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. Specify @subcmd{NORMAL} to
199 superimpose a normal curve on the histogram. Histograms are not
200 created for string variables.
203 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
204 slice represents one value, with the size of the slice proportional to
205 the value's frequency. By default, all non-missing values are given
206 slices. The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
207 displayed slices to a given range of values. The @subcmd{MISSING} keyword adds
208 slices for missing values.
210 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and @subcmd{PIECHART} are accepted
211 but not currently honoured.
217 @cindex Exploratory data analysis
218 @cindex normality, testing
222 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
223 [BY @var{factor1} [BY @var{subfactor1}]
224 [ @var{factor2} [BY @var{subfactor2}]]
226 [ @var{factor3} [BY @var{subfactor3}]]
228 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
229 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
231 /COMPARE=@{GROUPS,VARIABLES@}
232 /ID=@var{identity_variable}
234 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
235 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
236 [@{NOREPORT,REPORT@}]
240 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
241 In particular, it is useful for testing how closely a distribution follows a
242 normal distribution, and for finding outliers and extreme values.
244 The @subcmd{VARIABLES} subcommand is mandatory.
245 It specifies the dependent variables and optionally variables to use as
246 factors for the analysis.
247 Variables listed before the first @subcmd{BY} keyword (if any) are the
249 The dependent variables may optionally be followed by a list of
250 factors which tell @pspp{} how to break down the analysis for each
253 Following the dependent variables, factors may be specified.
254 The factors (if desired) should be preceeded by a single @subcmd{BY} keyword.
255 The format for each factor is
257 @var{factorvar} [BY @var{subfactorvar}].
259 Each unique combination of the values of @var{factorvar} and
260 @var{subfactorvar} divide the dataset into @dfn{cells}.
261 Statistics will be calculated for each cell
262 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
264 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
265 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
266 non-parametrics statistics.
267 @subcmd{EXTREME} produces a table showing the extremities of each cell.
268 A number in parentheses, @var{n} determines
269 how many upper and lower extremities to show.
270 The default number is 5.
272 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
273 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
274 as well as for each cell.
275 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
276 (unless no factor variables have been given).
277 These subcommands have no effect if there have been no factor variables
283 @cindex spreadlevel plot
284 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
285 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
286 @subcmd{SPREADLEVEL}.
287 The first three can be used to visualise how closely each cell conforms to a
288 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
289 how the variance of differs between factors.
290 Boxplots will also show you the outliers and extreme values.
292 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
293 median. It takes an optional parameter @var{t}, which specifies how the data
294 should be transformed prior to plotting.
295 The given value @var{t} is a power to which the data is raised. For example, if
296 @var{t} is given as 2, then the data will be squared.
297 Zero, however is a special value. If @var{t} is 0 or
298 is omitted, then data will be transformed by taking its natural logarithm instead of
299 raising to the power of @var{t}.
301 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
302 useful there is more than one dependent variable and at least one factor.
304 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
305 each of which contain boxplots for all the cells.
306 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
307 each containing one boxplot per dependent variable.
308 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
309 @subcmd{/COMPARE=GROUPS} were given.
311 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
312 @subcmd{/STATISTICS=EXTREME} has been given.
313 If given, it shoule provide the name of a variable which is to be used
314 to labels extreme values and outliers.
315 Numeric or string variables are permissible.
316 If the @subcmd{ID} subcommand is not given, then the casenumber will be used for
319 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
320 calculation of the descriptives command. The default is 95%.
323 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
324 and which algorithm to use for calculating them. The default is to
325 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
326 @subcmd{HAVERAGE} algorithm.
328 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
329 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
330 then then statistics for the unfactored dependent variables are
331 produced in addition to the factored variables. If there are no
332 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
335 The following example will generate descriptive statistics and histograms for
336 two variables @var{score1} and @var{score2}.
337 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
338 Therefore, the descriptives and histograms will be generated for each
340 of @var{gender} @emph{and} for each distinct combination of the values
341 of @var{gender} and @var{race}.
342 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
343 @var{score1} and @var{score2} covering the whole dataset are not produced.
345 EXAMINE @var{score1} @var{score2} BY
347 @var{gender} BY @var{culture}
348 /STATISTICS = DESCRIPTIVES
353 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
355 EXAMINE @var{height} @var{weight} BY
357 /STATISTICS = EXTREME (3)
362 In this example, we look at the height and weight of a sample of individuals and
363 how they differ between male and female.
364 A table showing the 3 largest and the 3 smallest values of @var{height} and
365 @var{weight} for each gender, and for the whole dataset will be shown.
