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.
11 * CORRELATIONS:: Correlation tables.
12 * CROSSTABS:: Crosstabulation tables.
13 * FACTOR:: Factor analysis and Principal Components analysis.
14 * LOGISTIC REGRESSION:: Bivariate Logistic Regression.
15 * MEANS:: Average values and other statistics.
16 * NPAR TESTS:: Nonparametric tests.
17 * T-TEST:: Test hypotheses about means.
18 * ONEWAY:: One way analysis of variance.
19 * QUICK CLUSTER:: K-Means clustering.
20 * RANK:: Compute rank scores.
21 * REGRESSION:: Linear regression.
22 * RELIABILITY:: Reliability analysis.
23 * ROC:: Receiver Operating Characteristic.
32 /VARIABLES=@var{var_list}
33 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
34 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
36 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
37 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
38 SESKEWNESS,SEKURTOSIS@}
39 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
40 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
44 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
46 statistics requested by the user. In addition, it can optionally
49 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
50 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
52 All other subcommands are optional:
54 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
55 @subcmd{INCLUDE} is set, then user-missing values are included in the
56 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
57 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
58 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
59 the entire case is excluded whenever any value in that case has a
60 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
62 The @subcmd{FORMAT} subcommand affects the output format. Currently the
63 @subcmd{LABELS/NOLABELS} and @subcmd{NOINDEX/INDEX} settings are not used.
64 When @subcmd{SERIAL} is
65 set, both valid and missing number of cases are listed in the output;
66 when @subcmd{NOSERIAL} is set, only valid cases are listed.
68 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
69 the specified variables. The Z scores are saved to new variables.
70 Variable names are generated by trying first the original variable name
71 with Z prepended and truncated to a maximum of 8 characters, then the
72 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
73 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
74 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
75 list by enclosing them in parentheses after each variable.
76 When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
77 treating temporary transformations as permanent.
79 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
83 All of the statistics below.
87 Standard error of the mean.
90 @item @subcmd{VARIANCE}
92 @item @subcmd{KURTOSIS}
93 Kurtosis and standard error of the kurtosis.
94 @item @subcmd{SKEWNESS}
95 Skewness and standard error of the skewness.
105 Mean, standard deviation of the mean, minimum, maximum.
107 Standard error of the kurtosis.
109 Standard error of the skewness.
112 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
113 of the possible values should be self-explanatory. @subcmd{NAME} causes the
114 statistics to be sorted by name. By default, the statistics are listed
115 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
116 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
117 sort order, respectively.
125 /VARIABLES=@var{var_list}
126 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
127 @{AVALUE,DVALUE,AFREQ,DFREQ@}
128 /MISSING=@{EXCLUDE,INCLUDE@}
129 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
130 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
131 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
133 /PERCENTILES=percent@dots{}
134 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
135 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
136 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
137 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
139 (These options are not currently implemented.)
145 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
147 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
148 (including median and mode) and percentiles,
149 @cmd{FREQUENCIES} can also output
150 histograms and pie charts.
152 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
153 variables to be analyzed.
155 The @subcmd{FORMAT} subcommand controls the output format. It has several
160 @subcmd{TABLE}, the default, causes a frequency table to be output for every
161 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
162 with a numeric argument causes them to be output except when there are
163 more than the specified number of values in the table.
166 Normally frequency tables are sorted in ascending order by value. This
167 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
168 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
169 respectively, by frequency count.
172 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
173 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
174 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
175 are included. System-missing values are never included in statistics,
176 but are listed in frequency tables.
178 The available @subcmd{STATISTICS} are the same as available
179 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
180 of @subcmd{MEDIAN}, the data's median
181 value, and MODE, the mode. (If there are multiple modes, the smallest
182 value is reported.) By default, the mean, standard deviation of the
183 mean, minimum, and maximum are reported for each variable.
186 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
187 The percentiles should be presented at a list of numbers between 0
189 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
190 boundaries of the data set divided into the specified number of ranges.
191 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
194 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
195 each specified numeric variable. The X axis by default ranges from
196 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
197 and @subcmd{MAXIMUM} keywords can set an explicit range. Specify @subcmd{NORMAL} to
198 superimpose a normal curve on the histogram. Histograms are not
199 created for string variables.
202 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
203 slice represents one value, with the size of the slice proportional to
204 the value's frequency. By default, all non-missing values are given
205 slices. The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
206 displayed slices to a given range of values. The @subcmd{MISSING} keyword adds
207 slices for missing values.
209 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and @subcmd{PIECHART} are accepted
210 but not currently honoured.
216 @cindex Exploratory data analysis
217 @cindex normality, testing
221 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
222 [BY @var{factor1} [BY @var{subfactor1}]
223 [ @var{factor2} [BY @var{subfactor2}]]
225 [ @var{factor3} [BY @var{subfactor3}]]
227 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
228 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
230 /COMPARE=@{GROUPS,VARIABLES@}
231 /ID=@var{identity_variable}
233 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
234 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
235 [@{NOREPORT,REPORT@}]
239 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
240 In particular, it is useful for testing how closely a distribution follows a
241 normal distribution, and for finding outliers and extreme values.
