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 * MEANS:: Average values and other statistics.
15 * NPAR TESTS:: Nonparametric tests.
16 * T-TEST:: Test hypotheses about means.
17 * ONEWAY:: One way analysis of variance.
18 * QUICK CLUSTER:: K-Means clustering.
19 * RANK:: Compute rank scores.
20 * REGRESSION:: Linear regression.
21 * RELIABILITY:: Reliability analysis.
22 * ROC:: Receiver Operating Characteristic.
31 /VARIABLES=@var{var_list}
32 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
33 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
35 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
36 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
37 SESKEWNESS,SEKURTOSIS@}
38 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
39 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
43 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
45 statistics requested by the user. In addition, it can optionally
48 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
49 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
51 All other subcommands are optional:
53 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
54 @subcmd{INCLUDE} is set, then user-missing values are included in the
55 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
56 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
57 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
58 the entire case is excluded whenever any value in that case has a
59 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
61 The @subcmd{FORMAT} subcommand affects the output format. Currently the
62 @subcmd{LABELS/NOLABELS} and @subcmd{NOINDEX/INDEX} settings are not used.
63 When @subcmd{SERIAL} is
64 set, both valid and missing number of cases are listed in the output;
65 when @subcmd{NOSERIAL} is set, only valid cases are listed.
67 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
68 the specified variables. The Z scores are saved to new variables.
69 Variable names are generated by trying first the original variable name
70 with Z prepended and truncated to a maximum of 8 characters, then the
71 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
72 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
73 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
74 list by enclosing them in parentheses after each variable.
76 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
80 All of the statistics below.
84 Standard error of the mean.
87 @item @subcmd{VARIANCE}
89 @item @subcmd{KURTOSIS}
90 Kurtosis and standard error of the kurtosis.
91 @item @subcmd{SKEWNESS}
92 Skewness and standard error of the skewness.
102 Mean, standard deviation of the mean, minimum, maximum.
104 Standard error of the kurtosis.
106 Standard error of the skewness.
109 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
110 of the possible values should be self-explanatory. @subcmd{NAME} causes the
111 statistics to be sorted by name. By default, the statistics are listed
112 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
113 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
114 sort order, respectively.
122 /VARIABLES=@var{var_list}
123 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
124 @{AVALUE,DVALUE,AFREQ,DFREQ@}
125 /MISSING=@{EXCLUDE,INCLUDE@}
126 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
127 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
128 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
130 /PERCENTILES=percent@dots{}
131 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
132 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
133 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
134 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
136 (These options are not currently implemented.)
142 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
144 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
145 (including median and mode) and percentiles,
146 @cmd{FREQUENCIES} can also output
147 histograms and pie charts.
149 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
150 variables to be analyzed.
152 The @subcmd{FORMAT} subcommand controls the output format. It has several
157 @subcmd{TABLE}, the default, causes a frequency table to be output for every
158 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
159 with a numeric argument causes them to be output except when there are
160 more than the specified number of values in the table.
163 Normally frequency tables are sorted in ascending order by value. This
164 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
165 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
166 respectively, by frequency count.
169 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
170 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
171 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
172 are included. System-missing values are never included in statistics,
173 but are listed in frequency tables.
175 The available @subcmd{STATISTICS} are the same as available
176 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
177 of @subcmd{MEDIAN}, the data's median
178 value, and MODE, the mode. (If there are multiple modes, the smallest
179 value is reported.) By default, the mean, standard deviation of the
180 mean, minimum, and maximum are reported for each variable.
183 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
184 The percentiles should be presented at a list of numbers between 0
186 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
187 boundaries of the data set divided into the specified number of ranges.
188 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
191 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
192 each specified numeric variable. The X axis by default ranges from
193 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
194 and @subcmd{MAXIMUM} keywords can set an explicit range. Specify @subcmd{NORMAL} to
195 superimpose a normal curve on the histogram. Histograms are not
196 created for string variables.
199 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
200 slice represents one value, with the size of the slice proportional to
201 the value's frequency. By default, all non-missing values are given
202 slices. The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
203 displayed slices to a given range of values. The @subcmd{MISSING} keyword adds
204 slices for missing values.
206 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and @subcmd{PIECHART} are accepted
207 but not currently honoured.
213 @cindex Exploratory data analysis
214 @cindex Normality, testing for
218 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
219 [BY @var{factor1} [BY @var{subfactor1}]
220 [ @var{factor2} [BY @var{subfactor2}]]
222 [ @var{factor3} [BY @var{subfactor3}]]
224 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
225 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
227 /COMPARE=@{GROUPS,VARIABLES@}
228 /ID=@var{identity_variable}
230 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
231 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
232 [@{NOREPORT,REPORT@}]
236 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
237 In particular, it is useful for testing how closely a distribution follows a
238 normal distribution, and for finding outliers and extreme values.