366 Boxplots will also be produced.
367 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
368 shown in the same graphic, allowing us to easily see the difference between
370 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
371 used to label the extreme values.
374 If many dependent variables are specified, or if factor variables are
376 there are many distinct values, then @cmd{EXAMINE} will produce a very
377 large quantity of output.
383 @cindex Exploratory data analysis
384 @cindex normality, testing
388 /HISTOGRAM = @var{var}
389 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
390 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
391 [@{NOREPORT,REPORT@}]
395 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
396 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
397 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
401 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the data. The different
402 values of the optional third variable @var{var3} will result in different colours and/or
403 markers for the plot. The following is an example for producing a scatterplot.
407 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
410 This example will produce a scatterplot where height is plotted versus weight. Depending
411 on the value of the gender variable, the colour of the datapoint is different. With
412 this plot it is possible to analyze gender differences for height vs. weight relation.
416 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
417 the histogram plot. For an alternative method to produce histograms @pxref{EXAMINE}. The
418 following example produces a histogram plot for variable weigth.
422 /HISTOGRAM = @var{weight}.
426 @section CORRELATIONS
431 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
436 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
437 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
440 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
441 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
442 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
446 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
447 for a set of variables. The significance of the coefficients are also given.
449 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
450 keyword is used, then a non-square correlation table will be produced.
451 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
452 and the variables following will be the columns of the table.
453 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
456 The @cmd{MISSING} subcommand determines the handling of missing variables.
457 If @subcmd{INCLUDE} is set, then user-missing values are included in the
458 calculations, but system-missing values are not.
459 If @subcmd{EXCLUDE} is set, which is the default, user-missing
460 values are excluded as well as system-missing values.
462 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
463 whenever any variable specified in any @cmd{/VARIABLES} subcommand
464 contains a missing value.
465 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
466 values for the particular coefficient are missing.
467 The default is @subcmd{PAIRWISE}.
469 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
470 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
471 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
472 The default is @subcmd{TWOTAIL}.
474 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
475 0.05 are highlighted.
476 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
479 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
480 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
481 estimator of the standard deviation are displayed.
482 These statistics will be displayed in a separated table, for all the variables listed
483 in any @subcmd{/VARIABLES} subcommand.
484 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
485 be displayed for each pair of variables.
486 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
494 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
495 /MISSING=@{TABLE,INCLUDE,REPORT@}
496 /WRITE=@{NONE,CELLS,ALL@}
497 /FORMAT=@{TABLES,NOTABLES@}
502 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
503 ASRESIDUAL,ALL,NONE@}
504 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
505 KAPPA,ETA,CORR,ALL,NONE@}
508 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
511 The @cmd{CROSSTABS} procedure displays crosstabulation
512 tables requested by the user. It can calculate several statistics for
513 each cell in the crosstabulation tables. In addition, a number of
514 statistics can be calculated for each table itself.
516 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
517 number of dimensions is permitted, and any number of variables per
518 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
519 times as needed. This is the only required subcommand in @dfn{general
522 Occasionally, one may want to invoke a special mode called @dfn{integer
523 mode}. Normally, in general mode, @pspp{} automatically determines
524 what values occur in the data. In integer mode, the user specifies the
525 range of values that the data assumes. To invoke this mode, specify the
526 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
527 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
528 the range are truncated to the nearest integer, then assigned to that
529 value. If values occur outside this range, they are discarded. When it
530 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
533 In general mode, numeric and string variables may be specified on
534 TABLES. In integer mode, only numeric variables are allowed.
536 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
537 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
538 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
539 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
540 integer mode, user-missing values are included in tables but marked with
541 an @samp{M} (for ``missing'') and excluded from statistical
544 Currently the @subcmd{WRITE} subcommand is ignored.
546 The @subcmd{FORMAT} subcommand controls the characteristics of the
547 crosstabulation tables to be displayed. It has a number of possible
552 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
553 @subcmd{NOTABLES} suppresses them.
556 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
557 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
561 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
562 @subcmd{DVALUE} asserts a descending sort order.
565 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
568 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
571 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
572 crosstabulation table. The possible settings are:
588 Standardized residual.
590 Adjusted standardized residual.
594 Suppress cells entirely.
597 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
598 @subcmd{COLUMN}, and @subcmd{TOTAL}.
599 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
602 The @subcmd{STATISTICS} subcommand selects statistics for computation:
609 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
610 correction, linear-by-linear association.
614 Contingency coefficient.
618 Uncertainty coefficient.
634 Spearman correlation, Pearson's r.
641 Selected statistics are only calculated when appropriate for the
642 statistic. Certain statistics require tables of a particular size, and
643 some statistics are calculated only in integer mode.
