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.
77 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
81 All of the statistics below.
85 Standard error of the mean.
88 @item @subcmd{VARIANCE}
90 @item @subcmd{KURTOSIS}
91 Kurtosis and standard error of the kurtosis.
92 @item @subcmd{SKEWNESS}
93 Skewness and standard error of the skewness.
103 Mean, standard deviation of the mean, minimum, maximum.
105 Standard error of the kurtosis.
107 Standard error of the skewness.
110 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
111 of the possible values should be self-explanatory. @subcmd{NAME} causes the
112 statistics to be sorted by name. By default, the statistics are listed
113 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
114 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
115 sort order, respectively.
123 /VARIABLES=@var{var_list}
124 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
125 @{AVALUE,DVALUE,AFREQ,DFREQ@}
126 /MISSING=@{EXCLUDE,INCLUDE@}
127 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
128 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
129 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
131 /PERCENTILES=percent@dots{}
132 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
133 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
134 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
135 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
137 (These options are not currently implemented.)
143 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
145 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
146 (including median and mode) and percentiles,
147 @cmd{FREQUENCIES} can also output
148 histograms and pie charts.
150 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
151 variables to be analyzed.
153 The @subcmd{FORMAT} subcommand controls the output format. It has several
158 @subcmd{TABLE}, the default, causes a frequency table to be output for every
159 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
160 with a numeric argument causes them to be output except when there are
161 more than the specified number of values in the table.
164 Normally frequency tables are sorted in ascending order by value. This
165 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
166 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
167 respectively, by frequency count.
170 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
171 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
172 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
173 are included. System-missing values are never included in statistics,
174 but are listed in frequency tables.
176 The available @subcmd{STATISTICS} are the same as available
177 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
178 of @subcmd{MEDIAN}, the data's median
179 value, and MODE, the mode. (If there are multiple modes, the smallest
180 value is reported.) By default, the mean, standard deviation of the
181 mean, minimum, and maximum are reported for each variable.
184 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
185 The percentiles should be presented at a list of numbers between 0
187 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
188 boundaries of the data set divided into the specified number of ranges.
189 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
192 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
193 each specified numeric variable. The X axis by default ranges from
194 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
195 and @subcmd{MAXIMUM} keywords can set an explicit range. Specify @subcmd{NORMAL} to
196 superimpose a normal curve on the histogram. Histograms are not
197 created for string variables.
200 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
201 slice represents one value, with the size of the slice proportional to
202 the value's frequency. By default, all non-missing values are given
203 slices. The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
204 displayed slices to a given range of values. The @subcmd{MISSING} keyword adds
205 slices for missing values.
207 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and @subcmd{PIECHART} are accepted
208 but not currently honoured.
214 @cindex Exploratory data analysis
215 @cindex Normality, testing for
219 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
220 [BY @var{factor1} [BY @var{subfactor1}]
221 [ @var{factor2} [BY @var{subfactor2}]]
223 [ @var{factor3} [BY @var{subfactor3}]]
225 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
226 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
228 /COMPARE=@{GROUPS,VARIABLES@}
229 /ID=@var{identity_variable}
231 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
232 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
233 [@{NOREPORT,REPORT@}]
237 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
238 In particular, it is useful for testing how closely a distribution follows a
239 normal distribution, and for finding outliers and extreme values.
241 The @subcmd{VARIABLES} subcommand is mandatory.
242 It specifies the dependent variables and optionally variables to use as
243 factors for the analysis.
244 Variables listed before the first @subcmd{BY} keyword (if any) are the
246 The dependent variables may optionally be followed by a list of
247 factors which tell @pspp{} how to break down the analysis for each
250 Following the dependent variables, factors may be specified.
251 The factors (if desired) should be preceeded by a single @subcmd{BY} keyword.
252 The format for each factor is
254 @var{factorvar} [BY @var{subfactorvar}].
256 Each unique combination of the values of @var{factorvar} and
257 @var{subfactorvar} divide the dataset into @dfn{cells}.
258 Statistics will be calculated for each cell
259 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
261 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
262 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
263 non-parametrics statistics.
264 @subcmd{EXTREME} produces a table showing the extremities of each cell.
265 A number in parentheses, @var{n} determines
266 how many upper and lower extremities to show.
267 The default number is 5.
269 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
270 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
271 as well as for each cell.
272 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
273 (unless no factor variables have been given).
274 These subcommands have no effect if there have been no factor variables
280 @cindex spreadlevel plot
281 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
282 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
283 @subcmd{SPREADLEVEL}.