240 The @subcmd{VARIABLES} subcommand is mandatory.
241 It specifies the dependent variables and optionally variables to use as
242 factors for the analysis.
243 Variables listed before the first @subcmd{BY} keyword (if any) are the
245 The dependent variables may optionally be followed by a list of
246 factors which tell @pspp{} how to break down the analysis for each
249 Following the dependent variables, factors may be specified.
250 The factors (if desired) should be preceeded by a single @subcmd{BY} keyword.
251 The format for each factor is
253 @var{factorvar} [BY @var{subfactorvar}].
255 Each unique combination of the values of @var{factorvar} and
256 @var{subfactorvar} divide the dataset into @dfn{cells}.
257 Statistics will be calculated for each cell
258 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
260 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
261 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
262 non-parametrics statistics.
263 @subcmd{EXTREME} produces a table showing the extremities of each cell.
264 A number in parentheses, @var{n} determines
265 how many upper and lower extremities to show.
266 The default number is 5.
268 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
269 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
270 as well as for each cell.
271 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
272 (unless no factor variables have been given).
273 These subcommands have no effect if there have been no factor variables
279 @cindex spreadlevel plot
280 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
281 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
282 @subcmd{SPREADLEVEL}.
283 The first three can be used to visualise how closely each cell conforms to a
284 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
285 how the variance of differs between factors.
286 Boxplots will also show you the outliers and extreme values.
288 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
289 median. It takes an optional parameter @var{t}, which specifies how the data
290 should be transformed prior to plotting.
291 The given value @var{t} is a power to which the data is raised. For example, if
292 @var{t} is given as 2, then the data will be squared.
293 Zero, however is a special value. If @var{t} is 0 or
294 is omitted, then data will be transformed by taking its natural logarithm instead of
295 raising to the power of @var{t}.
297 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
298 useful there is more than one dependent variable and at least one factor.
300 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
301 each of which contain boxplots for all the cells.
302 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
303 each containing one boxplot per dependent variable.
304 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
305 @subcmd{/COMPARE=GROUPS} were given.
307 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
308 @subcmd{/STATISTICS=EXTREME} has been given.
309 If given, it shoule provide the name of a variable which is to be used
310 to labels extreme values and outliers.
311 Numeric or string variables are permissible.
312 If the @subcmd{ID} subcommand is not given, then the casenumber will be used for
315 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
316 calculation of the descriptives command. The default is 95%.
319 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
320 and which algorithm to use for calculating them. The default is to
321 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
322 @subcmd{HAVERAGE} algorithm.
324 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
325 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
326 then then statistics for the unfactored dependent variables are
327 produced in addition to the factored variables. If there are no
328 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
331 The following example will generate descriptive statistics and histograms for
332 two variables @var{score1} and @var{score2}.
333 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
334 Therefore, the descriptives and histograms will be generated for each
336 of @var{gender} @emph{and} for each distinct combination of the values
337 of @var{gender} and @var{race}.
338 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
339 @var{score1} and @var{score2} covering the whole dataset are not produced.
341 EXAMINE @var{score1} @var{score2} BY
343 @var{gender} BY @var{culture}
344 /STATISTICS = DESCRIPTIVES
349 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
351 EXAMINE @var{height} @var{weight} BY
353 /STATISTICS = EXTREME (3)
358 In this example, we look at the height and weight of a sample of individuals and
359 how they differ between male and female.
360 A table showing the 3 largest and the 3 smallest values of @var{height} and
361 @var{weight} for each gender, and for the whole dataset will be shown.
362 Boxplots will also be produced.
363 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
364 shown in the same graphic, allowing us to easily see the difference between
366 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
367 used to label the extreme values.
370 If many dependent variables are specified, or if factor variables are
372 there are many distinct values, then @cmd{EXAMINE} will produce a very
373 large quantity of output.
376 @section CORRELATIONS
381 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
386 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
387 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
390 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
391 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
392 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
396 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
397 for a set of variables. The significance of the coefficients are also given.
399 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
400 keyword is used, then a non-square correlation table will be produced.
401 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
402 and the variables following will be the columns of the table.
403 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
406 The @cmd{MISSING} subcommand determines the handling of missing variables.
407 If @subcmd{INCLUDE} is set, then user-missing values are included in the
408 calculations, but system-missing values are not.
409 If @subcmd{EXCLUDE} is set, which is the default, user-missing
410 values are excluded as well as system-missing values.
412 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
413 whenever any variable specified in any @cmd{/VARIABLES} subcommand
414 contains a missing value.
415 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
416 values for the particular coefficient are missing.