243 The @subcmd{VARIABLES} subcommand is mandatory.
244 It specifies the dependent variables and optionally variables to use as
245 factors for the analysis.
246 Variables listed before the first @subcmd{BY} keyword (if any) are the
248 The dependent variables may optionally be followed by a list of
249 factors which tell @pspp{} how to break down the analysis for each
252 Following the dependent variables, factors may be specified.
253 The factors (if desired) should be preceeded by a single @subcmd{BY} keyword.
254 The format for each factor is
256 @var{factorvar} [BY @var{subfactorvar}].
258 Each unique combination of the values of @var{factorvar} and
259 @var{subfactorvar} divide the dataset into @dfn{cells}.
260 Statistics will be calculated for each cell
261 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
263 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
264 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
265 non-parametrics statistics.
266 @subcmd{EXTREME} produces a table showing the extremities of each cell.
267 A number in parentheses, @var{n} determines
268 how many upper and lower extremities to show.
269 The default number is 5.
271 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
272 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
273 as well as for each cell.
274 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
275 (unless no factor variables have been given).
276 These subcommands have no effect if there have been no factor variables
282 @cindex spreadlevel plot
283 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
284 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
285 @subcmd{SPREADLEVEL}.
286 The first three can be used to visualise how closely each cell conforms to a
287 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
288 how the variance of differs between factors.
289 Boxplots will also show you the outliers and extreme values.
291 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
292 median. It takes an optional parameter @var{t}, which specifies how the data
293 should be transformed prior to plotting.
294 The given value @var{t} is a power to which the data is raised. For example, if
295 @var{t} is given as 2, then the data will be squared.
296 Zero, however is a special value. If @var{t} is 0 or
297 is omitted, then data will be transformed by taking its natural logarithm instead of
298 raising to the power of @var{t}.
300 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
301 useful there is more than one dependent variable and at least one factor.
303 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
304 each of which contain boxplots for all the cells.
305 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
306 each containing one boxplot per dependent variable.
307 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
308 @subcmd{/COMPARE=GROUPS} were given.
310 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
311 @subcmd{/STATISTICS=EXTREME} has been given.
312 If given, it shoule provide the name of a variable which is to be used
313 to labels extreme values and outliers.
314 Numeric or string variables are permissible.
315 If the @subcmd{ID} subcommand is not given, then the casenumber will be used for
318 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
319 calculation of the descriptives command. The default is 95%.
322 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
323 and which algorithm to use for calculating them. The default is to
324 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
325 @subcmd{HAVERAGE} algorithm.
327 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
328 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
329 then then statistics for the unfactored dependent variables are
330 produced in addition to the factored variables. If there are no
331 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
334 The following example will generate descriptive statistics and histograms for
335 two variables @var{score1} and @var{score2}.
336 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
337 Therefore, the descriptives and histograms will be generated for each
339 of @var{gender} @emph{and} for each distinct combination of the values
340 of @var{gender} and @var{race}.
341 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
342 @var{score1} and @var{score2} covering the whole dataset are not produced.
344 EXAMINE @var{score1} @var{score2} BY
346 @var{gender} BY @var{culture}
347 /STATISTICS = DESCRIPTIVES
352 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
354 EXAMINE @var{height} @var{weight} BY
356 /STATISTICS = EXTREME (3)
361 In this example, we look at the height and weight of a sample of individuals and
362 how they differ between male and female.
363 A table showing the 3 largest and the 3 smallest values of @var{height} and
364 @var{weight} for each gender, and for the whole dataset will be shown.
365 Boxplots will also be produced.
366 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
367 shown in the same graphic, allowing us to easily see the difference between
369 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
370 used to label the extreme values.
373 If many dependent variables are specified, or if factor variables are
375 there are many distinct values, then @cmd{EXAMINE} will produce a very
376 large quantity of output.
379 @section CORRELATIONS
384 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
389 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
390 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
393 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
394 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
395 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
399 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
400 for a set of variables. The significance of the coefficients are also given.
402 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
403 keyword is used, then a non-square correlation table will be produced.
404 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
405 and the variables following will be the columns of the table.
406 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
409 The @cmd{MISSING} subcommand determines the handling of missing variables.
410 If @subcmd{INCLUDE} is set, then user-missing values are included in the
411 calculations, but system-missing values are not.
412 If @subcmd{EXCLUDE} is set, which is the default, user-missing
413 values are excluded as well as system-missing values.
415 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
416 whenever any variable specified in any @cmd{/VARIABLES} subcommand
417 contains a missing value.
418 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
419 values for the particular coefficient are missing.
420 The default is @subcmd{PAIRWISE}.
422 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
423 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
424 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
425 The default is @subcmd{TWOTAIL}.
427 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
428 0.05 are highlighted.
429 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
432 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
433 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
434 estimator of the standard deviation are displayed.
435 These statistics will be displayed in a separated table, for all the variables listed
436 in any @subcmd{/VARIABLES} subcommand.