284 The first three can be used to visualise how closely each cell conforms to a
285 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
286 how the variance of differs between factors.
287 Boxplots will also show you the outliers and extreme values.
289 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
290 median. It takes an optional parameter @var{t}, which specifies how the data
291 should be transformed prior to plotting.
292 The given value @var{t} is a power to which the data is raised. For example, if
293 @var{t} is given as 2, then the data will be squared.
294 Zero, however is a special value. If @var{t} is 0 or
295 is omitted, then data will be transformed by taking its natural logarithm instead of
296 raising to the power of @var{t}.
298 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
299 useful there is more than one dependent variable and at least one factor.
301 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
302 each of which contain boxplots for all the cells.
303 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
304 each containing one boxplot per dependent variable.
305 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
306 @subcmd{/COMPARE=GROUPS} were given.
308 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
309 @subcmd{/STATISTICS=EXTREME} has been given.
310 If given, it shoule provide the name of a variable which is to be used
311 to labels extreme values and outliers.
312 Numeric or string variables are permissible.
313 If the @subcmd{ID} subcommand is not given, then the casenumber will be used for
316 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
317 calculation of the descriptives command. The default is 95%.
320 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
321 and which algorithm to use for calculating them. The default is to
322 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
323 @subcmd{HAVERAGE} algorithm.
325 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
326 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
327 then then statistics for the unfactored dependent variables are
328 produced in addition to the factored variables. If there are no
329 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
332 The following example will generate descriptive statistics and histograms for
333 two variables @var{score1} and @var{score2}.
334 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
335 Therefore, the descriptives and histograms will be generated for each
337 of @var{gender} @emph{and} for each distinct combination of the values
338 of @var{gender} and @var{race}.
339 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
340 @var{score1} and @var{score2} covering the whole dataset are not produced.
342 EXAMINE @var{score1} @var{score2} BY
344 @var{gender} BY @var{culture}
345 /STATISTICS = DESCRIPTIVES
350 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
352 EXAMINE @var{height} @var{weight} BY
354 /STATISTICS = EXTREME (3)
359 In this example, we look at the height and weight of a sample of individuals and
360 how they differ between male and female.
361 A table showing the 3 largest and the 3 smallest values of @var{height} and
362 @var{weight} for each gender, and for the whole dataset will be shown.
363 Boxplots will also be produced.
364 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
365 shown in the same graphic, allowing us to easily see the difference between
367 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
368 used to label the extreme values.
371 If many dependent variables are specified, or if factor variables are
373 there are many distinct values, then @cmd{EXAMINE} will produce a very
374 large quantity of output.
377 @section CORRELATIONS
382 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
387 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
388 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
391 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
392 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
393 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
397 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
398 for a set of variables. The significance of the coefficients are also given.
400 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
401 keyword is used, then a non-square correlation table will be produced.
402 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
403 and the variables following will be the columns of the table.
404 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
407 The @cmd{MISSING} subcommand determines the handling of missing variables.
408 If @subcmd{INCLUDE} is set, then user-missing values are included in the
409 calculations, but system-missing values are not.
410 If @subcmd{EXCLUDE} is set, which is the default, user-missing
411 values are excluded as well as system-missing values.
413 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
414 whenever any variable specified in any @cmd{/VARIABLES} subcommand
415 contains a missing value.
416 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
417 values for the particular coefficient are missing.
418 The default is @subcmd{PAIRWISE}.
420 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
421 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
422 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
423 The default is @subcmd{TWOTAIL}.
425 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
426 0.05 are highlighted.
427 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
430 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
431 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
432 estimator of the standard deviation are displayed.
433 These statistics will be displayed in a separated table, for all the variables listed
434 in any @subcmd{/VARIABLES} subcommand.
435 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
436 be displayed for each pair of variables.
437 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
445 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
446 /MISSING=@{TABLE,INCLUDE,REPORT@}
447 /WRITE=@{NONE,CELLS,ALL@}
448 /FORMAT=@{TABLES,NOTABLES@}
453 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
454 ASRESIDUAL,ALL,NONE@}
455 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
456 KAPPA,ETA,CORR,ALL,NONE@}
459 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
462 The @cmd{CROSSTABS} procedure displays crosstabulation
463 tables requested by the user. It can calculate several statistics for
464 each cell in the crosstabulation tables. In addition, a number of
465 statistics can be calculated for each table itself.