417 The default is @subcmd{PAIRWISE}.
419 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
420 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
421 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
422 The default is @subcmd{TWOTAIL}.
424 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
425 0.05 are highlighted.
426 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
429 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
430 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
431 estimator of the standard deviation are displayed.
432 These statistics will be displayed in a separated table, for all the variables listed
433 in any @subcmd{/VARIABLES} subcommand.
434 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
435 be displayed for each pair of variables.
436 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
444 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
445 /MISSING=@{TABLE,INCLUDE,REPORT@}
446 /WRITE=@{NONE,CELLS,ALL@}
447 /FORMAT=@{TABLES,NOTABLES@}
452 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
453 ASRESIDUAL,ALL,NONE@}
454 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
455 KAPPA,ETA,CORR,ALL,NONE@}
458 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
461 The @cmd{CROSSTABS} procedure displays crosstabulation
462 tables requested by the user. It can calculate several statistics for
463 each cell in the crosstabulation tables. In addition, a number of
464 statistics can be calculated for each table itself.
466 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
467 number of dimensions is permitted, and any number of variables per
468 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
469 times as needed. This is the only required subcommand in @dfn{general
472 Occasionally, one may want to invoke a special mode called @dfn{integer
473 mode}. Normally, in general mode, @pspp{} automatically determines
474 what values occur in the data. In integer mode, the user specifies the
475 range of values that the data assumes. To invoke this mode, specify the
476 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
477 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
478 the range are truncated to the nearest integer, then assigned to that
479 value. If values occur outside this range, they are discarded. When it
480 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
483 In general mode, numeric and string variables may be specified on
484 TABLES. In integer mode, only numeric variables are allowed.
486 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
487 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
488 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
489 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
490 integer mode, user-missing values are included in tables but marked with
491 an @samp{M} (for ``missing'') and excluded from statistical
494 Currently the @subcmd{WRITE} subcommand is ignored.
496 The @subcmd{FORMAT} subcommand controls the characteristics of the
497 crosstabulation tables to be displayed. It has a number of possible
502 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
503 @subcmd{NOTABLES} suppresses them.
506 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
507 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
511 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
512 @subcmd{DVALUE} asserts a descending sort order.
515 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
518 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
521 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
522 crosstabulation table. The possible settings are:
538 Standardized residual.
540 Adjusted standardized residual.
544 Suppress cells entirely.
547 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
548 @subcmd{COLUMN}, and @subcmd{TOTAL}.
549 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
552 The @subcmd{STATISTICS} subcommand selects statistics for computation:
559 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
560 correction, linear-by-linear association.
564 Contingency coefficient.
568 Uncertainty coefficient.
584 Spearman correlation, Pearson's r.
591 Selected statistics are only calculated when appropriate for the
592 statistic. Certain statistics require tables of a particular size, and
593 some statistics are calculated only in integer mode.
595 @samp{/STATISTICS} without any settings selects CHISQ. If the
596 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
598 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
603 Pearson's R (but not Spearman) is off a little.
605 T values for Spearman's R and Pearson's R are wrong.
607 Significance of symmetric and directional measures is not calculated.
609 Asymmetric ASEs and T values for lambda are wrong.
611 ASE of Goodman and Kruskal's tau is not calculated.
613 ASE of symmetric somers' d is wrong.
615 Approximate T of uncertainty coefficient is wrong.
618 Fixes for any of these deficiencies would be welcomed.
624 @cindex factor analysis
625 @cindex principal components analysis
626 @cindex principal axis factoring
627 @cindex data reduction
630 FACTOR VARIABLES=@var{var_list}
632 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
634 [ /EXTRACTION=@{PC, PAF@}]
636 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
638 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
642 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
644 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
646 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
649 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
650 common factors in the data or for data reduction purposes.
652 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
654 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
655 If @subcmd{PC} is specified, then Principal Components Analysis is used.
656 If @subcmd{PAF} is specified, then Principal Axis Factoring is
657 used. By default Principal Components Analysis will be used.
659 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
660 Three methods are available: @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
661 If don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
662 rotation on the data. Oblique rotations are not supported.
664 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
665 to be analysed. By default, the correlation matrix is analysed.
667 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
670 @item @subcmd{UNIVARIATE}
671 A table of mean values, standard deviations and total weights are printed.
672 @item @subcmd{INITIAL}
673 Initial communalities and eigenvalues are printed.
674 @item @subcmd{EXTRACTION}
675 Extracted communalities and eigenvalues are printed.
676 @item @subcmd{ROTATION}
677 Rotated communalities and eigenvalues are printed.
678 @item @subcmd{CORRELATION}
679 The correlation matrix is printed.
680 @item @subcmd{COVARIANCE}
681 The covariance matrix is printed.
683 The determinant of the correlation or covariance matrix is printed.
685 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
687 The significance of the elements of correlation matrix is printed.
689 All of the above are printed.
690 @item @subcmd{DEFAULT}
691 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
694 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
695 which factors (components) should be retained.