437 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
438 be displayed for each pair of variables.
439 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
447 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
448 /MISSING=@{TABLE,INCLUDE,REPORT@}
449 /WRITE=@{NONE,CELLS,ALL@}
450 /FORMAT=@{TABLES,NOTABLES@}
455 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
456 ASRESIDUAL,ALL,NONE@}
457 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
458 KAPPA,ETA,CORR,ALL,NONE@}
461 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
464 The @cmd{CROSSTABS} procedure displays crosstabulation
465 tables requested by the user. It can calculate several statistics for
466 each cell in the crosstabulation tables. In addition, a number of
467 statistics can be calculated for each table itself.
469 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
470 number of dimensions is permitted, and any number of variables per
471 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
472 times as needed. This is the only required subcommand in @dfn{general
475 Occasionally, one may want to invoke a special mode called @dfn{integer
476 mode}. Normally, in general mode, @pspp{} automatically determines
477 what values occur in the data. In integer mode, the user specifies the
478 range of values that the data assumes. To invoke this mode, specify the
479 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
480 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
481 the range are truncated to the nearest integer, then assigned to that
482 value. If values occur outside this range, they are discarded. When it
483 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
486 In general mode, numeric and string variables may be specified on
487 TABLES. In integer mode, only numeric variables are allowed.
489 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
490 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
491 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
492 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
493 integer mode, user-missing values are included in tables but marked with
494 an @samp{M} (for ``missing'') and excluded from statistical
497 Currently the @subcmd{WRITE} subcommand is ignored.
499 The @subcmd{FORMAT} subcommand controls the characteristics of the
500 crosstabulation tables to be displayed. It has a number of possible
505 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
506 @subcmd{NOTABLES} suppresses them.
509 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
510 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
514 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
515 @subcmd{DVALUE} asserts a descending sort order.
518 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
521 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
524 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
525 crosstabulation table. The possible settings are:
541 Standardized residual.
543 Adjusted standardized residual.
547 Suppress cells entirely.
550 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
551 @subcmd{COLUMN}, and @subcmd{TOTAL}.
552 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
555 The @subcmd{STATISTICS} subcommand selects statistics for computation:
562 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
563 correction, linear-by-linear association.
567 Contingency coefficient.
571 Uncertainty coefficient.
587 Spearman correlation, Pearson's r.
594 Selected statistics are only calculated when appropriate for the
595 statistic. Certain statistics require tables of a particular size, and
596 some statistics are calculated only in integer mode.
598 @samp{/STATISTICS} without any settings selects CHISQ. If the
599 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
601 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
606 T values for Spearman's R and Pearson's R are wrong.
608 Significance of symmetric and directional measures is not calculated.
610 Asymmetric ASEs and T values for lambda are wrong.
612 ASE of Goodman and Kruskal's tau is not calculated.
614 ASE of symmetric somers' d is wrong.
616 Approximate T of uncertainty coefficient is wrong.
619 Fixes for any of these deficiencies would be welcomed.
625 @cindex factor analysis
626 @cindex principal components analysis
627 @cindex principal axis factoring
628 @cindex data reduction
631 FACTOR VARIABLES=@var{var_list}
633 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
635 [ /EXTRACTION=@{PC, PAF@}]
637 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
639 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
643 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
645 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
647 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
650 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
651 common factors in the data or for data reduction purposes.
653 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
655 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
656 If @subcmd{PC} is specified, then Principal Components Analysis is used.
657 If @subcmd{PAF} is specified, then Principal Axis Factoring is
658 used. By default Principal Components Analysis will be used.
660 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
661 Three methods are available: @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
662 If don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
663 rotation on the data. Oblique rotations are not supported.
665 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
666 to be analysed. By default, the correlation matrix is analysed.
668 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
671 @item @subcmd{UNIVARIATE}
672 A table of mean values, standard deviations and total weights are printed.
673 @item @subcmd{INITIAL}
674 Initial communalities and eigenvalues are printed.
675 @item @subcmd{EXTRACTION}
676 Extracted communalities and eigenvalues are printed.
677 @item @subcmd{ROTATION}
678 Rotated communalities and eigenvalues are printed.
679 @item @subcmd{CORRELATION}
680 The correlation matrix is printed.
681 @item @subcmd{COVARIANCE}
682 The covariance matrix is printed.
684 The determinant of the correlation or covariance matrix is printed.
686 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
688 The significance of the elements of correlation matrix is printed.
690 All of the above are printed.
691 @item @subcmd{DEFAULT}
692 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
695 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
696 which factors (components) should be retained.
698 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
699 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
700 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
701 performed, and all coefficients will be printed.
703 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
704 If @subcmd{FACTORS(@var{n})} is
705 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
707 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
708 The default value of @var{l} is 1.
709 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
710 extraction (such as Principal Axis Factoring) are used.
711 @subcmd{ECONVERGE(@var{delta})} specifies that
712 iteration should cease when
713 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
714 default value of @var{delta} is 0.001.
