1 @c PSPP - a program for statistical analysis.
2 @c Copyright (C) 2017 Free Software Foundation, Inc.
3 @c Permission is granted to copy, distribute and/or modify this document
4 @c under the terms of the GNU Free Documentation License, Version 1.3
5 @c or any later version published by the Free Software Foundation;
6 @c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
7 @c A copy of the license is included in the section entitled "GNU
8 @c Free Documentation License".
13 This chapter documents the statistical procedures that @pspp{} supports so
17 * DESCRIPTIVES:: Descriptive statistics.
18 * FREQUENCIES:: Frequency tables.
19 * EXAMINE:: Testing data for normality.
21 * CORRELATIONS:: Correlation tables.
22 * CROSSTABS:: Crosstabulation tables.
23 * FACTOR:: Factor analysis and Principal Components analysis.
24 * GLM:: Univariate Linear Models.
25 * LOGISTIC REGRESSION:: Bivariate Logistic Regression.
26 * MEANS:: Average values and other statistics.
27 * NPAR TESTS:: Nonparametric tests.
28 * T-TEST:: Test hypotheses about means.
29 * ONEWAY:: One way analysis of variance.
30 * QUICK CLUSTER:: K-Means clustering.
31 * RANK:: Compute rank scores.
32 * REGRESSION:: Linear regression.
33 * RELIABILITY:: Reliability analysis.
34 * ROC:: Receiver Operating Characteristic.
43 /VARIABLES=@var{var_list}
44 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
45 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
47 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
48 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
49 SESKEWNESS,SEKURTOSIS@}
50 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
51 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
55 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
57 statistics requested by the user. In addition, it can optionally
60 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
61 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
63 All other subcommands are optional:
65 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
66 @subcmd{INCLUDE} is set, then user-missing values are included in the
67 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
68 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
69 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
70 the entire case is excluded whenever any value in that case has a
71 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
73 The @subcmd{FORMAT} subcommand has no effect. It is accepted for
74 backward compatibility.
76 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
77 the specified variables. The Z scores are saved to new variables.
78 Variable names are generated by trying first the original variable name
79 with Z prepended and truncated to a maximum of 8 characters, then the
80 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
81 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
82 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
83 list by enclosing them in parentheses after each variable.
84 When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
85 treating temporary transformations as permanent.
87 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
91 All of the statistics below.
95 Standard error of the mean.
98 @item @subcmd{VARIANCE}
100 @item @subcmd{KURTOSIS}
101 Kurtosis and standard error of the kurtosis.
102 @item @subcmd{SKEWNESS}
103 Skewness and standard error of the skewness.
113 Mean, standard deviation of the mean, minimum, maximum.
115 Standard error of the kurtosis.
117 Standard error of the skewness.
120 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
121 of the possible values should be self-explanatory. @subcmd{NAME} causes the
122 statistics to be sorted by name. By default, the statistics are listed
123 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
124 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
125 sort order, respectively.
133 /VARIABLES=@var{var_list}
134 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
135 @{AVALUE,DVALUE,AFREQ,DFREQ@}
136 /MISSING=@{EXCLUDE,INCLUDE@}
137 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
138 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
139 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
141 /PERCENTILES=percent@dots{}
142 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
143 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
144 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
145 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
146 /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
148 /ORDER=@{ANALYSIS,VARIABLE@}
151 (These options are not currently implemented.)
156 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
158 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
159 (including median and mode) and percentiles, and various graphical representations
160 of the frequency distribution.
162 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
163 variables to be analyzed.
165 The @subcmd{FORMAT} subcommand controls the output format. It has several
170 @subcmd{TABLE}, the default, causes a frequency table to be output for every
171 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
172 with a numeric argument causes them to be output except when there are
173 more than the specified number of values in the table.
176 Normally frequency tables are sorted in ascending order by value. This
177 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
178 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
179 respectively, by frequency count.
182 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
183 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
184 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
185 are included. System-missing values are never included in statistics,
186 but are listed in frequency tables.
188 The available @subcmd{STATISTICS} are the same as available
189 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
190 of @subcmd{MEDIAN}, the data's median
191 value, and MODE, the mode. (If there are multiple modes, the smallest
192 value is reported.) By default, the mean, standard deviation of the
193 mean, minimum, and maximum are reported for each variable.