697 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
698 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
699 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
700 performed, and all coefficients will be printed.
702 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
703 If @subcmd{FACTORS(@var{n})} is
704 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
705 be used. @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
706 The default value of @var{l} is 1. The @subcmd{ECONVERGE} and @subcmd{ITERATE} settings have effect only when iterative algorithms for factor
707 extraction (such as Principal Axis Factoring) are used. @subcmd{ECONVERGE(@var{delta})} specifies that
708 iteration should cease when
709 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
710 default value of @var{delta} is 0.001.
711 The @subcmd{ITERATE(@var{m})} setting sets the maximum number of iterations to @var{m}. The default value of @var{m} is 25.
713 The @cmd{MISSING} subcommand determines the handling of missing variables.
714 If @subcmd{INCLUDE} is set, then user-missing values are included in the
715 calculations, but system-missing values are not.
716 If @subcmd{EXCLUDE} is set, which is the default, user-missing
717 values are excluded as well as system-missing values.
719 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
720 whenever any variable specified in the @cmd{VARIABLES} subcommand
721 contains a missing value.
722 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
723 values for the particular coefficient are missing.
724 The default is @subcmd{LISTWISE}.
735 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
737 [ /@{@var{var_list}@}
738 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
740 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
741 [VARIANCE] [KURT] [SEKURT]
742 [SKEW] [SESKEW] [FIRST] [LAST]
743 [HARMONIC] [GEOMETRIC]
748 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
751 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
752 statistics, either for the dataset as a whole or for categories of data.
754 The simplest form of the command is
758 @noindent which calculates the mean, count and standard deviation for @var{v}.
759 If you specify a grouping variable, for example
761 MEANS @var{v} BY @var{g}.
763 @noindent then the means, counts and standard deviations for @var{v} after having
764 been grouped by @var{g} will be calculated.
765 Instead of the mean, count and standard deviation, you could specify the statistics
766 in which you are interested:
768 MEANS @var{x} @var{y} BY @var{g}
769 /CELLS = HARMONIC SUM MIN.
771 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
774 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
778 @cindex arithmetic mean
781 The count of the values.
782 @item @subcmd{STDDEV}
783 The standard deviation.
784 @item @subcmd{SEMEAN}
785 The standard error of the mean.
787 The sum of the values.
793 The difference between the maximum and minimum values.
794 @item @subcmd{VARIANCE}
797 The first value in the category.
799 The last value in the category.
802 @item @subcmd{SESKEW}
803 The standard error of the skewness.
806 @item @subcmd{SEKURT}
807 The standard error of the kurtosis.
808 @item @subcmd{HARMONIC}
809 @cindex harmonic mean
811 @item @subcmd{GEOMETRIC}
812 @cindex geometric mean
816 In addition, three special keywords are recognized:
818 @item @subcmd{DEFAULT}
819 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
821 All of the above statistics will be calculated.
823 No statistics will be calculated (only a summary will be shown).
827 More than one @dfn{table} can be specified in a single command.
828 Each table is separated by a @samp{/}. For
832 @var{c} @var{d} @var{e} BY @var{x}
833 /@var{a} @var{b} BY @var{x} @var{y}
834 /@var{f} BY @var{y} BY @var{z}.
836 has three tables (the @samp{TABLE =} is optional).
837 The first table has three dependent variables @var{c}, @var{d} and @var{e}
838 and a single categorical variable @var{x}.
839 The second table has two dependent variables @var{a} and @var{b},
840 and two categorical variables @var{x} and @var{y}.
841 The third table has a single dependent variables @var{f}
842 and a categorical variable formed by the combination of @var{y} and @var{z}.
845 By default values are omitted from the analysis only if missing values
846 (either system missing or user missing)
847 for any of the variables directly involved in their calculation are
849 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
850 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
852 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
853 in the table specification currently being processed, regardless of
854 whether it is needed to calculate the statistic.
856 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
857 variables or in the categorical variables should be taken at their face
858 value, and not excluded.
860 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
861 variables should be taken at their face value, however cases which
862 have user missing values for the categorical variables should be omitted
863 from the calculation.
869 @cindex nonparametric tests
874 nonparametric test subcommands
879 [ /STATISTICS=@{DESCRIPTIVES@} ]
881 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
883 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
886 @cmd{NPAR TESTS} performs nonparametric tests.
887 Non parametric tests make very few assumptions about the distribution of the
889 One or more tests may be specified by using the corresponding subcommand.
890 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
891 produces for each variable that is the subject of any test.