645 @samp{/STATISTICS} without any settings selects CHISQ. If the
646 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
648 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
653 Significance of some symmetric and directional measures is not calculated.
655 Asymptotic standard error is not calculated for
656 Goodman and Kruskal's tau or symmetric Somers' d.
658 Approximate T is not calculated for symmetric uncertainty coefficient.
661 Fixes for any of these deficiencies would be welcomed.
667 @cindex factor analysis
668 @cindex principal components analysis
669 @cindex principal axis factoring
670 @cindex data reduction
673 FACTOR VARIABLES=@var{var_list}
675 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
677 [ /EXTRACTION=@{PC, PAF@}]
679 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
681 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
685 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
687 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
689 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
692 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
693 common factors in the data or for data reduction purposes.
695 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
697 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
698 If @subcmd{PC} is specified, then Principal Components Analysis is used.
699 If @subcmd{PAF} is specified, then Principal Axis Factoring is
700 used. By default Principal Components Analysis will be used.
702 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
703 Three methods are available: @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
704 If don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
705 rotation on the data. Oblique rotations are not supported.
707 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
708 to be analysed. By default, the correlation matrix is analysed.
710 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
713 @item @subcmd{UNIVARIATE}
714 A table of mean values, standard deviations and total weights are printed.
715 @item @subcmd{INITIAL}
716 Initial communalities and eigenvalues are printed.
717 @item @subcmd{EXTRACTION}
718 Extracted communalities and eigenvalues are printed.
719 @item @subcmd{ROTATION}
720 Rotated communalities and eigenvalues are printed.
721 @item @subcmd{CORRELATION}
722 The correlation matrix is printed.
723 @item @subcmd{COVARIANCE}
724 The covariance matrix is printed.
726 The determinant of the correlation or covariance matrix is printed.
728 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
730 The significance of the elements of correlation matrix is printed.
732 All of the above are printed.
733 @item @subcmd{DEFAULT}
734 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
737 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
738 which factors (components) should be retained.
740 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
741 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
742 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
743 performed, and all coefficients will be printed.
745 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
746 If @subcmd{FACTORS(@var{n})} is
747 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
749 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
750 The default value of @var{l} is 1.
751 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
752 extraction (such as Principal Axis Factoring) are used.
753 @subcmd{ECONVERGE(@var{delta})} specifies that
754 iteration should cease when
755 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
756 default value of @var{delta} is 0.001.
757 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
758 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
760 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
761 If @subcmd{EXTRACTION} follows, it affects convergence.
762 If @subcmd{ROTATION} follows, it affects rotation.
763 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
764 The default value of @var{m} is 25.
766 The @cmd{MISSING} subcommand determines the handling of missing variables.
767 If @subcmd{INCLUDE} is set, then user-missing values are included in the
768 calculations, but system-missing values are not.
769 If @subcmd{EXCLUDE} is set, which is the default, user-missing
770 values are excluded as well as system-missing values.
772 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
773 whenever any variable specified in the @cmd{VARIABLES} subcommand
774 contains a missing value.
775 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
776 values for the particular coefficient are missing.
777 The default is @subcmd{LISTWISE}.
779 @node LOGISTIC REGRESSION
780 @section LOGISTIC REGRESSION
782 @vindex LOGISTIC REGRESSION
783 @cindex logistic regression
784 @cindex bivariate logistic regression
787 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
789 [/CATEGORICAL = @var{categorical_predictors}]
791 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
793 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
795 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
796 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
797 [CUT(@var{cut_point})]]
799 [/MISSING = @{INCLUDE|EXCLUDE@}]
802 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
803 variable in terms of one or more predictor variables.
805 The minimum command is
807 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
809 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
810 are the predictor variables whose coefficients the procedure estimates.
812 By default, a constant term is included in the model.
813 Hence, the full model is
816 = b_0 + b_1 {\bf x_1}
822 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
823 Simple variables as well as interactions between variables may be listed here.
825 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
826 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
828 An iterative Newton-Raphson procedure is used to fit the model.
829 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
830 and other parameters.
831 The value of @var{cut_point} is used in the classification table. It is the
832 threshold above which predicted values are considered to be 1. Values
833 of @var{cut_point} must lie in the range [0,1].
834 During iterations, if any one of the stopping criteria are satisfied, the procedure is
836 The stopping criteria are:
838 @item The number of iterations exceeds @var{max_iterations}.
839 The default value of @var{max_iterations} is 20.
840 @item The change in the all coefficient estimates are less than @var{min_delta}.