196 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
197 The percentiles should be presented at a list of numbers between 0
199 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
200 boundaries of the data set divided into the specified number of ranges.
201 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
204 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
205 each specified numeric variable. The X axis by default ranges from
206 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
207 and @subcmd{MAXIMUM} keywords can set an explicit range.
208 @footnote{The number of
209 bins is chosen according to the Freedman-Diaconis rule:
210 @math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
211 and @math{n} is the number of samples. Note that
212 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
213 Histograms are not created for string variables.
215 Specify @subcmd{NORMAL} to superimpose a normal curve on the
219 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
220 slice represents one value, with the size of the slice proportional to
221 the value's frequency. By default, all non-missing values are given
223 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
224 displayed slices to a given range of values.
225 The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
226 piechart. This is the default.
227 If instead, @subcmd{MISSING} is specified, then a single slice
228 will be included representing all system missing and user-missing cases.
231 The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
232 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
233 categories whose counts which lie outside the specified limits.
234 The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
235 of each category, whereas the @subcmd{PERCENT} option will display relative
238 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
239 @subcmd{PIECHART} are accepted but not currently honoured.
241 The @subcmd{ORDER} subcommand is accepted but ignored.
247 @cindex Exploratory data analysis
248 @cindex normality, testing
252 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
253 [BY @var{factor1} [BY @var{subfactor1}]
254 [ @var{factor2} [BY @var{subfactor2}]]
256 [ @var{factor3} [BY @var{subfactor3}]]
258 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
259 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
261 /COMPARE=@{GROUPS,VARIABLES@}
262 /ID=@var{identity_variable}
264 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
265 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
266 [@{NOREPORT,REPORT@}]
270 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
271 In particular, it is useful for testing how closely a distribution follows a
272 normal distribution, and for finding outliers and extreme values.
274 The @subcmd{VARIABLES} subcommand is mandatory.
275 It specifies the dependent variables and optionally variables to use as
276 factors for the analysis.
277 Variables listed before the first @subcmd{BY} keyword (if any) are the
279 The dependent variables may optionally be followed by a list of
280 factors which tell @pspp{} how to break down the analysis for each
283 Following the dependent variables, factors may be specified.
284 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
285 The format for each factor is
287 @var{factorvar} [BY @var{subfactorvar}].
289 Each unique combination of the values of @var{factorvar} and
290 @var{subfactorvar} divide the dataset into @dfn{cells}.
291 Statistics will be calculated for each cell
292 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
294 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
295 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
296 non-parametrics statistics.
297 @subcmd{EXTREME} produces a table showing the extremities of each cell.
298 A number in parentheses, @var{n} determines
299 how many upper and lower extremities to show.
300 The default number is 5.
302 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
303 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
304 as well as for each cell.
305 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
306 (unless no factor variables have been given).
307 These subcommands have no effect if there have been no factor variables
313 @cindex spreadlevel plot
314 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
315 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
316 @subcmd{SPREADLEVEL}.
317 The first three can be used to visualise how closely each cell conforms to a
318 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
319 how the variance of differs between factors.
320 Boxplots will also show you the outliers and extreme values.
321 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
322 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
323 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
325 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
326 median. It takes an optional parameter @var{t}, which specifies how the data
327 should be transformed prior to plotting.
328 The given value @var{t} is a power to which the data is raised. For example, if
329 @var{t} is given as 2, then the data will be squared.
330 Zero, however is a special value. If @var{t} is 0 or
331 is omitted, then data will be transformed by taking its natural logarithm instead of
332 raising to the power of @var{t}.
335 When one or more plots are requested, @subcmd{EXAMINE} also performs the
336 Shapiro-Wilk test for each category.
337 There are however a number of provisos:
339 @item All weight values must be integer.
340 @item The cumulative weight value must be in the range [3, 5000]
343 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
344 useful there is more than one dependent variable and at least one factor.
346 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
347 each of which contain boxplots for all the cells.
348 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
349 each containing one boxplot per dependent variable.
350 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
351 @subcmd{/COMPARE=GROUPS} were given.
353 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
354 @subcmd{/STATISTICS=EXTREME} has been given.
355 If given, it should provide the name of a variable which is to be used
356 to labels extreme values and outliers.