715 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
716 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
718 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
719 If @subcmd{EXTRACTION} follows, it affects convergence.
720 If @subcmd{ROTATION} follows, it affects rotation.
721 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
722 The default value of @var{m} is 25.
724 The @cmd{MISSING} subcommand determines the handling of missing variables.
725 If @subcmd{INCLUDE} is set, then user-missing values are included in the
726 calculations, but system-missing values are not.
727 If @subcmd{EXCLUDE} is set, which is the default, user-missing
728 values are excluded as well as system-missing values.
730 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
731 whenever any variable specified in the @cmd{VARIABLES} subcommand
732 contains a missing value.
733 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
734 values for the particular coefficient are missing.
735 The default is @subcmd{LISTWISE}.
737 @node LOGISTIC REGRESSION
738 @section LOGISTIC REGRESSION
740 @vindex LOGISTIC REGRESSION
741 @cindex logistic regression
742 @cindex bivariate logistic regression
745 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
747 [/CATEGORICAL = @var{categorical_predictors}]
749 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
751 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
753 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
754 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
755 [CUT(@var{cut_point})]]
757 [/MISSING = @{INCLUDE|EXCLUDE@}]
760 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
761 variable in terms of one or more predictor variables.
763 The minimum command is
765 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
767 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
768 are the predictor variables whose coefficients the procedure estimates.
770 By default, a constant term is included in the model.
771 Hence, the full model is
774 = b_0 + b_1 {\bf x_1}
780 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
781 Simple variables as well as interactions between variables may be listed here.
783 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
784 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
786 An iterative Newton-Raphson procedure is used to fit the model.
787 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
788 and other parameters.
789 The value of @var{cut_point} is used in the classification table. It is the
790 threshold above which predicted values are considered to be 1. Values
791 of @var{cut_point} must lie in the range [0,1].
792 During iterations, if any one of the stopping criteria are satisfied, the procedure is
794 The stopping criteria are:
796 @item The number of iterations exceeds @var{max_iterations}.
797 The default value of @var{max_iterations} is 20.
798 @item The change in the all coefficient estimates are less than @var{min_delta}.
799 The default value of @var{min_delta} is 0.001.
800 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
801 The default value of @var{min_delta} is zero.
802 This means that this criterion is disabled.
803 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
804 In other words, the probabilities are close to zero or one.
805 The default value of @var{min_epsilon} is 0.00000001.
809 The @subcmd{PRINT} subcommand controls the display of optional statistics.
810 Currently there is one such option, @subcmd{CI}, which indicates that the
811 confidence interval of the odds ratio should be displayed as well as its value.
812 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
813 confidence level of the desired confidence interval.
815 The @subcmd{MISSING} subcommand determines the handling of missing
817 If @subcmd{INCLUDE} is set, then user-missing values are included in the
818 calculations, but system-missing values are not.
819 If @subcmd{EXCLUDE} is set, which is the default, user-missing
820 values are excluded as well as system-missing values.
832 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
834 [ /@{@var{var_list}@}
835 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
837 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
838 [VARIANCE] [KURT] [SEKURT]
839 [SKEW] [SESKEW] [FIRST] [LAST]
840 [HARMONIC] [GEOMETRIC]
845 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
848 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
849 statistics, either for the dataset as a whole or for categories of data.
851 The simplest form of the command is
855 @noindent which calculates the mean, count and standard deviation for @var{v}.
856 If you specify a grouping variable, for example
858 MEANS @var{v} BY @var{g}.
860 @noindent then the means, counts and standard deviations for @var{v} after having
861 been grouped by @var{g} will be calculated.
862 Instead of the mean, count and standard deviation, you could specify the statistics
863 in which you are interested:
865 MEANS @var{x} @var{y} BY @var{g}
866 /CELLS = HARMONIC SUM MIN.
868 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
871 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
875 @cindex arithmetic mean
878 The count of the values.
879 @item @subcmd{STDDEV}
880 The standard deviation.
881 @item @subcmd{SEMEAN}
882 The standard error of the mean.
884 The sum of the values.
890 The difference between the maximum and minimum values.
891 @item @subcmd{VARIANCE}
894 The first value in the category.
896 The last value in the category.
899 @item @subcmd{SESKEW}
900 The standard error of the skewness.
903 @item @subcmd{SEKURT}
904 The standard error of the kurtosis.
905 @item @subcmd{HARMONIC}
906 @cindex harmonic mean
908 @item @subcmd{GEOMETRIC}
909 @cindex geometric mean
913 In addition, three special keywords are recognized:
915 @item @subcmd{DEFAULT}
916 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
918 All of the above statistics will be calculated.
920 No statistics will be calculated (only a summary will be shown).
924 More than one @dfn{table} can be specified in a single command.
925 Each table is separated by a @samp{/}. For
929 @var{c} @var{d} @var{e} BY @var{x}
930 /@var{a} @var{b} BY @var{x} @var{y}
931 /@var{f} BY @var{y} BY @var{z}.
933 has three tables (the @samp{TABLE =} is optional).