467 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
468 number of dimensions is permitted, and any number of variables per
469 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
470 times as needed. This is the only required subcommand in @dfn{general
473 Occasionally, one may want to invoke a special mode called @dfn{integer
474 mode}. Normally, in general mode, @pspp{} automatically determines
475 what values occur in the data. In integer mode, the user specifies the
476 range of values that the data assumes. To invoke this mode, specify the
477 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
478 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
479 the range are truncated to the nearest integer, then assigned to that
480 value. If values occur outside this range, they are discarded. When it
481 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
484 In general mode, numeric and string variables may be specified on
485 TABLES. In integer mode, only numeric variables are allowed.
487 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
488 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
489 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
490 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
491 integer mode, user-missing values are included in tables but marked with
492 an @samp{M} (for ``missing'') and excluded from statistical
495 Currently the @subcmd{WRITE} subcommand is ignored.
497 The @subcmd{FORMAT} subcommand controls the characteristics of the
498 crosstabulation tables to be displayed. It has a number of possible
503 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
504 @subcmd{NOTABLES} suppresses them.
507 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
508 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
512 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
513 @subcmd{DVALUE} asserts a descending sort order.
516 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
519 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
522 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
523 crosstabulation table. The possible settings are:
539 Standardized residual.
541 Adjusted standardized residual.
545 Suppress cells entirely.
548 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
549 @subcmd{COLUMN}, and @subcmd{TOTAL}.
550 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
553 The @subcmd{STATISTICS} subcommand selects statistics for computation:
560 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
561 correction, linear-by-linear association.
565 Contingency coefficient.
569 Uncertainty coefficient.
585 Spearman correlation, Pearson's r.
592 Selected statistics are only calculated when appropriate for the
593 statistic. Certain statistics require tables of a particular size, and
594 some statistics are calculated only in integer mode.
596 @samp{/STATISTICS} without any settings selects CHISQ. If the
597 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
599 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
604 Pearson's R (but not Spearman) is off a little.
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
706 be used. @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
707 The default value of @var{l} is 1. The @subcmd{ECONVERGE} and @subcmd{ITERATE} settings have effect only when iterative algorithms for factor
708 extraction (such as Principal Axis Factoring) are used. @subcmd{ECONVERGE(@var{delta})} specifies that
709 iteration should cease when
710 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
711 default value of @var{delta} is 0.001.
712 The @subcmd{ITERATE(@var{m})} setting sets the maximum number of iterations to @var{m}. The default value of @var{m} is 25.
714 The @cmd{MISSING} subcommand determines the handling of missing variables.
715 If @subcmd{INCLUDE} is set, then user-missing values are included in the
716 calculations, but system-missing values are not.
717 If @subcmd{EXCLUDE} is set, which is the default, user-missing
718 values are excluded as well as system-missing values.
720 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
721 whenever any variable specified in the @cmd{VARIABLES} subcommand
722 contains a missing value.
723 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
724 values for the particular coefficient are missing.
725 The default is @subcmd{LISTWISE}.
727 @node LOGISTIC REGRESSION
728 @section LOGISTIC REGRESSION
730 @vindex LOGISTIC REGRESSION
731 @cindex logistic regression
732 @cindex bivariate logistic regression
735 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
737 [/CATEGORICAL = @var{categorical_predictors}]
739 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
741 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
743 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
744 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]]
746 [/MISSING = @{INCLUDE|EXCLUDE@}]
749 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
750 variable in terms of one or more predictor variables.
752 The minimum command is
754 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
756 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
757 are the predictor variables whose coefficients the procedure estimates.
759 By default, a constant term is included in the model.
760 Hence, the full model is
763 = b_0 + b_1 {\bf x_1}
769 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
770 Simple variables as well as interactions between variables may be listed here.
772 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
773 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
775 An iterative Newton-Raphson procedure is used to fit the model.
776 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure.
777 During iterations, if any one of the stopping criteria are satisfied, the procedure is
781 @item The number of iterations exceeds @var{max_iterations}.
782 The default value of @var{max_iterations} is 20.
783 @item The change in the all coefficient estimates are less than @var{min_delta}.
784 The default value of @var{min_delta} is 0.001.
785 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
786 The default value of @var{min_delta} is zero.
787 This means that this criterion is disabled.
788 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
789 In other words, the probabilities are close to zero or one.
790 The default value of @var{min_epsilon} is 0.00000001.
793 The @subcmd{PRINT} subcommand controls the display of optional statistics.
794 Currently there is one such option, @subcmd{CI}, which indicates that the
795 confidence interval of the odds ratio should be displayed as well as its value.