841 The default value of @var{min_delta} is 0.001.
842 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
843 The default value of @var{min_delta} is zero.
844 This means that this criterion is disabled.
845 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
846 In other words, the probabilities are close to zero or one.
847 The default value of @var{min_epsilon} is 0.00000001.
851 The @subcmd{PRINT} subcommand controls the display of optional statistics.
852 Currently there is one such option, @subcmd{CI}, which indicates that the
853 confidence interval of the odds ratio should be displayed as well as its value.
854 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
855 confidence level of the desired confidence interval.
857 The @subcmd{MISSING} subcommand determines the handling of missing
859 If @subcmd{INCLUDE} is set, then user-missing values are included in the
860 calculations, but system-missing values are not.
861 If @subcmd{EXCLUDE} is set, which is the default, user-missing
862 values are excluded as well as system-missing values.
874 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
876 [ /@{@var{var_list}@}
877 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
879 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
880 [VARIANCE] [KURT] [SEKURT]
881 [SKEW] [SESKEW] [FIRST] [LAST]
882 [HARMONIC] [GEOMETRIC]
887 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
890 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
891 statistics, either for the dataset as a whole or for categories of data.
893 The simplest form of the command is
897 @noindent which calculates the mean, count and standard deviation for @var{v}.
898 If you specify a grouping variable, for example
900 MEANS @var{v} BY @var{g}.
902 @noindent then the means, counts and standard deviations for @var{v} after having
903 been grouped by @var{g} will be calculated.
904 Instead of the mean, count and standard deviation, you could specify the statistics
905 in which you are interested:
907 MEANS @var{x} @var{y} BY @var{g}
908 /CELLS = HARMONIC SUM MIN.
910 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
913 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
917 @cindex arithmetic mean
920 The count of the values.
921 @item @subcmd{STDDEV}
922 The standard deviation.
923 @item @subcmd{SEMEAN}
924 The standard error of the mean.
926 The sum of the values.
932 The difference between the maximum and minimum values.
933 @item @subcmd{VARIANCE}
936 The first value in the category.
938 The last value in the category.
941 @item @subcmd{SESKEW}
942 The standard error of the skewness.
945 @item @subcmd{SEKURT}
946 The standard error of the kurtosis.
947 @item @subcmd{HARMONIC}
948 @cindex harmonic mean
950 @item @subcmd{GEOMETRIC}
951 @cindex geometric mean
955 In addition, three special keywords are recognized:
957 @item @subcmd{DEFAULT}
958 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
960 All of the above statistics will be calculated.
962 No statistics will be calculated (only a summary will be shown).
966 More than one @dfn{table} can be specified in a single command.
967 Each table is separated by a @samp{/}. For
971 @var{c} @var{d} @var{e} BY @var{x}
972 /@var{a} @var{b} BY @var{x} @var{y}
973 /@var{f} BY @var{y} BY @var{z}.
975 has three tables (the @samp{TABLE =} is optional).
976 The first table has three dependent variables @var{c}, @var{d} and @var{e}
977 and a single categorical variable @var{x}.
978 The second table has two dependent variables @var{a} and @var{b},
979 and two categorical variables @var{x} and @var{y}.
980 The third table has a single dependent variables @var{f}
981 and a categorical variable formed by the combination of @var{y} and @var{z}.
984 By default values are omitted from the analysis only if missing values
985 (either system missing or user missing)
986 for any of the variables directly involved in their calculation are
988 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
989 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
991 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
992 in the table specification currently being processed, regardless of
993 whether it is needed to calculate the statistic.
995 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
996 variables or in the categorical variables should be taken at their face
997 value, and not excluded.
999 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1000 variables should be taken at their face value, however cases which
1001 have user missing values for the categorical variables should be omitted
1002 from the calculation.
1008 @cindex nonparametric tests
1013 nonparametric test subcommands
1018 [ /STATISTICS=@{DESCRIPTIVES@} ]
1020 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1022 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1025 @cmd{NPAR TESTS} performs nonparametric tests.
1026 Non parametric tests make very few assumptions about the distribution of the
1028 One or more tests may be specified by using the corresponding subcommand.
1029 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1030 produces for each variable that is the subject of any test.
1032 Certain tests may take a long time to execute, if an exact figure is required.
1033 Therefore, by default asymptotic approximations are used unless the
1034 subcommand @subcmd{/METHOD=EXACT} is specified.
1035 Exact tests give more accurate results, but may take an unacceptably long
1036 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1037 after which the test will be abandoned, and a warning message printed.