893 Certain tests may take a long time to execute, if an exact figure is required.
894 Therefore, by default asymptotic approximations are used unless the
895 subcommand @subcmd{/METHOD=EXACT} is specified.
896 Exact tests give more accurate results, but may take an unacceptably long
897 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
898 after which the test will be abandoned, and a warning message printed.
899 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
900 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
905 * BINOMIAL:: Binomial Test
906 * CHISQUARE:: Chisquare Test
907 * COCHRAN:: Cochran Q Test
908 * FRIEDMAN:: Friedman Test
909 * KENDALL:: Kendall's W Test
910 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
911 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
912 * MANN-WHITNEY:: Mann Whitney U Test
913 * MCNEMAR:: McNemar Test
914 * MEDIAN:: Median Test
916 * SIGN:: The Sign Test
917 * WILCOXON:: Wilcoxon Signed Ranks Test
922 @subsection Binomial test
924 @cindex binomial test
927 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
930 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
931 variable with that of a binomial distribution.
932 The variable @var{p} specifies the test proportion of the binomial
934 The default value of 0.5 is assumed if @var{p} is omitted.
936 If a single value appears after the variable list, then that value is
937 used as the threshold to partition the observed values. Values less
938 than or equal to the threshold value form the first category. Values
939 greater than the threshold form the second category.
941 If two values appear after the variable list, then they will be used
942 as the values which a variable must take to be in the respective
944 Cases for which a variable takes a value equal to neither of the specified
945 values, take no part in the test for that variable.
947 If no values appear, then the variable must assume dichotomous
949 If more than two distinct, non-missing values for a variable
950 under test are encountered then an error occurs.
952 If the test proportion is equal to 0.5, then a two tailed test is
953 reported. For any other test proportion, a one tailed test is
955 For one tailed tests, if the test proportion is less than
956 or equal to the observed proportion, then the significance of
957 observing the observed proportion or more is reported.
958 If the test proportion is more than the observed proportion, then the
959 significance of observing the observed proportion or less is reported.
960 That is to say, the test is always performed in the observed
963 @pspp{} uses a very precise approximation to the gamma function to
964 compute the binomial significance. Thus, exact results are reported
965 even for very large sample sizes.
970 @subsection Chisquare Test
972 @cindex chisquare test
976 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
980 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
981 between the expected and observed frequencies of the categories of a variable.
982 Optionally, a range of values may appear after the variable list.
983 If a range is given, then non integer values are truncated, and values
984 outside the specified range are excluded from the analysis.
986 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
988 There must be exactly one non-zero expected value, for each observed
989 category, or the @subcmd{EQUAL} keywork must be specified.
990 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
991 consecutive expected categories all taking a frequency of @var{f}.
992 The frequencies given are proportions, not absolute frequencies. The
993 sum of the frequencies need not be 1.
994 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
999 @subsection Cochran Q Test
1001 @cindex Cochran Q test
1002 @cindex Q, Cochran Q
1005 [ /COCHRAN = @var{var_list} ]
1008 The Cochran Q test is used to test for differences between three or more groups.
1009 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1011 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1014 @subsection Friedman Test
1016 @cindex Friedman test
1019 [ /FRIEDMAN = @var{var_list} ]
1022 The Friedman test is used to test for differences between repeated measures when
1023 there is no indication that the distributions are normally distributed.
1025 A list of variables which contain the measured data must be given. The procedure
1026 prints the sum of ranks for each variable, the test statistic and its significance.
1029 @subsection Kendall's W Test
1031 @cindex Kendall's W test
1032 @cindex coefficient of concordance
1035 [ /KENDALL = @var{var_list} ]
1038 The Kendall test investigates whether an arbitrary number of related samples come from the
1040 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1041 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1042 unity indicates complete agreement.
1045 @node KOLMOGOROV-SMIRNOV
1046 @subsection Kolmogorov-Smirnov Test
1047 @vindex KOLMOGOROV-SMIRNOV
1049 @cindex Kolmogorov-Smirnov test
1052 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1055 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1056 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1057 Normal, Uniform, Poisson and Exponential.
1059 Ideally you should provide the parameters of the distribution against which you wish to test
1060 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1061 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1063 However, if the parameters are omitted they will be imputed from the data. Imputing the
1064 parameters reduces the power of the test so should be avoided if possible.
1066 In the following example, two variables @var{score} and @var{age} are tested to see if
1067 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1070 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1072 If the variables need to be tested against different distributions, then a separate
1073 subcommand must be used. For example the following syntax tests @var{score} against
1074 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1075 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1078 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1079 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1082 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1084 @node KRUSKAL-WALLIS
1085 @subsection Kruskal-Wallis Test
1086 @vindex KRUSKAL-WALLIS
1088 @cindex Kruskal-Wallis test
1091 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1094 The Kruskal-Wallis test is used to compare data from an
1095 arbitrary number of populations. It does not assume normality.