934 The first table has three dependent variables @var{c}, @var{d} and @var{e}
935 and a single categorical variable @var{x}.
936 The second table has two dependent variables @var{a} and @var{b},
937 and two categorical variables @var{x} and @var{y}.
938 The third table has a single dependent variables @var{f}
939 and a categorical variable formed by the combination of @var{y} and @var{z}.
942 By default values are omitted from the analysis only if missing values
943 (either system missing or user missing)
944 for any of the variables directly involved in their calculation are
946 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
947 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
949 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
950 in the table specification currently being processed, regardless of
951 whether it is needed to calculate the statistic.
953 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
954 variables or in the categorical variables should be taken at their face
955 value, and not excluded.
957 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
958 variables should be taken at their face value, however cases which
959 have user missing values for the categorical variables should be omitted
960 from the calculation.
966 @cindex nonparametric tests
971 nonparametric test subcommands
976 [ /STATISTICS=@{DESCRIPTIVES@} ]
978 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
980 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
983 @cmd{NPAR TESTS} performs nonparametric tests.
984 Non parametric tests make very few assumptions about the distribution of the
986 One or more tests may be specified by using the corresponding subcommand.
987 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
988 produces for each variable that is the subject of any test.
990 Certain tests may take a long time to execute, if an exact figure is required.
991 Therefore, by default asymptotic approximations are used unless the
992 subcommand @subcmd{/METHOD=EXACT} is specified.
993 Exact tests give more accurate results, but may take an unacceptably long
994 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
995 after which the test will be abandoned, and a warning message printed.
996 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
997 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1002 * BINOMIAL:: Binomial Test
1003 * CHISQUARE:: Chisquare Test
1004 * COCHRAN:: Cochran Q Test
1005 * FRIEDMAN:: Friedman Test
1006 * KENDALL:: Kendall's W Test
1007 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1008 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1009 * MANN-WHITNEY:: Mann Whitney U Test
1010 * MCNEMAR:: McNemar Test
1011 * MEDIAN:: Median Test
1013 * SIGN:: The Sign Test
1014 * WILCOXON:: Wilcoxon Signed Ranks Test
1019 @subsection Binomial test
1021 @cindex binomial test
1024 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1027 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1028 variable with that of a binomial distribution.
1029 The variable @var{p} specifies the test proportion of the binomial
1031 The default value of 0.5 is assumed if @var{p} is omitted.
1033 If a single value appears after the variable list, then that value is
1034 used as the threshold to partition the observed values. Values less
1035 than or equal to the threshold value form the first category. Values
1036 greater than the threshold form the second category.
1038 If two values appear after the variable list, then they will be used
1039 as the values which a variable must take to be in the respective
1041 Cases for which a variable takes a value equal to neither of the specified
1042 values, take no part in the test for that variable.
1044 If no values appear, then the variable must assume dichotomous
1046 If more than two distinct, non-missing values for a variable
1047 under test are encountered then an error occurs.
1049 If the test proportion is equal to 0.5, then a two tailed test is
1050 reported. For any other test proportion, a one tailed test is
1052 For one tailed tests, if the test proportion is less than
1053 or equal to the observed proportion, then the significance of
1054 observing the observed proportion or more is reported.
1055 If the test proportion is more than the observed proportion, then the
1056 significance of observing the observed proportion or less is reported.
1057 That is to say, the test is always performed in the observed
1060 @pspp{} uses a very precise approximation to the gamma function to
1061 compute the binomial significance. Thus, exact results are reported
1062 even for very large sample sizes.
1067 @subsection Chisquare Test
1069 @cindex chisquare test
1073 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1077 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1078 between the expected and observed frequencies of the categories of a variable.
1079 Optionally, a range of values may appear after the variable list.
1080 If a range is given, then non integer values are truncated, and values
1081 outside the specified range are excluded from the analysis.
1083 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1085 There must be exactly one non-zero expected value, for each observed
1086 category, or the @subcmd{EQUAL} keywork must be specified.
1087 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1088 consecutive expected categories all taking a frequency of @var{f}.
1089 The frequencies given are proportions, not absolute frequencies. The
1090 sum of the frequencies need not be 1.
1091 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1096 @subsection Cochran Q Test
1098 @cindex Cochran Q test
1099 @cindex Q, Cochran Q
1102 [ /COCHRAN = @var{var_list} ]
1105 The Cochran Q test is used to test for differences between three or more groups.
1106 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1108 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1111 @subsection Friedman Test
1113 @cindex Friedman test
1116 [ /FRIEDMAN = @var{var_list} ]
1119 The Friedman test is used to test for differences between repeated measures when
1120 there is no indication that the distributions are normally distributed.
1122 A list of variables which contain the measured data must be given. The procedure
1123 prints the sum of ranks for each variable, the test statistic and its significance.
1126 @subsection Kendall's W Test
1128 @cindex Kendall's W test
1129 @cindex coefficient of concordance
1132 [ /KENDALL = @var{var_list} ]
1135 The Kendall test investigates whether an arbitrary number of related samples come from the
1137 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1138 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1139 unity indicates complete agreement.