1038 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1039 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1044 * BINOMIAL:: Binomial Test
1045 * CHISQUARE:: Chisquare Test
1046 * COCHRAN:: Cochran Q Test
1047 * FRIEDMAN:: Friedman Test
1048 * KENDALL:: Kendall's W Test
1049 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1050 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1051 * MANN-WHITNEY:: Mann Whitney U Test
1052 * MCNEMAR:: McNemar Test
1053 * MEDIAN:: Median Test
1055 * SIGN:: The Sign Test
1056 * WILCOXON:: Wilcoxon Signed Ranks Test
1061 @subsection Binomial test
1063 @cindex binomial test
1066 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1069 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1070 variable with that of a binomial distribution.
1071 The variable @var{p} specifies the test proportion of the binomial
1073 The default value of 0.5 is assumed if @var{p} is omitted.
1075 If a single value appears after the variable list, then that value is
1076 used as the threshold to partition the observed values. Values less
1077 than or equal to the threshold value form the first category. Values
1078 greater than the threshold form the second category.
1080 If two values appear after the variable list, then they will be used
1081 as the values which a variable must take to be in the respective
1083 Cases for which a variable takes a value equal to neither of the specified
1084 values, take no part in the test for that variable.
1086 If no values appear, then the variable must assume dichotomous
1088 If more than two distinct, non-missing values for a variable
1089 under test are encountered then an error occurs.
1091 If the test proportion is equal to 0.5, then a two tailed test is
1092 reported. For any other test proportion, a one tailed test is
1094 For one tailed tests, if the test proportion is less than
1095 or equal to the observed proportion, then the significance of
1096 observing the observed proportion or more is reported.
1097 If the test proportion is more than the observed proportion, then the
1098 significance of observing the observed proportion or less is reported.
1099 That is to say, the test is always performed in the observed
1102 @pspp{} uses a very precise approximation to the gamma function to
1103 compute the binomial significance. Thus, exact results are reported
1104 even for very large sample sizes.
1109 @subsection Chisquare Test
1111 @cindex chisquare test
1115 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1119 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1120 between the expected and observed frequencies of the categories of a variable.
1121 Optionally, a range of values may appear after the variable list.
1122 If a range is given, then non integer values are truncated, and values
1123 outside the specified range are excluded from the analysis.
1125 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1127 There must be exactly one non-zero expected value, for each observed
1128 category, or the @subcmd{EQUAL} keywork must be specified.
1129 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1130 consecutive expected categories all taking a frequency of @var{f}.
1131 The frequencies given are proportions, not absolute frequencies. The
1132 sum of the frequencies need not be 1.
1133 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1138 @subsection Cochran Q Test
1140 @cindex Cochran Q test
1141 @cindex Q, Cochran Q
1144 [ /COCHRAN = @var{var_list} ]
1147 The Cochran Q test is used to test for differences between three or more groups.
1148 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1150 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1153 @subsection Friedman Test
1155 @cindex Friedman test
1158 [ /FRIEDMAN = @var{var_list} ]
1161 The Friedman test is used to test for differences between repeated measures when
1162 there is no indication that the distributions are normally distributed.
1164 A list of variables which contain the measured data must be given. The procedure
1165 prints the sum of ranks for each variable, the test statistic and its significance.
1168 @subsection Kendall's W Test
1170 @cindex Kendall's W test
1171 @cindex coefficient of concordance
1174 [ /KENDALL = @var{var_list} ]
1177 The Kendall test investigates whether an arbitrary number of related samples come from the
1179 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1180 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1181 unity indicates complete agreement.
1184 @node KOLMOGOROV-SMIRNOV
1185 @subsection Kolmogorov-Smirnov Test
1186 @vindex KOLMOGOROV-SMIRNOV
1188 @cindex Kolmogorov-Smirnov test
1191 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1194 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1195 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1196 Normal, Uniform, Poisson and Exponential.
1198 Ideally you should provide the parameters of the distribution against which you wish to test
1199 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1200 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1202 However, if the parameters are omitted they will be imputed from the data. Imputing the
1203 parameters reduces the power of the test so should be avoided if possible.
1205 In the following example, two variables @var{score} and @var{age} are tested to see if
1206 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1209 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1211 If the variables need to be tested against different distributions, then a separate
1212 subcommand must be used. For example the following syntax tests @var{score} against
1213 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1214 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1217 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1218 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1221 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1223 @node KRUSKAL-WALLIS
1224 @subsection Kruskal-Wallis Test
1225 @vindex KRUSKAL-WALLIS
1227 @cindex Kruskal-Wallis test
1230 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1233 The Kruskal-Wallis test is used to compare data from an
1234 arbitrary number of populations. It does not assume normality.