796 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
797 confidence level of the desired confidence interval.
799 The @subcmd{MISSING} subcommand determines the handling of missing
801 If @subcmd{INCLUDE} is set, then user-missing values are included in the
802 calculations, but system-missing values are not.
803 If @subcmd{EXCLUDE} is set, which is the default, user-missing
804 values are excluded as well as system-missing values.
816 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
818 [ /@{@var{var_list}@}
819 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
821 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
822 [VARIANCE] [KURT] [SEKURT]
823 [SKEW] [SESKEW] [FIRST] [LAST]
824 [HARMONIC] [GEOMETRIC]
829 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
832 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
833 statistics, either for the dataset as a whole or for categories of data.
835 The simplest form of the command is
839 @noindent which calculates the mean, count and standard deviation for @var{v}.
840 If you specify a grouping variable, for example
842 MEANS @var{v} BY @var{g}.
844 @noindent then the means, counts and standard deviations for @var{v} after having
845 been grouped by @var{g} will be calculated.
846 Instead of the mean, count and standard deviation, you could specify the statistics
847 in which you are interested:
849 MEANS @var{x} @var{y} BY @var{g}
850 /CELLS = HARMONIC SUM MIN.
852 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
855 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
859 @cindex arithmetic mean
862 The count of the values.
863 @item @subcmd{STDDEV}
864 The standard deviation.
865 @item @subcmd{SEMEAN}
866 The standard error of the mean.
868 The sum of the values.
874 The difference between the maximum and minimum values.
875 @item @subcmd{VARIANCE}
878 The first value in the category.
880 The last value in the category.
883 @item @subcmd{SESKEW}
884 The standard error of the skewness.
887 @item @subcmd{SEKURT}
888 The standard error of the kurtosis.
889 @item @subcmd{HARMONIC}
890 @cindex harmonic mean
892 @item @subcmd{GEOMETRIC}
893 @cindex geometric mean
897 In addition, three special keywords are recognized:
899 @item @subcmd{DEFAULT}
900 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
902 All of the above statistics will be calculated.
904 No statistics will be calculated (only a summary will be shown).
908 More than one @dfn{table} can be specified in a single command.
909 Each table is separated by a @samp{/}. For
913 @var{c} @var{d} @var{e} BY @var{x}
914 /@var{a} @var{b} BY @var{x} @var{y}
915 /@var{f} BY @var{y} BY @var{z}.
917 has three tables (the @samp{TABLE =} is optional).
918 The first table has three dependent variables @var{c}, @var{d} and @var{e}
919 and a single categorical variable @var{x}.
920 The second table has two dependent variables @var{a} and @var{b},
921 and two categorical variables @var{x} and @var{y}.
922 The third table has a single dependent variables @var{f}
923 and a categorical variable formed by the combination of @var{y} and @var{z}.
926 By default values are omitted from the analysis only if missing values
927 (either system missing or user missing)
928 for any of the variables directly involved in their calculation are
930 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
931 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
933 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
934 in the table specification currently being processed, regardless of
935 whether it is needed to calculate the statistic.
937 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
938 variables or in the categorical variables should be taken at their face
939 value, and not excluded.
941 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
942 variables should be taken at their face value, however cases which
943 have user missing values for the categorical variables should be omitted
944 from the calculation.
950 @cindex nonparametric tests
955 nonparametric test subcommands
960 [ /STATISTICS=@{DESCRIPTIVES@} ]
962 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
964 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
967 @cmd{NPAR TESTS} performs nonparametric tests.
968 Non parametric tests make very few assumptions about the distribution of the
970 One or more tests may be specified by using the corresponding subcommand.
971 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
972 produces for each variable that is the subject of any test.
974 Certain tests may take a long time to execute, if an exact figure is required.
975 Therefore, by default asymptotic approximations are used unless the
976 subcommand @subcmd{/METHOD=EXACT} is specified.
977 Exact tests give more accurate results, but may take an unacceptably long
978 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
979 after which the test will be abandoned, and a warning message printed.
980 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
981 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
986 * BINOMIAL:: Binomial Test
987 * CHISQUARE:: Chisquare Test
988 * COCHRAN:: Cochran Q Test
989 * FRIEDMAN:: Friedman Test
990 * KENDALL:: Kendall's W Test
991 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
992 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
993 * MANN-WHITNEY:: Mann Whitney U Test
994 * MCNEMAR:: McNemar Test
995 * MEDIAN:: Median Test
997 * SIGN:: The Sign Test
998 * WILCOXON:: Wilcoxon Signed Ranks Test
1003 @subsection Binomial test
1005 @cindex binomial test
1008 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1011 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1012 variable with that of a binomial distribution.