357 Numeric or string variables are permissible.
358 If the @subcmd{ID} subcommand is not given, then the case number will be used for
361 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
362 calculation of the descriptives command. The default is 95%.
365 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
366 and which algorithm to use for calculating them. The default is to
367 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
368 @subcmd{HAVERAGE} algorithm.
370 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
371 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
372 then statistics for the unfactored dependent variables are
373 produced in addition to the factored variables. If there are no
374 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
377 The following example will generate descriptive statistics and histograms for
378 two variables @var{score1} and @var{score2}.
379 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
380 Therefore, the descriptives and histograms will be generated for each
382 of @var{gender} @emph{and} for each distinct combination of the values
383 of @var{gender} and @var{race}.
384 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
385 @var{score1} and @var{score2} covering the whole dataset are not produced.
387 EXAMINE @var{score1} @var{score2} BY
389 @var{gender} BY @var{culture}
390 /STATISTICS = DESCRIPTIVES
395 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
397 EXAMINE @var{height} @var{weight} BY
399 /STATISTICS = EXTREME (3)
404 In this example, we look at the height and weight of a sample of individuals and
405 how they differ between male and female.
406 A table showing the 3 largest and the 3 smallest values of @var{height} and
407 @var{weight} for each gender, and for the whole dataset will be shown.
408 Boxplots will also be produced.
409 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
410 shown in the same graphic, allowing us to easily see the difference between
412 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
413 used to label the extreme values.
416 If many dependent variables are specified, or if factor variables are
418 there are many distinct values, then @cmd{EXAMINE} will produce a very
419 large quantity of output.
425 @cindex Exploratory data analysis
426 @cindex normality, testing
430 /HISTOGRAM [(NORMAL)]= @var{var}
431 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
432 /BAR = @{@var{summary-function}(@var{var1}) | @var{count-function}@} BY @var{var2} [BY @var{var3}]
433 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
434 [@{NOREPORT,REPORT@}]
438 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
439 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
440 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
443 * SCATTERPLOT:: Cartesian Plots
444 * HISTOGRAM:: Histograms
445 * BAR CHART:: Bar Charts
449 @subsection Scatterplot
452 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the
453 data. The different values of the optional third variable @var{var3}
454 will result in different colours and/or markers for the plot. The
455 following is an example for producing a scatterplot.
459 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
462 This example will produce a scatterplot where @var{height} is plotted versus @var{weight}. Depending
463 on the value of the @var{gender} variable, the colour of the datapoint is different. With
464 this plot it is possible to analyze gender differences for @var{height} vs.@: @var{weight} relation.
467 @subsection Histogram
470 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
472 The keyword @subcmd{NORMAL} may be specified in parentheses, to indicate that the ideal normal curve
473 should be superimposed over the histogram.
474 For an alternative method to produce histograms @pxref{EXAMINE}. The
475 following example produces a histogram plot for the variable @var{weight}.
479 /HISTOGRAM = @var{weight}.
483 @subsection Bar Chart
486 The subcommand @subcmd{BAR} produces a bar chart.
487 This subcommand requires that a @var{count-function} be specified (with no arguments) or a @var{summary-function} with a variable @var{var1} in parentheses.
488 Following the summary or count function, the keyword @subcmd{BY} should be specified and then a catagorical variable, @var{var2}.
489 The values of the variable @var{var2} determine the labels of the bars to be plotted.
490 Optionally a second categorical variable @var{var3} may be specified in which case a clustered (grouped) bar chart is produced.
492 Valid count functions are
495 The weighted counts of the cases in each category.
497 The weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
499 The cumulative weighted counts of the cases in each category.
501 The cumulative weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
504 The summary function is applied to @var{var1} across all cases in each category.
505 The recognised summary functions are:
517 The following examples assume a dataset which is the results of a survey.
518 Each respondent has indicated annual income, their sex and city of residence.
519 One could create a bar chart showing how the mean income varies between of residents of different cities, thus:
521 GRAPH /BAR = MEAN(@var{income}) BY @var{city}.
524 This can be extended to also indicate how income in each city differs between the sexes.
526 GRAPH /BAR = MEAN(@var{income}) BY @var{city} BY @var{sex}.
529 One might also want to see how many respondents there are from each city. This can be achieved as follows:
531 GRAPH /BAR = COUNT BY @var{city}.
534 Bar charts can also be produced using the @ref{FREQUENCIES} and @ref{CROSSTABS} commands.
537 @section CORRELATIONS
542 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
547 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
548 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
551 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
552 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
553 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
557 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
558 for a set of variables. The significance of the coefficients are also given.
