable names are automatically created.
1701 The @subcmd{MISSING} subcommand determines how user missing values are to be
1702 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1703 user-missing are to be excluded from the rank scores. A setting of
1704 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1706 @include regression.texi
1710 @section RELIABILITY
1715 /VARIABLES=@var{var_list}
1716 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1717 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1718 /SUMMARY=@{TOTAL,ALL@}
1719 /MISSING=@{EXCLUDE,INCLUDE@}
1722 @cindex Cronbach's Alpha
1723 The @cmd{RELIABILTY} command performs reliability analysis on the data.
1725 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1726 upon which analysis is to be performed.
1728 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1729 calculated for. If it is omitted, then analysis for all variables named
1730 in the @subcmd{VARIABLES} subcommand will be used.
1731 Optionally, the @var{name} parameter may be specified to set a string name
1734 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1735 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1736 then the variables are divided into 2 subsets. An optional parameter
1737 @var{n} may be given, to specify how many variables to be in the first subset.
1738 If @var{n} is omitted, then it defaults to one half of the variables in the
1739 scale, or one half minus one if there are an odd number of variables.
1740 The default model is @subcmd{ALPHA}.
1742 By default, any cases with user missing, or system missing values for
1744 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1745 The @subcmd{MISSING} subcommand determines whether user missing values are to
1746 be included or excluded in the analysis.
1748 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1749 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1750 analysis tested against the totals.
1758 @cindex Receiver Operating Characteristic
1759 @cindex Area under curve
1762 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1763 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1764 /PRINT = [ SE ] [ COORDINATES ]
1765 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1766 [ TESTPOS (@{LARGE,SMALL@}) ]
1767 [ CI (@var{confidence}) ]
1768 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1769 /MISSING=@{EXCLUDE,INCLUDE@}
1773 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1774 of a dataset, and to estimate the area under the curve.
1775 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1777 The mandatory @var{var_list} is the list of predictor variables.
1778 The variable @var{state_var} is the variable whose values represent the actual states,
1779 and @var{state_value} is the value of this variable which represents the positive state.
1781 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1782 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1783 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1784 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1785 By default, the curve is drawn with no reference line.
1787 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1788 Two additional tables are available.
1789 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1791 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1793 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1795 The @subcmd{CRITERIA} subcommand has four optional parameters:
1797 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1798 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1799 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1801 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1802 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1804 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1806 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1807 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1808 exponential distribution estimate.
1809 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1810 equal to the number of negative actual states.
1811 The default is @subcmd{FREE}.
1813 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1816 The @subcmd{MISSING} subcommand determines whether user missing values are to
1817 be included or excluded in the analysis. The default behaviour is to
1819 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1820 or if the variable @var{state_var} is missing, then the entire case will be