1013 The variable @var{p} specifies the test proportion of the binomial
1015 The default value of 0.5 is assumed if @var{p} is omitted.
1017 If a single value appears after the variable list, then that value is
1018 used as the threshold to partition the observed values. Values less
1019 than or equal to the threshold value form the first category. Values
1020 greater than the threshold form the second category.
1022 If two values appear after the variable list, then they will be used
1023 as the values which a variable must take to be in the respective
1025 Cases for which a variable takes a value equal to neither of the specified
1026 values, take no part in the test for that variable.
1028 If no values appear, then the variable must assume dichotomous
1030 If more than two distinct, non-missing values for a variable
1031 under test are encountered then an error occurs.
1033 If the test proportion is equal to 0.5, then a two tailed test is
1034 reported. For any other test proportion, a one tailed test is
1036 For one tailed tests, if the test proportion is less than
1037 or equal to the observed proportion, then the significance of
1038 observing the observed proportion or more is reported.
1039 If the test proportion is more than the observed proportion, then the
1040 significance of observing the observed proportion or less is reported.
1041 That is to say, the test is always performed in the observed
1044 @pspp{} uses a very precise approximation to the gamma function to
1045 compute the binomial significance. Thus, exact results are reported
1046 even for very large sample sizes.
1051 @subsection Chisquare Test
1053 @cindex chisquare test
1057 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1061 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1062 between the expected and observed frequencies of the categories of a variable.
1063 Optionally, a range of values may appear after the variable list.
1064 If a range is given, then non integer values are truncated, and values
1065 outside the specified range are excluded from the analysis.
1067 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1069 There must be exactly one non-zero expected value, for each observed
1070 category, or the @subcmd{EQUAL} keywork must be specified.
1071 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1072 consecutive expected categories all taking a frequency of @var{f}.
1073 The frequencies given are proportions, not absolute frequencies. The
1074 sum of the frequencies need not be 1.
1075 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1080 @subsection Cochran Q Test
1082 @cindex Cochran Q test
1083 @cindex Q, Cochran Q
1086 [ /COCHRAN = @var{var_list} ]
1089 The Cochran Q test is used to test for differences between three or more groups.
1090 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1092 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1095 @subsection Friedman Test
1097 @cindex Friedman test
1100 [ /FRIEDMAN = @var{var_list} ]
1103 The Friedman test is used to test for differences between repeated measures when
1104 there is no indication that the distributions are normally distributed.
1106 A list of variables which contain the measured data must be given. The procedure
1107 prints the sum of ranks for each variable, the test statistic and its significance.
1110 @subsection Kendall's W Test
1112 @cindex Kendall's W test
1113 @cindex coefficient of concordance
1116 [ /KENDALL = @var{var_list} ]
1119 The Kendall test investigates whether an arbitrary number of related samples come from the
1121 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1122 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1123 unity indicates complete agreement.
1126 @node KOLMOGOROV-SMIRNOV
1127 @subsection Kolmogorov-Smirnov Test
1128 @vindex KOLMOGOROV-SMIRNOV
1130 @cindex Kolmogorov-Smirnov test
1133 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1136 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1137 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1138 Normal, Uniform, Poisson and Exponential.
1140 Ideally you should provide the parameters of the distribution against which you wish to test
1141 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1142 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1144 However, if the parameters are omitted they will be imputed from the data. Imputing the
1145 parameters reduces the power of the test so should be avoided if possible.
1147 In the following example, two variables @var{score} and @var{age} are tested to see if
1148 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1151 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1153 If the variables need to be tested against different distributions, then a separate
1154 subcommand must be used. For example the following syntax tests @var{score} against
1155 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1156 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1159 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1160 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1163 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1165 @node KRUSKAL-WALLIS
1166 @subsection Kruskal-Wallis Test
1167 @vindex KRUSKAL-WALLIS
1169 @cindex Kruskal-Wallis test
1172 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1175 The Kruskal-Wallis test is used to compare data from an
1176 arbitrary number of populations. It does not assume normality.
1177 The data to be compared are specified by @var{var_list}.
1178 The categorical variable determining the groups to which the
1179 data belongs is given by @var{var}. The limits @var{lower} and
1180 @var{upper} specify the valid range of @var{var}. Any cases for
1181 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1184 The mean rank of each group as well as the chi-squared value and significance
1185 of the test will be printed.