560 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
561 keyword is used, then a non-square correlation table will be produced.
562 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
563 and the variables following will be the columns of the table.
564 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
567 The @cmd{MISSING} subcommand determines the handling of missing variables.
568 If @subcmd{INCLUDE} is set, then user-missing values are included in the
569 calculations, but system-missing values are not.
570 If @subcmd{EXCLUDE} is set, which is the default, user-missing
571 values are excluded as well as system-missing values.
573 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
574 whenever any variable specified in any @cmd{/VARIABLES} subcommand
575 contains a missing value.
576 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
577 values for the particular coefficient are missing.
578 The default is @subcmd{PAIRWISE}.
580 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
581 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
582 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
583 The default is @subcmd{TWOTAIL}.
585 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
586 0.05 are highlighted.
587 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
590 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
591 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
592 estimator of the standard deviation are displayed.
593 These statistics will be displayed in a separated table, for all the variables listed
594 in any @subcmd{/VARIABLES} subcommand.
595 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
596 be displayed for each pair of variables.
597 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
605 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
606 /MISSING=@{TABLE,INCLUDE,REPORT@}
607 /WRITE=@{NONE,CELLS,ALL@}
608 /FORMAT=@{TABLES,NOTABLES@}
613 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
614 ASRESIDUAL,ALL,NONE@}
615 /COUNT=@{ASIS,CASE,CELL@}
617 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
618 KAPPA,ETA,CORR,ALL,NONE@}
622 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
625 The @cmd{CROSSTABS} procedure displays crosstabulation
626 tables requested by the user. It can calculate several statistics for
627 each cell in the crosstabulation tables. In addition, a number of
628 statistics can be calculated for each table itself.
630 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
631 number of dimensions is permitted, and any number of variables per
632 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
633 times as needed. This is the only required subcommand in @dfn{general
636 Occasionally, one may want to invoke a special mode called @dfn{integer
637 mode}. Normally, in general mode, @pspp{} automatically determines
638 what values occur in the data. In integer mode, the user specifies the
639 range of values that the data assumes. To invoke this mode, specify the
640 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
641 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
642 the range are truncated to the nearest integer, then assigned to that
643 value. If values occur outside this range, they are discarded. When it
644 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
647 In general mode, numeric and string variables may be specified on
648 TABLES. In integer mode, only numeric variables are allowed.
650 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
651 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
652 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
653 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
654 integer mode, user-missing values are included in tables but marked with
655 a footnote and excluded from statistical calculations.
657 Currently the @subcmd{WRITE} subcommand is ignored.
659 The @subcmd{FORMAT} subcommand controls the characteristics of the
660 crosstabulation tables to be displayed. It has a number of possible
665 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
666 @subcmd{NOTABLES} suppresses them.
669 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
670 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
674 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
675 @subcmd{DVALUE} asserts a descending sort order.
678 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
681 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
684 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
685 crosstabulation table. The possible settings are:
701 Standardized residual.
703 Adjusted standardized residual.
707 Suppress cells entirely.
710 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
711 @subcmd{COLUMN}, and @subcmd{TOTAL}.
712 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
715 By default, crosstabulation and statistics use raw case weights,
716 without rounding. Use the @subcmd{/COUNT} subcommand to perform
717 rounding: CASE rounds the weights of individual weights as cases are
718 read, CELL rounds the weights of cells within each crosstabulation
719 table after it has been constructed, and ASIS explicitly specifies the
720 default non-rounding behavior. When rounding is requested, ROUND, the
721 default, rounds to the nearest integer and TRUNCATE rounds toward
724 The @subcmd{STATISTICS} subcommand selects statistics for computation:
731 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
732 correction, linear-by-linear association.
736 Contingency coefficient.
740 Uncertainty coefficient.
756 Spearman correlation, Pearson's r.
763 Selected statistics are only calculated when appropriate for the
764 statistic. Certain statistics require tables of a particular size, and
765 some statistics are calculated only in integer mode.