1235 The data to be compared are specified by @var{var_list}.
1236 The categorical variable determining the groups to which the
1237 data belongs is given by @var{var}. The limits @var{lower} and
1238 @var{upper} specify the valid range of @var{var}. Any cases for
1239 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1242 The mean rank of each group as well as the chi-squared value and significance
1243 of the test will be printed.
1244 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1248 @subsection Mann-Whitney U Test
1249 @vindex MANN-WHITNEY
1251 @cindex Mann-Whitney U test
1252 @cindex U, Mann-Whitney U
1255 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1258 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1259 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}.
1260 @var{Var} may be either a string or an alpha variable.
1261 @var{Group1} and @var{group2} specify the
1262 two values of @var{var} which determine the groups of the test data.
1263 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1265 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1266 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1269 @subsection McNemar Test
1271 @cindex McNemar test
1274 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1277 Use McNemar's test to analyse the significance of the difference between
1278 pairs of correlated proportions.
1280 If the @code{WITH} keyword is omitted, then tests for all
1281 combinations of the listed variables are performed.
1282 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1283 is also given, then the number of variables preceding @code{WITH}
1284 must be the same as the number following it.
1285 In this case, tests for each respective pair of variables are
1287 If the @code{WITH} keyword is given, but the
1288 @code{(PAIRED)} keyword is omitted, then tests for each combination
1289 of variable preceding @code{WITH} against variable following
1290 @code{WITH} are performed.
1292 The data in each variable must be dichotomous. If there are more
1293 than two distinct variables an error will occur and the test will
1297 @subsection Median Test
1302 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1305 The median test is used to test whether independent samples come from
1306 populations with a common median.
1307 The median of the populations against which the samples are to be tested
1308 may be given in parentheses immediately after the
1309 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1310 union of all the samples.
1312 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1313 keyword @code{BY} must come next, and then the grouping variable. Two values
1314 in parentheses should follow. If the first value is greater than the second,
1315 then a 2 sample test is performed using these two values to determine the groups.
1316 If however, the first variable is less than the second, then a @i{k} sample test is
1317 conducted and the group values used are all values encountered which lie in the
1318 range [@var{value1},@var{value2}].
1322 @subsection Runs Test
1327 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1330 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1332 It works by examining the number of times a variable's value crosses a given threshold.
1333 The desired threshold must be specified within parentheses.
1334 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1335 Following the threshold specification comes the list of variables whose values are to be
1338 The subcommand shows the number of runs, the asymptotic significance based on the
1342 @subsection Sign Test
1347 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1350 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1352 The test does not make any assumptions about the
1353 distribution of the data.
1355 If the @code{WITH} keyword is omitted, then tests for all
1356 combinations of the listed variables are performed.
1357 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1358 is also given, then the number of variables preceding @code{WITH}
1359 must be the same as the number following it.
1360 In this case, tests for each respective pair of variables are
1362 If the @code{WITH} keyword is given, but the
1363 @code{(PAIRED)} keyword is omitted, then tests for each combination
1364 of variable preceding @code{WITH} against variable following
1365 @code{WITH} are performed.
1368 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1370 @cindex wilcoxon matched pairs signed ranks test
1373 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1376 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1378 The test does not make any assumptions about the variances of the samples.
1379 It does however assume that the distribution is symetrical.
1381 If the @subcmd{WITH} keyword is omitted, then tests for all
1382 combinations of the listed variables are performed.
1383 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1384 is also given, then the number of variables preceding @subcmd{WITH}
1385 must be the same as the number following it.
1386 In this case, tests for each respective pair of variables are
1388 If the @subcmd{WITH} keyword is given, but the
1389 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1390 of variable preceding @subcmd{WITH} against variable following
1391 @subcmd{WITH} are performed.
1400 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1401 /CRITERIA=CIN(@var{confidence})
1405 TESTVAL=@var{test_value}
1406 /VARIABLES=@var{var_list}
1409 (Independent Samples mode.)
1410 GROUPS=var(@var{value1} [, @var{value2}])
1411 /VARIABLES=@var{var_list}
1414 (Paired Samples mode.)
1415 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1420 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1422 It operates in one of three modes:
1424 @item One Sample mode.
1425 @item Independent Groups mode.
1430 Each of these modes are described in more detail below.
1431 There are two optional subcommands which are common to all modes.
1433 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1434 in the tests. The default value is 0.95.
1437 The @cmd{MISSING} subcommand determines the handling of missing
1439 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1440 calculations, but system-missing values are not.
1441 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1442 values are excluded as well as system-missing values.
1443 This is the default.
1445 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1446 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1447 @subcmd{/GROUPS} subcommands contains a missing value.