1186 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1190 @subsection Mann-Whitney U Test
1191 @vindex MANN-WHITNEY
1193 @cindex Mann-Whitney U test
1194 @cindex U, Mann-Whitney U
1197 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1200 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1201 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}.
1202 @var{Var} may be either a string or an alpha variable.
1203 @var{Group1} and @var{group2} specify the
1204 two values of @var{var} which determine the groups of the test data.
1205 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1207 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1208 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1211 @subsection McNemar Test
1213 @cindex McNemar test
1216 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1219 Use McNemar's test to analyse the significance of the difference between
1220 pairs of correlated proportions.
1222 If the @code{WITH} keyword is omitted, then tests for all
1223 combinations of the listed variables are performed.
1224 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1225 is also given, then the number of variables preceding @code{WITH}
1226 must be the same as the number following it.
1227 In this case, tests for each respective pair of variables are
1229 If the @code{WITH} keyword is given, but the
1230 @code{(PAIRED)} keyword is omitted, then tests for each combination
1231 of variable preceding @code{WITH} against variable following
1232 @code{WITH} are performed.
1234 The data in each variable must be dichotomous. If there are more
1235 than two distinct variables an error will occur and the test will
1239 @subsection Median Test
1244 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1247 The median test is used to test whether independent samples come from
1248 populations with a common median.
1249 The median of the populations against which the samples are to be tested
1250 may be given in parentheses immediately after the
1251 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1252 union of all the samples.
1254 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1255 keyword @code{BY} must come next, and then the grouping variable. Two values
1256 in parentheses should follow. If the first value is greater than the second,
1257 then a 2 sample test is performed using these two values to determine the groups.
1258 If however, the first variable is less than the second, then a @i{k} sample test is
1259 conducted and the group values used are all values encountered which lie in the
1260 range [@var{value1},@var{value2}].
1264 @subsection Runs Test
1269 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1272 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1274 It works by examining the number of times a variable's value crosses a given threshold.
1275 The desired threshold must be specified within parentheses.
1276 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1277 Following the threshold specification comes the list of variables whose values are to be
1280 The subcommand shows the number of runs, the asymptotic significance based on the
1284 @subsection Sign Test
1289 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1292 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1294 The test does not make any assumptions about the
1295 distribution of the data.
1297 If the @code{WITH} keyword is omitted, then tests for all
1298 combinations of the listed variables are performed.
1299 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1300 is also given, then the number of variables preceding @code{WITH}
1301 must be the same as the number following it.
1302 In this case, tests for each respective pair of variables are
1304 If the @code{WITH} keyword is given, but the
1305 @code{(PAIRED)} keyword is omitted, then tests for each combination
1306 of variable preceding @code{WITH} against variable following
1307 @code{WITH} are performed.
1310 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1312 @cindex wilcoxon matched pairs signed ranks test
1315 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1318 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1320 The test does not make any assumptions about the variances of the samples.
1321 It does however assume that the distribution is symetrical.
1323 If the @subcmd{WITH} keyword is omitted, then tests for all
1324 combinations of the listed variables are performed.
1325 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1326 is also given, then the number of variables preceding @subcmd{WITH}
1327 must be the same as the number following it.
1328 In this case, tests for each respective pair of variables are
1330 If the @subcmd{WITH} keyword is given, but the
1331 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1332 of variable preceding @subcmd{WITH} against variable following
1333 @subcmd{WITH} are performed.
1342 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1343 /CRITERIA=CIN(@var{confidence})
1347 TESTVAL=@var{test_value}
1348 /VARIABLES=@var{var_list}
1351 (Independent Samples mode.)
1352 GROUPS=var(@var{value1} [, @var{value2}])
1353 /VARIABLES=@var{var_list}
1356 (Paired Samples mode.)
1357 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1362 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1364 It operates in one of three modes:
1366 @item One Sample mode.
1367 @item Independent Groups mode.
1372 Each of these modes are described in more detail below.
1373 There are two optional subcommands which are common to all modes.
1375 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1376 in the tests. The default value is 0.95.
1379 The @cmd{MISSING} subcommand determines the handling of missing
1381 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1382 calculations, but system-missing values are not.
1383 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1384 values are excluded as well as system-missing values.
1385 This is the default.
1387 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1388 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1389 @subcmd{/GROUPS} subcommands contains a missing value.
1390 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1391 which they would be needed. This is the default.