1096 The data to be compared are specified by @var{var_list}.
1097 The categorical variable determining the groups to which the
1098 data belongs is given by @var{var}. The limits @var{lower} and
1099 @var{upper} specify the valid range of @var{var}. Any cases for
1100 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1103 The mean rank of each group as well as the chi-squared value and significance
1104 of the test will be printed.
1105 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1109 @subsection Mann-Whitney U Test
1110 @vindex MANN-WHITNEY
1112 @cindex Mann-Whitney U test
1113 @cindex U, Mann-Whitney U
1116 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1119 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1120 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}.
1121 @var{Var} may be either a string or an alpha variable.
1122 @var{Group1} and @var{group2} specify the
1123 two values of @var{var} which determine the groups of the test data.
1124 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1126 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1127 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1130 @subsection McNemar Test
1132 @cindex McNemar test
1135 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1138 Use McNemar's test to analyse the significance of the difference between
1139 pairs of correlated proportions.
1141 If the @code{WITH} keyword is omitted, then tests for all
1142 combinations of the listed variables are performed.
1143 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1144 is also given, then the number of variables preceding @code{WITH}
1145 must be the same as the number following it.
1146 In this case, tests for each respective pair of variables are
1148 If the @code{WITH} keyword is given, but the
1149 @code{(PAIRED)} keyword is omitted, then tests for each combination
1150 of variable preceding @code{WITH} against variable following
1151 @code{WITH} are performed.
1153 The data in each variable must be dichotomous. If there are more
1154 than two distinct variables an error will occur and the test will
1158 @subsection Median Test
1163 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1166 The median test is used to test whether independent samples come from
1167 populations with a common median.
1168 The median of the populations against which the samples are to be tested
1169 may be given in parentheses immediately after the
1170 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1171 union of all the samples.
1173 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1174 keyword @code{BY} must come next, and then the grouping variable. Two values
1175 in parentheses should follow. If the first value is greater than the second,
1176 then a 2 sample test is performed using these two values to determine the groups.
1177 If however, the first variable is less than the second, then a @i{k} sample test is
1178 conducted and the group values used are all values encountered which lie in the
1179 range [@var{value1},@var{value2}].
1183 @subsection Runs Test
1188 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1191 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1193 It works by examining the number of times a variable's value crosses a given threshold.
1194 The desired threshold must be specified within parentheses.
1195 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1196 Following the threshold specification comes the list of variables whose values are to be
1199 The subcommand shows the number of runs, the asymptotic significance based on the
1203 @subsection Sign Test
1208 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1211 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1213 The test does not make any assumptions about the
1214 distribution of the data.
1216 If the @code{WITH} keyword is omitted, then tests for all
1217 combinations of the listed variables are performed.
1218 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1219 is also given, then the number of variables preceding @code{WITH}
1220 must be the same as the number following it.
1221 In this case, tests for each respective pair of variables are
1223 If the @code{WITH} keyword is given, but the
1224 @code{(PAIRED)} keyword is omitted, then tests for each combination
1225 of variable preceding @code{WITH} against variable following
1226 @code{WITH} are performed.
1229 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1231 @cindex wilcoxon matched pairs signed ranks test
1234 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1237 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1239 The test does not make any assumptions about the variances of the samples.
1240 It does however assume that the distribution is symetrical.
1242 If the @subcmd{WITH} keyword is omitted, then tests for all
1243 combinations of the listed variables are performed.
1244 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1245 is also given, then the number of variables preceding @subcmd{WITH}
1246 must be the same as the number following it.
1247 In this case, tests for each respective pair of variables are
1249 If the @subcmd{WITH} keyword is given, but the
1250 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1251 of variable preceding @subcmd{WITH} against variable following
1252 @subcmd{WITH} are performed.
1261 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1262 /CRITERIA=CIN(@var{confidence})
1266 TESTVAL=@var{test_value}
1267 /VARIABLES=@var{var_list}
1270 (Independent Samples mode.)
1271 GROUPS=var(@var{value1} [, @var{value2}])
1272 /VARIABLES=@var{var_list}
1275 (Paired Samples mode.)
1276 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1281 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1283 It operates in one of three modes:
1285 @item One Sample mode.
1286 @item Independent Groups mode.
1291 Each of these modes are described in more detail below.
1292 There are two optional subcommands which are common to all modes.
1294 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1295 in the tests. The default value is 0.95.
1298 The @cmd{MISSING} subcommand determines the handling of missing
1300 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1301 calculations, but system-missing values are not.