1448 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1449 which they would be needed. This is the default.
1453 * One Sample Mode:: Testing against a hypothesized mean
1454 * Independent Samples Mode:: Testing two independent groups for equal mean
1455 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1458 @node One Sample Mode
1459 @subsection One Sample Mode
1461 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1462 This mode is used to test a population mean against a hypothesized
1464 The value given to the @subcmd{TESTVAL} subcommand is the value against
1465 which you wish to test.
1466 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1467 tell @pspp{} which variables you wish to test.
1469 @node Independent Samples Mode
1470 @subsection Independent Samples Mode
1472 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1474 This mode is used to test whether two groups of values have the
1475 same population mean.
1476 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1477 tell @pspp{} the dependent variables you wish to test.
1479 The variable given in the @subcmd{GROUPS} subcommand is the independent
1480 variable which determines to which group the samples belong.
1481 The values in parentheses are the specific values of the independent
1482 variable for each group.
1483 If the parentheses are omitted and no values are given, the default values
1484 of 1.0 and 2.0 are assumed.
1486 If the independent variable is numeric,
1487 it is acceptable to specify only one value inside the parentheses.
1488 If you do this, cases where the independent variable is
1489 greater than or equal to this value belong to the first group, and cases
1490 less than this value belong to the second group.
1491 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1492 the independent variable are excluded on a listwise basis, regardless
1493 of whether @subcmd{/MISSING=LISTWISE} was specified.
1496 @node Paired Samples Mode
1497 @subsection Paired Samples Mode
1499 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1500 Use this mode when repeated measures have been taken from the same
1502 If the @subcmd{WITH} keyword is omitted, then tables for all
1503 combinations of variables given in the @cmd{PAIRS} subcommand are
1505 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1506 is also given, then the number of variables preceding @subcmd{WITH}
1507 must be the same as the number following it.
1508 In this case, tables for each respective pair of variables are
1510 In the event that the @subcmd{WITH} keyword is given, but the
1511 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1512 of variable preceding @subcmd{WITH} against variable following
1513 @subcmd{WITH} are generated.
1520 @cindex analysis of variance
1525 [/VARIABLES = ] @var{var_list} BY @var{var}
1526 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1527 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1528 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1529 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1532 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1533 variables factored by a single independent variable.
1534 It is used to compare the means of a population
1535 divided into more than two groups.
1537 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1539 The list of variables must be followed by the @subcmd{BY} keyword and
1540 the name of the independent (or factor) variable.
1542 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1543 ancilliary information. The options accepted are:
1546 Displays descriptive statistics about the groups factored by the independent
1549 Displays the Levene test of Homogeneity of Variance for the
1550 variables and their groups.
1553 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1554 differences between the groups.
1555 The subcommand must be followed by a list of numerals which are the
1556 coefficients of the groups to be tested.
1557 The number of coefficients must correspond to the number of distinct
1558 groups (or values of the independent variable).
1559 If the total sum of the coefficients are not zero, then @pspp{} will
1560 display a warning, but will proceed with the analysis.
1561 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1562 to specify different contrast tests.
1563 The @subcmd{MISSING} subcommand defines how missing values are handled.
1564 If @subcmd{LISTWISE} is specified then cases which have missing values for
1565 the independent variable or any dependent variable will be ignored.
1566 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1567 variable is missing or if the dependent variable currently being
1568 analysed is missing. The default is @subcmd{ANALYSIS}.
1569 A setting of @subcmd{EXCLUDE} means that variables whose values are
1570 user-missing are to be excluded from the analysis. A setting of
1571 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1573 Using the @code{POSTHOC} subcommand you can perform multiple
1574 pairwise comparisons on the data. The following comparison methods
1578 Least Significant Difference.
1579 @item @subcmd{TUKEY}
1580 Tukey Honestly Significant Difference.
1581 @item @subcmd{BONFERRONI}
1583 @item @subcmd{SCHEFFE}
1585 @item @subcmd{SIDAK}
1588 The Games-Howell test.
1592 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1593 that @var{value} should be used as the
1594 confidence level for which the posthoc tests will be performed.
1595 The default is 0.05.
1598 @section QUICK CLUSTER
1599 @vindex QUICK CLUSTER
1601 @cindex K-means clustering
1605 QUICK CLUSTER @var{var_list}
1606 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1607 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1610 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1611 dataset. This is useful when you wish to allocate cases into clusters
1612 of similar values and you already know the number of clusters.
1614 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1615 of the variables which contain the cluster data. Normally you will also
1616 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1617 number of clusters. If this is not given, then @var{k} defaults to 2.