1142 @node KOLMOGOROV-SMIRNOV
1143 @subsection Kolmogorov-Smirnov Test
1144 @vindex KOLMOGOROV-SMIRNOV
1146 @cindex Kolmogorov-Smirnov test
1149 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1152 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1153 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1154 Normal, Uniform, Poisson and Exponential.
1156 Ideally you should provide the parameters of the distribution against which you wish to test
1157 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1158 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1160 However, if the parameters are omitted they will be imputed from the data. Imputing the
1161 parameters reduces the power of the test so should be avoided if possible.
1163 In the following example, two variables @var{score} and @var{age} are tested to see if
1164 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1167 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1169 If the variables need to be tested against different distributions, then a separate
1170 subcommand must be used. For example the following syntax tests @var{score} against
1171 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1172 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1175 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1176 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1179 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1181 @node KRUSKAL-WALLIS
1182 @subsection Kruskal-Wallis Test
1183 @vindex KRUSKAL-WALLIS
1185 @cindex Kruskal-Wallis test
1188 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1191 The Kruskal-Wallis test is used to compare data from an
1192 arbitrary number of populations. It does not assume normality.
1193 The data to be compared are specified by @var{var_list}.
1194 The categorical variable determining the groups to which the
1195 data belongs is given by @var{var}. The limits @var{lower} and
1196 @var{upper} specify the valid range of @var{var}. Any cases for
1197 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1200 The mean rank of each group as well as the chi-squared value and significance
1201 of the test will be printed.
1202 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1206 @subsection Mann-Whitney U Test
1207 @vindex MANN-WHITNEY
1209 @cindex Mann-Whitney U test
1210 @cindex U, Mann-Whitney U
1213 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1216 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1217 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}.
1218 @var{Var} may be either a string or an alpha variable.
1219 @var{Group1} and @var{group2} specify the
1220 two values of @var{var} which determine the groups of the test data.
1221 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1223 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1224 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1227 @subsection McNemar Test
1229 @cindex McNemar test
1232 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1235 Use McNemar's test to analyse the significance of the difference between
1236 pairs of correlated proportions.
1238 If the @code{WITH} keyword is omitted, then tests for all
1239 combinations of the listed variables are performed.
1240 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1241 is also given, then the number of variables preceding @code{WITH}
1242 must be the same as the number following it.
1243 In this case, tests for each respective pair of variables are
1245 If the @code{WITH} keyword is given, but the
1246 @code{(PAIRED)} keyword is omitted, then tests for each combination
1247 of variable preceding @code{WITH} against variable following
1248 @code{WITH} are performed.
1250 The data in each variable must be dichotomous. If there are more
1251 than two distinct variables an error will occur and the test will
1255 @subsection Median Test
1260 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1263 The median test is used to test whether independent samples come from
1264 populations with a common median.
1265 The median of the populations against which the samples are to be tested
1266 may be given in parentheses immediately after the
1267 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1268 union of all the samples.
1270 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1271 keyword @code{BY} must come next, and then the grouping variable. Two values
1272 in parentheses should follow. If the first value is greater than the second,
1273 then a 2 sample test is performed using these two values to determine the groups.
1274 If however, the first variable is less than the second, then a @i{k} sample test is
1275 conducted and the group values used are all values encountered which lie in the
1276 range [@var{value1},@var{value2}].
1280 @subsection Runs Test
1285 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1288 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1290 It works by examining the number of times a variable's value crosses a given threshold.
1291 The desired threshold must be specified within parentheses.
1292 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1293 Following the threshold specification comes the list of variables whose values are to be
1296 The subcommand shows the number of runs, the asymptotic significance based on the
1300 @subsection Sign Test
1305 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1308 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1310 The test does not make any assumptions about the
1311 distribution of the data.
1313 If the @code{WITH} keyword is omitted, then tests for all
1314 combinations of the listed variables are performed.
1315 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1316 is also given, then the number of variables preceding @code{WITH}
1317 must be the same as the number following it.
1318 In this case, tests for each respective pair of variables are
1320 If the @code{WITH} keyword is given, but the
1321 @code{(PAIRED)} keyword is omitted, then tests for each combination
1322 of variable preceding @code{WITH} against variable following
1323 @code{WITH} are performed.
1326 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1328 @cindex wilcoxon matched pairs signed ranks test
1331 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1334 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1336 The test does not make any assumptions about the variances of the samples.
1337 It does however assume that the distribution is symetrical.
1339 If the @subcmd{WITH} keyword is omitted, then tests for all
1340 combinations of the listed variables are performed.
1341 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1342 is also given, then the number of variables preceding @subcmd{WITH}
1343 must be the same as the number following it.
1344 In this case, tests for each respective pair of variables are
1346 If the @subcmd{WITH} keyword is given, but the
1347 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1348 of variable preceding @subcmd{WITH} against variable following
1349 @subcmd{WITH} are performed.