1395 * One Sample Mode:: Testing against a hypothesized mean
1396 * Independent Samples Mode:: Testing two independent groups for equal mean
1397 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1400 @node One Sample Mode
1401 @subsection One Sample Mode
1403 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1404 This mode is used to test a population mean against a hypothesized
1406 The value given to the @subcmd{TESTVAL} subcommand is the value against
1407 which you wish to test.
1408 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1409 tell @pspp{} which variables you wish to test.
1411 @node Independent Samples Mode
1412 @subsection Independent Samples Mode
1414 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1416 This mode is used to test whether two groups of values have the
1417 same population mean.
1418 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1419 tell @pspp{} the dependent variables you wish to test.
1421 The variable given in the @subcmd{GROUPS} subcommand is the independent
1422 variable which determines to which group the samples belong.
1423 The values in parentheses are the specific values of the independent
1424 variable for each group.
1425 If the parentheses are omitted and no values are given, the default values
1426 of 1.0 and 2.0 are assumed.
1428 If the independent variable is numeric,
1429 it is acceptable to specify only one value inside the parentheses.
1430 If you do this, cases where the independent variable is
1431 greater than or equal to this value belong to the first group, and cases
1432 less than this value belong to the second group.
1433 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1434 the independent variable are excluded on a listwise basis, regardless
1435 of whether @subcmd{/MISSING=LISTWISE} was specified.
1438 @node Paired Samples Mode
1439 @subsection Paired Samples Mode
1441 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1442 Use this mode when repeated measures have been taken from the same
1444 If the @subcmd{WITH} keyword is omitted, then tables for all
1445 combinations of variables given in the @cmd{PAIRS} subcommand are
1447 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1448 is also given, then the number of variables preceding @subcmd{WITH}
1449 must be the same as the number following it.
1450 In this case, tables for each respective pair of variables are
1452 In the event that the @subcmd{WITH} keyword is given, but the
1453 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1454 of variable preceding @subcmd{WITH} against variable following
1455 @subcmd{WITH} are generated.
1462 @cindex analysis of variance
1467 [/VARIABLES = ] @var{var_list} BY @var{var}
1468 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1469 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1470 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1471 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1474 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1475 variables factored by a single independent variable.
1476 It is used to compare the means of a population
1477 divided into more than two groups.
1479 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1481 The list of variables must be followed by the @subcmd{BY} keyword and
1482 the name of the independent (or factor) variable.
1484 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1485 ancilliary information. The options accepted are:
1488 Displays descriptive statistics about the groups factored by the independent
1491 Displays the Levene test of Homogeneity of Variance for the
1492 variables and their groups.
1495 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1496 differences between the groups.
1497 The subcommand must be followed by a list of numerals which are the
1498 coefficients of the groups to be tested.
1499 The number of coefficients must correspond to the number of distinct
1500 groups (or values of the independent variable).
1501 If the total sum of the coefficients are not zero, then @pspp{} will
1502 display a warning, but will proceed with the analysis.
1503 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1504 to specify different contrast tests.
1505 The @subcmd{MISSING} subcommand defines how missing values are handled.
1506 If @subcmd{LISTWISE} is specified then cases which have missing values for
1507 the independent variable or any dependent variable will be ignored.
1508 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1509 variable is missing or if the dependent variable currently being
1510 analysed is missing. The default is @subcmd{ANALYSIS}.
1511 A setting of @subcmd{EXCLUDE} means that variables whose values are
1512 user-missing are to be excluded from the analysis. A setting of
1513 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1515 Using the @code{POSTHOC} subcommand you can perform multiple
1516 pairwise comparisons on the data. The following comparison methods
1520 Least Significant Difference.
1521 @item @subcmd{TUKEY}
1522 Tukey Honestly Significant Difference.
1523 @item @subcmd{BONFERRONI}
1525 @item @subcmd{SCHEFFE}
1527 @item @subcmd{SIDAK}
1530 The Games-Howell test.
1534 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1535 that @var{value} should be used as the
1536 confidence level for which the posthoc tests will be performed.
1537 The default is 0.05.
1540 @section QUICK CLUSTER
1541 @vindex QUICK CLUSTER
1543 @cindex K-means clustering
1547 QUICK CLUSTER @var{var_list}
1548 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1549 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1552 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1553 dataset. This is useful when you wish to allocate cases into clusters
1554 of similar values and you already know the number of clusters.
1556 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1557 of the variables which contain the cluster data. Normally you will also
1558 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1559 number of clusters. If this is not given, then @var{k} defaults to 2.