1619 The command uses an iterative algorithm to determine the clusters for
1620 each case. It will continue iterating until convergence, or until @var{max_iter}
1621 iterations have been done. The default value of @var{max_iter} is 2.
1623 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1624 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1625 value and not as missing values.
1626 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1627 values are excluded as well as system-missing values.
1629 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1630 whenever any of the clustering variables contains a missing value.
1631 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1632 clustering variables contain missing values. Otherwise it is clustered
1633 on the basis of the non-missing values.
1634 The default is @subcmd{LISTWISE}.
1643 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1644 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1645 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1647 /MISSING=@{EXCLUDE,INCLUDE@}
1649 /RANK [INTO @var{var_list}]
1650 /NTILES(k) [INTO @var{var_list}]
1651 /NORMAL [INTO @var{var_list}]
1652 /PERCENT [INTO @var{var_list}]
1653 /RFRACTION [INTO @var{var_list}]
1654 /PROPORTION [INTO @var{var_list}]
1655 /N [INTO @var{var_list}]
1656 /SAVAGE [INTO @var{var_list}]
1659 The @cmd{RANK} command ranks variables and stores the results into new
1662 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1663 more variables whose values are to be ranked.
1664 After each variable, @samp{A} or @samp{D} may appear, indicating that
1665 the variable is to be ranked in ascending or descending order.
1666 Ascending is the default.
1667 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1668 which are to serve as group variables.
1669 In this case, the cases are gathered into groups, and ranks calculated
1672 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1673 default is to take the mean value of all the tied cases.
1675 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1676 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1677 functions are requested.
1679 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1680 variables created should appear in the output.
1682 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1683 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1684 If none are given, then the default is RANK.
1685 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1686 partitions into which values should be ranked.
1687 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1688 variables which are the variables to be created and receive the rank
1689 scores. There may be as many variables specified as there are
1690 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1691 then the variable names are automatically created.
1693 The @subcmd{MISSING} subcommand determines how user missing values are to be
1694 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1695 user-missing are to be excluded from the rank scores. A setting of
1696 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1698 @include regression.texi
1702 @section RELIABILITY
1707 /VARIABLES=@var{var_list}
1708 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1709 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1710 /SUMMARY=@{TOTAL,ALL@}
1711 /MISSING=@{EXCLUDE,INCLUDE@}
1714 @cindex Cronbach's Alpha
1715 The @cmd{RELIABILTY} command performs reliability analysis on the data.
1717 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1718 upon which analysis is to be performed.
1720 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1721 calculated for. If it is omitted, then analysis for all variables named
1722 in the @subcmd{VARIABLES} subcommand will be used.
1723 Optionally, the @var{name} parameter may be specified to set a string name
1726 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1727 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1728 then the variables are divided into 2 subsets. An optional parameter
1729 @var{n} may be given, to specify how many variables to be in the first subset.
1730 If @var{n} is omitted, then it defaults to one half of the variables in the
1731 scale, or one half minus one if there are an odd number of variables.
1732 The default model is @subcmd{ALPHA}.
1734 By default, any cases with user missing, or system missing values for
1736 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1737 The @subcmd{MISSING} subcommand determines whether user missing values are to
1738 be included or excluded in the analysis.
1740 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1741 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1742 analysis tested against the totals.
1750 @cindex Receiver Operating Characteristic
1751 @cindex Area under curve
1754 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1755 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1756 /PRINT = [ SE ] [ COORDINATES ]
1757 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1758 [ TESTPOS (@{LARGE,SMALL@}) ]
1759 [ CI (@var{confidence}) ]
1760 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1761 /MISSING=@{EXCLUDE,INCLUDE@}
1765 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1766 of a dataset, and to estimate the area under the curve.
1767 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1769 The mandatory @var{var_list} is the list of predictor variables.
1770 The variable @var{state_var} is the variable whose values represent the actual states,
1771 and @var{state_value} is the value of this variable which represents the positive state.
1773 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1774 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1775 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1776 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1777 By default, the curve is drawn with no reference line.
1779 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1780 Two additional tables are available.
1781 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1783 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1785 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1787 The @subcmd{CRITERIA} subcommand has four optional parameters:
1789 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1790 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1791 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1793 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1794 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1796 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1798 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1799 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1800 exponential distribution estimate.
1801 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1802 equal to the number of negative actual states.
1803 The default is @subcmd{FREE}.
1805 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1808 The @subcmd{MISSING} subcommand determines whether user missing values are to
1809 be included or excluded in the analysis. The default behaviour is to
1811 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1812 or if the variable @var{state_var} is missing, then the entire case will be