1302 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1303 values are excluded as well as system-missing values.
1304 This is the default.
1306 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1307 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1308 @subcmd{/GROUPS} subcommands contains a missing value.
1309 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1310 which they would be needed. This is the default.
1314 * One Sample Mode:: Testing against a hypothesized mean
1315 * Independent Samples Mode:: Testing two independent groups for equal mean
1316 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1319 @node One Sample Mode
1320 @subsection One Sample Mode
1322 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1323 This mode is used to test a population mean against a hypothesized
1325 The value given to the @subcmd{TESTVAL} subcommand is the value against
1326 which you wish to test.
1327 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1328 tell @pspp{} which variables you wish to test.
1330 @node Independent Samples Mode
1331 @subsection Independent Samples Mode
1333 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1335 This mode is used to test whether two groups of values have the
1336 same population mean.
1337 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1338 tell @pspp{} the dependent variables you wish to test.
1340 The variable given in the @subcmd{GROUPS} subcommand is the independent
1341 variable which determines to which group the samples belong.
1342 The values in parentheses are the specific values of the independent
1343 variable for each group.
1344 If the parentheses are omitted and no values are given, the default values
1345 of 1.0 and 2.0 are assumed.
1347 If the independent variable is numeric,
1348 it is acceptable to specify only one value inside the parentheses.
1349 If you do this, cases where the independent variable is
1350 greater than or equal to this value belong to the first group, and cases
1351 less than this value belong to the second group.
1352 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1353 the independent variable are excluded on a listwise basis, regardless
1354 of whether @subcmd{/MISSING=LISTWISE} was specified.
1357 @node Paired Samples Mode
1358 @subsection Paired Samples Mode
1360 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1361 Use this mode when repeated measures have been taken from the same
1363 If the @subcmd{WITH} keyword is omitted, then tables for all
1364 combinations of variables given in the @cmd{PAIRS} subcommand are
1366 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1367 is also given, then the number of variables preceding @subcmd{WITH}
1368 must be the same as the number following it.
1369 In this case, tables for each respective pair of variables are
1371 In the event that the @subcmd{WITH} keyword is given, but the
1372 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1373 of variable preceding @subcmd{WITH} against variable following
1374 @subcmd{WITH} are generated.
1381 @cindex analysis of variance
1386 [/VARIABLES = ] @var{var_list} BY @var{var}
1387 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1388 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1389 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1390 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1393 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1394 variables factored by a single independent variable.
1395 It is used to compare the means of a population
1396 divided into more than two groups.
1398 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1400 The list of variables must be followed by the @subcmd{BY} keyword and
1401 the name of the independent (or factor) variable.
1403 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1404 ancilliary information. The options accepted are:
1407 Displays descriptive statistics about the groups factored by the independent
1410 Displays the Levene test of Homogeneity of Variance for the
1411 variables and their groups.
1414 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1415 differences between the groups.
1416 The subcommand must be followed by a list of numerals which are the
1417 coefficients of the groups to be tested.
1418 The number of coefficients must correspond to the number of distinct
1419 groups (or values of the independent variable).
1420 If the total sum of the coefficients are not zero, then @pspp{} will
1421 display a warning, but will proceed with the analysis.
1422 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1423 to specify different contrast tests.
1424 The @subcmd{MISSING} subcommand defines how missing values are handled.
1425 If @subcmd{LISTWISE} is specified then cases which have missing values for
1426 the independent variable or any dependent variable will be ignored.
1427 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1428 variable is missing or if the dependent variable currently being
1429 analysed is missing. The default is @subcmd{ANALYSIS}.
1430 A setting of @subcmd{EXCLUDE} means that variables whose values are
1431 user-missing are to be excluded from the analysis. A setting of
1432 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1434 Using the @code{POSTHOC} subcommand you can perform multiple
1435 pairwise comparisons on the data. The following comparison methods
1439 Least Significant Difference.
1440 @item @subcmd{TUKEY}
1441 Tukey Honestly Significant Difference.
1442 @item @subcmd{BONFERRONI}
1444 @item @subcmd{SCHEFFE}
1446 @item @subcmd{SIDAK}
1449 The Games-Howell test.
1453 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1454 that @var{value} should be used as the
1455 confidence level for which the posthoc tests will be performed.
1456 The default is 0.05.
1459 @section QUICK CLUSTER
1460 @vindex QUICK CLUSTER
1462 @cindex K-means clustering
1466 QUICK CLUSTER @var{var_list}
1467 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1468 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1471 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1472 dataset. This is useful when you wish to allocate cases into clusters
1473 of similar values and you already know the number of clusters.