767 @samp{/STATISTICS} without any settings selects CHISQ. If the
768 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
771 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
772 variables on each table.
773 If a table has more than two variables, the counts for the third and subsequent levels
774 will be aggregated and the chart will be produces as if there were only two variables.
777 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
778 following limitations:
782 Significance of some symmetric and directional measures is not calculated.
784 Asymptotic standard error is not calculated for
785 Goodman and Kruskal's tau or symmetric Somers' d.
787 Approximate T is not calculated for symmetric uncertainty coefficient.
790 Fixes for any of these deficiencies would be welcomed.
796 @cindex factor analysis
797 @cindex principal components analysis
798 @cindex principal axis factoring
799 @cindex data reduction
803 VARIABLES=@var{var_list},
804 MATRIX IN (@{CORR,COV@}=@{*,@var{file_spec}@})
807 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
809 [ /ANALYSIS=@var{var_list} ]
811 [ /EXTRACTION=@{PC, PAF@}]
813 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
815 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [AIC] [SIG] [ALL] [DEFAULT] ]
819 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
821 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
823 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
826 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
827 common factors in the data or for data reduction purposes.
829 The @subcmd{VARIABLES} subcommand is required (unless the @subcmd{MATRIX IN}
831 It lists the variables which are to partake in the analysis. (The @subcmd{ANALYSIS}
832 subcommand may optionally further limit the variables that
833 participate; it is useful primarily in conjunction with @subcmd{MATRIX IN}.)
835 If @subcmd{MATRIX IN} instead of @subcmd{VARIABLES} is specified, then the analysis
836 is performed on a pre-prepared correlation or covariance matrix file instead of on
837 individual data cases. Typically the matrix file will have been generated by
838 @cmd{MATRIX DATA} (@pxref{MATRIX DATA}) or provided by a third party.
839 If specified, @subcmd{MATRIX IN} must be followed by @samp{COV} or @samp{CORR},
840 then by @samp{=} and @var{file_spec} all in parentheses.
841 @var{file_spec} may either be an asterisk, which indicates the currently loaded
842 dataset, or it may be a filename to be loaded. @xref{MATRIX DATA}, for the expected
845 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
846 If @subcmd{PC} is specified, then Principal Components Analysis is used.
847 If @subcmd{PAF} is specified, then Principal Axis Factoring is
848 used. By default Principal Components Analysis will be used.
850 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
851 Three orthogonal rotation methods are available:
852 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
853 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
854 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
855 The default value of @var{k} is 5.
856 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
857 rotation on the data.
859 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
860 to be analysed. By default, the correlation matrix is analysed.
862 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
865 @item @subcmd{UNIVARIATE}
866 A table of mean values, standard deviations and total weights are printed.
867 @item @subcmd{INITIAL}
868 Initial communalities and eigenvalues are printed.
869 @item @subcmd{EXTRACTION}
870 Extracted communalities and eigenvalues are printed.
871 @item @subcmd{ROTATION}
872 Rotated communalities and eigenvalues are printed.
873 @item @subcmd{CORRELATION}
874 The correlation matrix is printed.
875 @item @subcmd{COVARIANCE}
876 The covariance matrix is printed.
878 The determinant of the correlation or covariance matrix is printed.
880 The anti-image covariance and anti-image correlation matrices are printed.
882 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
884 The significance of the elements of correlation matrix is printed.
886 All of the above are printed.
887 @item @subcmd{DEFAULT}
888 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
891 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
892 which factors (components) should be retained.
894 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
895 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
896 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
897 performed, and all coefficients will be printed.
899 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
900 If @subcmd{FACTORS(@var{n})} is
901 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
903 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
904 The default value of @var{l} is 1.
905 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
906 extraction (such as Principal Axis Factoring) are used.
907 @subcmd{ECONVERGE(@var{delta})} specifies that
908 iteration should cease when
909 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
910 default value of @var{delta} is 0.001.
911 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
912 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
914 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
915 If @subcmd{EXTRACTION} follows, it affects convergence.
916 If @subcmd{ROTATION} follows, it affects rotation.
917 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
918 The default value of @var{m} is 25.
920 The @cmd{MISSING} subcommand determines the handling of missing variables.
921 If @subcmd{INCLUDE} is set, then user-missing values are included in the
922 calculations, but system-missing values are not.