1358 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1359 /CRITERIA=CIN(@var{confidence})
1363 TESTVAL=@var{test_value}
1364 /VARIABLES=@var{var_list}
1367 (Independent Samples mode.)
1368 GROUPS=var(@var{value1} [, @var{value2}])
1369 /VARIABLES=@var{var_list}
1372 (Paired Samples mode.)
1373 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1378 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1380 It operates in one of three modes:
1382 @item One Sample mode.
1383 @item Independent Groups mode.
1388 Each of these modes are described in more detail below.
1389 There are two optional subcommands which are common to all modes.
1391 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1392 in the tests. The default value is 0.95.
1395 The @cmd{MISSING} subcommand determines the handling of missing
1397 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1398 calculations, but system-missing values are not.
1399 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1400 values are excluded as well as system-missing values.
1401 This is the default.
1403 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1404 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1405 @subcmd{/GROUPS} subcommands contains a missing value.
1406 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1407 which they would be needed. This is the default.
1411 * One Sample Mode:: Testing against a hypothesized mean
1412 * Independent Samples Mode:: Testing two independent groups for equal mean
1413 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1416 @node One Sample Mode
1417 @subsection One Sample Mode
1419 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1420 This mode is used to test a population mean against a hypothesized
1422 The value given to the @subcmd{TESTVAL} subcommand is the value against
1423 which you wish to test.
1424 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1425 tell @pspp{} which variables you wish to test.
1427 @node Independent Samples Mode
1428 @subsection Independent Samples Mode
1430 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1432 This mode is used to test whether two groups of values have the
1433 same population mean.
1434 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1435 tell @pspp{} the dependent variables you wish to test.
1437 The variable given in the @subcmd{GROUPS} subcommand is the independent
1438 variable which determines to which group the samples belong.
1439 The values in parentheses are the specific values of the independent
1440 variable for each group.
1441 If the parentheses are omitted and no values are given, the default values
1442 of 1.0 and 2.0 are assumed.
1444 If the independent variable is numeric,
1445 it is acceptable to specify only one value inside the parentheses.
1446 If you do this, cases where the independent variable is
1447 greater than or equal to this value belong to the first group, and cases
1448 less than this value belong to the second group.
1449 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1450 the independent variable are excluded on a listwise basis, regardless
1451 of whether @subcmd{/MISSING=LISTWISE} was specified.
1454 @node Paired Samples Mode
1455 @subsection Paired Samples Mode
1457 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1458 Use this mode when repeated measures have been taken from the same
1460 If the @subcmd{WITH} keyword is omitted, then tables for all
1461 combinations of variables given in the @cmd{PAIRS} subcommand are
1463 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1464 is also given, then the number of variables preceding @subcmd{WITH}
1465 must be the same as the number following it.
1466 In this case, tables for each respective pair of variables are
1468 In the event that the @subcmd{WITH} keyword is given, but the
1469 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1470 of variable preceding @subcmd{WITH} against variable following
1471 @subcmd{WITH} are generated.
1478 @cindex analysis of variance
1483 [/VARIABLES = ] @var{var_list} BY @var{var}
1484 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1485 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1486 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1487 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1490 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1491 variables factored by a single independent variable.
1492 It is used to compare the means of a population
1493 divided into more than two groups.
1495 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1497 The list of variables must be followed by the @subcmd{BY} keyword and
1498 the name of the independent (or factor) variable.
1500 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1501 ancilliary information. The options accepted are:
1504 Displays descriptive statistics about the groups factored by the independent
1507 Displays the Levene test of Homogeneity of Variance for the
1508 variables and their groups.
1511 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1512 differences between the groups.
1513 The subcommand must be followed by a list of numerals which are the
1514 coefficients of the groups to be tested.
1515 The number of coefficients must correspond to the number of distinct
1516 groups (or values of the independent variable).
1517 If the total sum of the coefficients are not zero, then @pspp{} will
1518 display a warning, but will proceed with the analysis.
1519 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1520 to specify different contrast tests.
1521 The @subcmd{MISSING} subcommand defines how missing values are handled.
1522 If @subcmd{LISTWISE} is specified then cases which have missing values for
1523 the independent variable or any dependent variable will be ignored.
1524 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1525 variable is missing or if the dependent variable currently being
1526 analysed is missing. The default is @subcmd{ANALYSIS}.
1527 A setting of @subcmd{EXCLUDE} means that variables whose values are
1528 user-missing are to be excluded from the analysis. A setting of
1529 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1531 Using the @code{POSTHOC} subcommand you can perform multiple
1532 pairwise comparisons on the data. The following comparison methods
1536 Least Significant Difference.
1537 @item @subcmd{TUKEY}
1538 Tukey Honestly Significant Difference.
1539 @item @subcmd{BONFERRONI}
1541 @item @subcmd{SCHEFFE}
1543 @item @subcmd{SIDAK}
1546 The Games-Howell test.
1550 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1551 that @var{value} should be used as the
1552 confidence level for which the posthoc tests will be performed.