1475 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1476 of the variables which contain the cluster data. Normally you will also
1477 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1478 number of clusters. If this is not given, then @var{k} defaults to 2.
1480 The command uses an iterative algorithm to determine the clusters for
1481 each case. It will continue iterating until convergence, or until @var{max_iter}
1482 iterations have been done. The default value of @var{max_iter} is 2.
1484 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1485 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1486 value and not as missing values.
1487 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1488 values are excluded as well as system-missing values.
1490 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1491 whenever any of the clustering variables contains a missing value.
1492 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1493 clustering variables contain missing values. Otherwise it is clustered
1494 on the basis of the non-missing values.
1495 The default is @subcmd{LISTWISE}.
1504 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1505 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1506 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1508 /MISSING=@{EXCLUDE,INCLUDE@}
1510 /RANK [INTO @var{var_list}]
1511 /NTILES(k) [INTO @var{var_list}]
1512 /NORMAL [INTO @var{var_list}]
1513 /PERCENT [INTO @var{var_list}]
1514 /RFRACTION [INTO @var{var_list}]
1515 /PROPORTION [INTO @var{var_list}]
1516 /N [INTO @var{var_list}]
1517 /SAVAGE [INTO @var{var_list}]
1520 The @cmd{RANK} command ranks variables and stores the results into new
1523 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1524 more variables whose values are to be ranked.
1525 After each variable, @samp{A} or @samp{D} may appear, indicating that
1526 the variable is to be ranked in ascending or descending order.
1527 Ascending is the default.
1528 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1529 which are to serve as group variables.
1530 In this case, the cases are gathered into groups, and ranks calculated
1533 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1534 default is to take the mean value of all the tied cases.
1536 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1537 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1538 functions are requested.
1540 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1541 variables created should appear in the output.
1543 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1544 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1545 If none are given, then the default is RANK.
1546 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1547 partitions into which values should be ranked.
1548 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1549 variables which are the variables to be created and receive the rank
1550 scores. There may be as many variables specified as there are
1551 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1552 then the variable names are automatically created.
1554 The @subcmd{MISSING} subcommand determines how user missing values are to be
1555 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1556 user-missing are to be excluded from the rank scores. A setting of
1557 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1559 @include regression.texi
1563 @section RELIABILITY
1568 /VARIABLES=@var{var_list}
1569 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1570 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1571 /SUMMARY=@{TOTAL,ALL@}
1572 /MISSING=@{EXCLUDE,INCLUDE@}
1575 @cindex Cronbach's Alpha
1576 The @cmd{RELIABILTY} command performs reliability analysis on the data.
1578 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1579 upon which analysis is to be performed.
1581 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1582 calculated for. If it is omitted, then analysis for all variables named
1583 in the @subcmd{VARIABLES} subcommand will be used.
1584 Optionally, the @var{name} parameter may be specified to set a string name
1587 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1588 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1589 then the variables are divided into 2 subsets. An optional parameter
1590 @var{n} may be given, to specify how many variables to be in the first subset.
1591 If @var{n} is omitted, then it defaults to one half of the variables in the
1592 scale, or one half minus one if there are an odd number of variables.
1593 The default model is @subcmd{ALPHA}.
1595 By default, any cases with user missing, or system missing values for
1597 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1598 The @subcmd{MISSING} subcommand determines whether user missing values are to
1599 be included or excluded in the analysis.
1601 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1602 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1603 analysis tested against the totals.
1611 @cindex Receiver Operating Characteristic
1612 @cindex Area under curve
1615 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1616 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1617 /PRINT = [ SE ] [ COORDINATES ]
1618 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1619 [ TESTPOS (@{LARGE,SMALL@}) ]
1620 [ CI (@var{confidence}) ]
1621 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1622 /MISSING=@{EXCLUDE,INCLUDE@}
1626 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1627 of a dataset, and to estimate the area under the curve.
1628 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1630 The mandatory @var{var_list} is the list of predictor variables.
1631 The variable @var{state_var} is the variable whose values represent the actual states,
1632 and @var{state_value} is the value of this variable which represents the positive state.
1634 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1635 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1636 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1637 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1638 By default, the curve is drawn with no reference line.
1640 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1641 Two additional tables are available.
1642 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1644 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1646 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1648 The @subcmd{CRITERIA} subcommand has four optional parameters:
1650 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1651 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1652 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1654 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1655 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1657 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1659 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1660 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1661 exponential distribution estimate.
1662 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1663 equal to the number of negative actual states.
1664 The default is @subcmd{FREE}.
1666 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1669 The @subcmd{MISSING} subcommand determines whether user missing values are to
1670 be included or excluded in the analysis. The default behaviour is to
1672 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1673 or if the variable @var{state_var} is missing, then the entire case will be