923 If @subcmd{EXCLUDE} is set, which is the default, user-missing
924 values are excluded as well as system-missing values.
926 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
927 whenever any variable specified in the @cmd{VARIABLES} subcommand
928 contains a missing value.
929 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
930 values for the particular coefficient are missing.
931 The default is @subcmd{LISTWISE}.
937 @cindex univariate analysis of variance
938 @cindex fixed effects
939 @cindex factorial anova
940 @cindex analysis of variance
945 GLM @var{dependent_vars} BY @var{fixed_factors}
946 [/METHOD = SSTYPE(@var{type})]
947 [/DESIGN = @var{interaction_0} [@var{interaction_1} [... @var{interaction_n}]]]
948 [/INTERCEPT = @{INCLUDE|EXCLUDE@}]
949 [/MISSING = @{INCLUDE|EXCLUDE@}]
952 The @cmd{GLM} procedure can be used for fixed effects factorial Anova.
954 The @var{dependent_vars} are the variables to be analysed.
955 You may analyse several variables in the same command in which case they should all
956 appear before the @code{BY} keyword.
958 The @var{fixed_factors} list must be one or more categorical variables. Normally it
959 will not make sense to enter a scalar variable in the @var{fixed_factors} and doing
960 so may cause @pspp{} to do a lot of unnecessary processing.
962 The @subcmd{METHOD} subcommand is used to change the method for producing the sums of
963 squares. Available values of @var{type} are 1, 2 and 3. The default is type 3.
965 You may specify a custom design using the @subcmd{DESIGN} subcommand.
966 The design comprises a list of interactions where each interaction is a
967 list of variables separated by a @samp{*}. For example the command
969 GLM subject BY sex age_group race
970 /DESIGN = age_group sex group age_group*sex age_group*race
972 @noindent specifies the model @math{subject = age_group + sex + race + age_group*sex + age_group*race}.
973 If no @subcmd{DESIGN} subcommand is specified, then the default is all possible combinations
974 of the fixed factors. That is to say
976 GLM subject BY sex age_group race
979 @math{subject = age_group + sex + race + age_group*sex + age_group*race + sex*race + age_group*sex*race}.
982 The @subcmd{MISSING} subcommand determines the handling of missing
984 If @subcmd{INCLUDE} is set then, for the purposes of GLM analysis,
985 only system-missing values are considered
986 to be missing; user-missing values are not regarded as missing.
987 If @subcmd{EXCLUDE} is set, which is the default, then user-missing
988 values are considered to be missing as well as system-missing values.
989 A case for which any dependent variable or any factor
990 variable has a missing value is excluded from the analysis.
992 @node LOGISTIC REGRESSION
993 @section LOGISTIC REGRESSION
995 @vindex LOGISTIC REGRESSION
996 @cindex logistic regression
997 @cindex bivariate logistic regression
1000 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
1002 [/CATEGORICAL = @var{categorical_predictors}]
1004 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
1006 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
1008 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
1009 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
1010 [CUT(@var{cut_point})]]
1012 [/MISSING = @{INCLUDE|EXCLUDE@}]
1015 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
1016 variable in terms of one or more predictor variables.
1018 The minimum command is
1020 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
1022 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
1023 are the predictor variables whose coefficients the procedure estimates.
1025 By default, a constant term is included in the model.
1026 Hence, the full model is
1029 = b_0 + b_1 {\bf x_1}
1035 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
1036 Simple variables as well as interactions between variables may be listed here.
1038 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
1039 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
1041 An iterative Newton-Raphson procedure is used to fit the model.
1042 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
1043 and other parameters.
1044 The value of @var{cut_point} is used in the classification table. It is the
1045 threshold above which predicted values are considered to be 1. Values
1046 of @var{cut_point} must lie in the range [0,1].
1047 During iterations, if any one of the stopping criteria are satisfied, the procedure is
1048 considered complete.
1049 The stopping criteria are:
1051 @item The number of iterations exceeds @var{max_iterations}.
1052 The default value of @var{max_iterations} is 20.
1053 @item The change in the all coefficient estimates are less than @var{min_delta}.