1553 The default is 0.05.
1556 @section QUICK CLUSTER
1557 @vindex QUICK CLUSTER
1559 @cindex K-means clustering
1563 QUICK CLUSTER @var{var_list}
1564 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1565 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1568 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1569 dataset. This is useful when you wish to allocate cases into clusters
1570 of similar values and you already know the number of clusters.
1572 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1573 of the variables which contain the cluster data. Normally you will also
1574 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1575 number of clusters. If this is not given, then @var{k} defaults to 2.
1577 The command uses an iterative algorithm to determine the clusters for
1578 each case. It will continue iterating until convergence, or until @var{max_iter}
1579 iterations have been done. The default value of @var{max_iter} is 2.
1581 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1582 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1583 value and not as missing values.
1584 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1585 values are excluded as well as system-missing values.
1587 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1588 whenever any of the clustering variables contains a missing value.
1589 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1590 clustering variables contain missing values. Otherwise it is clustered
1591 on the basis of the non-missing values.
1592 The default is @subcmd{LISTWISE}.
1601 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1602 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1603 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1605 /MISSING=@{EXCLUDE,INCLUDE@}
1607 /RANK [INTO @var{var_list}]
1608 /NTILES(k) [INTO @var{var_list}]
1609 /NORMAL [INTO @var{var_list}]
1610 /PERCENT [INTO @var{var_list}]
1611 /RFRACTION [INTO @var{var_list}]
1612 /PROPORTION [INTO @var{var_list}]
1613 /N [INTO @var{var_list}]
1614 /SAVAGE [INTO @var{var_list}]
1617 The @cmd{RANK} command ranks variables and stores the results into new
1620 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1621 more variables whose values are to be ranked.
1622 After each variable, @samp{A} or @samp{D} may appear, indicating that
1623 the variable is to be ranked in ascending or descending order.
1624 Ascending is the default.
1625 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1626 which are to serve as group variables.
1627 In this case, the cases are gathered into groups, and ranks calculated
1630 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1631 default is to take the mean value of all the tied cases.
1633 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1634 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1635 functions are requested.
1637 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1638 variables created should appear in the output.
1640 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1641 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1642 If none are given, then the default is RANK.
1643 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1644 partitions into which values should be ranked.
1645 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1646 variables which are the variables to be created and receive the rank
1647 scores. There may be as many variables specified as there are
1648 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1649 then the variable names are automatically created.
1651 The @subcmd{MISSING} subcommand determines how user missing values are to be
1652 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1653 user-missing are to be excluded from the rank scores. A setting of
1654 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1656 @include regression.texi
1660 @section RELIABILITY
1665 /VARIABLES=@var{var_list}
1666 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1667 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1668 /SUMMARY=@{TOTAL,ALL@}
1669 /MISSING=@{EXCLUDE,INCLUDE@}
1672 @cindex Cronbach's Alpha
1673 The @cmd{RELIABILTY} command performs reliability analysis on the data.
1675 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1676 upon which analysis is to be performed.
1678 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1679 calculated for. If it is omitted, then analysis for all variables named
1680 in the @subcmd{VARIABLES} subcommand will be used.
1681 Optionally, the @var{name} parameter may be specified to set a string name
1684 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1685 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1686 then the variables are divided into 2 subsets. An optional parameter
1687 @var{n} may be given, to specify how many variables to be in the first subset.
1688 If @var{n} is omitted, then it defaults to one half of the variables in the
1689 scale, or one half minus one if there are an odd number of variables.
1690 The default model is @subcmd{ALPHA}.
1692 By default, any cases with user missing, or system missing values for
1694 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1695 The @subcmd{MISSING} subcommand determines whether user missing values are to
1696 be included or excluded in the analysis.
1698 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1699 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1700 analysis tested against the totals.
1708 @cindex Receiver Operating Characteristic
1709 @cindex Area under curve
1712 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1713 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1714 /PRINT = [ SE ] [ COORDINATES ]
1715 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1716 [ TESTPOS (@{LARGE,SMALL@}) ]
1717 [ CI (@var{confidence}) ]
1718 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1719 /MISSING=@{EXCLUDE,INCLUDE@}
1723 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1724 of a dataset, and to estimate the area under the curve.
1725 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1727 The mandatory @var{var_list} is the list of predictor variables.
1728 The variable @var{state_var} is the variable whose values represent the actual states,
1729 and @var{state_value} is the value of this variable which represents the positive state.
1731 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1732 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1733 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1734 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1735 By default, the curve is drawn with no reference line.
1737 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1738 Two additional tables are available.
1739 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1741 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1743 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1745 The @subcmd{CRITERIA} subcommand has four optional parameters:
1747 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1748 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1749 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1751 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1752 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1754 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1756 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1757 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1758 exponential distribution estimate.
1759 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1760 equal to the number of negative actual states.
1761 The default is @subcmd{FREE}.
1763 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1766 The @subcmd{MISSING} subcommand determines whether user missing values are to
1767 be included or excluded in the analysis. The default behaviour is to
1769 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1770 or if the variable @var{state_var} is missing, then the entire case will be