1561 The command uses an iterative algorithm to determine the clusters for
1562 each case. It will continue iterating until convergence, or until @var{max_iter}
1563 iterations have been done. The default value of @var{max_iter} is 2.
1565 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1566 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1567 value and not as missing values.
1568 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1569 values are excluded as well as system-missing values.
1571 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1572 whenever any of the clustering variables contains a missing value.
1573 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1574 clustering variables contain missing values. Otherwise it is clustered
1575 on the basis of the non-missing values.
1576 The default is @subcmd{LISTWISE}.
1585 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1586 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1587 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1589 /MISSING=@{EXCLUDE,INCLUDE@}
1591 /RANK [INTO @var{var_list}]
1592 /NTILES(k) [INTO @var{var_list}]
1593 /NORMAL [INTO @var{var_list}]
1594 /PERCENT [INTO @var{var_list}]
1595 /RFRACTION [INTO @var{var_list}]
1596 /PROPORTION [INTO @var{var_list}]
1597 /N [INTO @var{var_list}]
1598 /SAVAGE [INTO @var{var_list}]
1601 The @cmd{RANK} command ranks variables and stores the results into new
1604 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1605 more variables whose values are to be ranked.
1606 After each variable, @samp{A} or @samp{D} may appear, indicating that
1607 the variable is to be ranked in ascending or descending order.
1608 Ascending is the default.
1609 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1610 which are to serve as group variables.
1611 In this case, the cases are gathered into groups, and ranks calculated
1614 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1615 default is to take the mean value of all the tied cases.
1617 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1618 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1619 functions are requested.
1621 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1622 variables created should appear in the output.
1624 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1625 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1626 If none are given, then the default is RANK.
1627 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1628 partitions into which values should be ranked.
1629 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1630 variables which are the variables to be created and receive the rank
1631 scores. There may be as many variables specified as there are
1632 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1633 then the variable names are automatically created.
1635 The @subcmd{MISSING} subcommand determines how user missing values are to be
1636 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1637 user-missing are to be excluded from the rank scores. A setting of
1638 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1640 @include regression.texi
1644 @section RELIABILITY
1649 /VARIABLES=@var{var_list}
1650 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1651 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1652 /SUMMARY=@{TOTAL,ALL@}
1653 /MISSING=@{EXCLUDE,INCLUDE@}
1656 @cindex Cronbach's Alpha
1657 The @cmd{RELIABILTY} command performs reliability analysis on the data.
1659 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1660 upon which analysis is to be performed.
1662 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1663 calculated for. If it is omitted, then analysis for all variables named
1664 in the @subcmd{VARIABLES} subcommand will be used.
1665 Optionally, the @var{name} parameter may be specified to set a string name
1668 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1669 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1670 then the variables are divided into 2 subsets. An optional parameter
1671 @var{n} may be given, to specify how many variables to be in the first subset.
1672 If @var{n} is omitted, then it defaults to one half of the variables in the
1673 scale, or one half minus one if there are an odd number of variables.
1674 The default model is @subcmd{ALPHA}.
1676 By default, any cases with user missing, or system missing values for
1678 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1679 The @subcmd{MISSING} subcommand determines whether user missing values are to
1680 be included or excluded in the analysis.
1682 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1683 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1684 analysis tested against the totals.
1692 @cindex Receiver Operating Characteristic
1693 @cindex Area under curve
1696 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1697 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1698 /PRINT = [ SE ] [ COORDINATES ]
1699 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1700 [ TESTPOS (@{LARGE,SMALL@}) ]
1701 [ CI (@var{confidence}) ]
1702 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1703 /MISSING=@{EXCLUDE,INCLUDE@}
1707 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1708 of a dataset, and to estimate the area under the curve.
1709 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1711 The mandatory @var{var_list} is the list of predictor variables.
1712 The variable @var{state_var} is the variable whose values represent the actual states,
1713 and @var{state_value} is the value of this variable which represents the positive state.
1715 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1716 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1717 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1718 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1719 By default, the curve is drawn with no reference line.
1721 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1722 Two additional tables are available.
1723 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1725 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1727 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1729 The @subcmd{CRITERIA} subcommand has four optional parameters:
1731 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1732 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1733 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1735 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1736 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1738 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1740 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1741 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1742 exponential distribution estimate.
1743 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1744 equal to the number of negative actual states.
1745 The default is @subcmd{FREE}.
1747 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1750 The @subcmd{MISSING} subcommand determines whether user missing values are to
1751 be included or excluded in the analysis. The default behaviour is to
1753 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1754 or if the variable @var{state_var} is missing, then the entire case will be