1054 The default value of @var{min_delta} is 0.001.
1055 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
1056 The default value of @var{min_delta} is zero.
1057 This means that this criterion is disabled.
1058 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
1059 In other words, the probabilities are close to zero or one.
1060 The default value of @var{min_epsilon} is 0.00000001.
1064 The @subcmd{PRINT} subcommand controls the display of optional statistics.
1065 Currently there is one such option, @subcmd{CI}, which indicates that the
1066 confidence interval of the odds ratio should be displayed as well as its value.
1067 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
1068 confidence level of the desired confidence interval.
1070 The @subcmd{MISSING} subcommand determines the handling of missing
1072 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1073 calculations, but system-missing values are not.
1074 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1075 values are excluded as well as system-missing values.
1076 This is the default.
1087 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
1089 [ /@{@var{var_list}@}
1090 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
1092 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
1093 [VARIANCE] [KURT] [SEKURT]
1094 [SKEW] [SESKEW] [FIRST] [LAST]
1095 [HARMONIC] [GEOMETRIC]
1100 [/MISSING = [INCLUDE] [DEPENDENT]]
1103 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
1104 statistics, either for the dataset as a whole or for categories of data.
1106 The simplest form of the command is
1110 @noindent which calculates the mean, count and standard deviation for @var{v}.
1111 If you specify a grouping variable, for example
1113 MEANS @var{v} BY @var{g}.
1115 @noindent then the means, counts and standard deviations for @var{v} after having
1116 been grouped by @var{g} will be calculated.
1117 Instead of the mean, count and standard deviation, you could specify the statistics
1118 in which you are interested:
1120 MEANS @var{x} @var{y} BY @var{g}
1121 /CELLS = HARMONIC SUM MIN.
1123 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
1126 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
1130 @cindex arithmetic mean
1131 The arithmetic mean.
1132 @item @subcmd{COUNT}
1133 The count of the values.
1134 @item @subcmd{STDDEV}
1135 The standard deviation.
1136 @item @subcmd{SEMEAN}
1137 The standard error of the mean.
1139 The sum of the values.
1144 @item @subcmd{RANGE}
1145 The difference between the maximum and minimum values.
1146 @item @subcmd{VARIANCE}
1148 @item @subcmd{FIRST}
1149 The first value in the category.
1151 The last value in the category.
1154 @item @subcmd{SESKEW}
1155 The standard error of the skewness.
1158 @item @subcmd{SEKURT}
1159 The standard error of the kurtosis.
1160 @item @subcmd{HARMONIC}
1161 @cindex harmonic mean
1163 @item @subcmd{GEOMETRIC}
1164 @cindex geometric mean
1168 In addition, three special keywords are recognized:
1170 @item @subcmd{DEFAULT}
1171 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
1173 All of the above statistics will be calculated.
1175 No statistics will be calculated (only a summary will be shown).
1179 More than one @dfn{table} can be specified in a single command.
1180 Each table is separated by a @samp{/}. For
1184 @var{c} @var{d} @var{e} BY @var{x}
1185 /@var{a} @var{b} BY @var{x} @var{y}
1186 /@var{f} BY @var{y} BY @var{z}.
1188 has three tables (the @samp{TABLE =} is optional).
1189 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1190 and a single categorical variable @var{x}.
1191 The second table has two dependent variables @var{a} and @var{b},
1192 and two categorical variables @var{x} and @var{y}.
1193 The third table has a single dependent variables @var{f}
1194 and a categorical variable formed by the combination of @var{y} and @var{z}.
1197 By default values are omitted from the analysis only if missing values
1198 (either system missing or user missing)
1199 for any of the variables directly involved in their calculation are
1201 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1202 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1204 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1205 variables or in the categorical variables should be taken at their face
1206 value, and not excluded.
1208 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1209 variables should be taken at their face value, however cases which
1210 have user missing values for the categorical variables should be omitted
1211 from the calculation.
1217 @cindex nonparametric tests
1222 nonparametric test subcommands
1227 [ /STATISTICS=@{DESCRIPTIVES@} ]
1229 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1231 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1234 @cmd{NPAR TESTS} performs nonparametric tests.
1235 Non parametric tests make very few assumptions about the distribution of the
1237 One or more tests may be specified by using the corresponding subcommand.
1238 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1239 produces for each variable that is the subject of any test.
1241 Certain tests may take a long time to execute, if an exact figure is required.
1242 Therefore, by default asymptotic approximations are used unless the
1243 subcommand @subcmd{/METHOD=EXACT} is specified.
1244 Exact tests give more accurate results, but may take an unacceptably long
1245 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1246 after which the test will be abandoned, and a warning message printed.
1247 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1248 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1253 * BINOMIAL:: Binomial Test
1254 * CHISQUARE:: Chisquare Test
1255 * COCHRAN:: Cochran Q Test
1256 * FRIEDMAN:: Friedman Test
1257 * KENDALL:: Kendall's W Test
1258 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1259 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1260 * MANN-WHITNEY:: Mann Whitney U Test
1261 * MCNEMAR:: McNemar Test
1262 * MEDIAN:: Median Test
1264 * SIGN:: The Sign Test
1265 * WILCOXON:: Wilcoxon Signed Ranks Test
1270 @subsection Binomial test
1272 @cindex binomial test
1275 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1278 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1279 variable with that of a binomial distribution.
1280 The variable @var{p} specifies the test proportion of the binomial
1282 The default value of 0.5 is assumed if @var{p} is omitted.
1284 If a single value appears after the variable list, then that value is
1285 used as the threshold to partition the observed values. Values less
1286 than or equal to the threshold value form the first category. Values
1287 greater than the threshold form the second category.
1289 If two values appear after the variable list, then they will be used
1290 as the values which a variable must take to be in the respective
1292 Cases for which a variable takes a value equal to neither of the specified
1293 values, take no part in the test for that variable.
1295 If no values appear, then the variable must assume dichotomous
1297 If more than two distinct, non-missing values for a variable
1298 under test are encountered then an error occurs.
1300 If the test proportion is equal to 0.5, then a two tailed test is
1301 reported. For any other test proportion, a one tailed test is
1303 For one tailed tests, if the test proportion is less than
1304 or equal to the observed proportion, then the significance of
1305 observing the observed proportion or more is reported.
1306 If the test proportion is more than the observed proportion, then the
1307 significance of observing the observed proportion or less is reported.
1308 That is to say, the test is always performed in the observed
1311 @pspp{} uses a very precise approximation to the gamma function to
1312 compute the binomial significance. Thus, exact results are reported
1313 even for very large sample sizes.
1318 @subsection Chisquare Test
1320 @cindex chisquare test
1324 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1328 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1329 between the expected and observed frequencies of the categories of a variable.
1330 Optionally, a range of values may appear after the variable list.
1331 If a range is given, then non integer values are truncated, and values
1332 outside the specified range are excluded from the analysis.
1334 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1336 There must be exactly one non-zero expected value, for each observed
1337 category, or the @subcmd{EQUAL} keyword must be specified.
1338 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1339 consecutive expected categories all taking a frequency of @var{f}.
1340 The frequencies given are proportions, not absolute frequencies. The
1341 sum of the frequencies need not be 1.
1342 If no @subcmd{/EXPECTED} subcommand is given, then equal frequencies
1347 @subsection Cochran Q Test
1349 @cindex Cochran Q test
1350 @cindex Q, Cochran Q
1353 [ /COCHRAN = @var{var_list} ]
1356 The Cochran Q test is used to test for differences between three or more groups.
1357 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1359 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1362 @subsection Friedman Test
1364 @cindex Friedman test
1367 [ /FRIEDMAN = @var{var_list} ]
1370 The Friedman test is used to test for differences between repeated measures when
1371 there is no indication that the distributions are normally distributed.
1373 A list of variables which contain the measured data must be given. The procedure
1374 prints the sum of ranks for each variable, the test statistic and its significance.
1377 @subsection Kendall's W Test
1379 @cindex Kendall's W test
1380 @cindex coefficient of concordance
1383 [ /KENDALL = @var{var_list} ]
1386 The Kendall test investigates whether an arbitrary number of related samples come from the
1388 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1389 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1390 unity indicates complete agreement.
1393 @node KOLMOGOROV-SMIRNOV
1394 @subsection Kolmogorov-Smirnov Test
1395 @vindex KOLMOGOROV-SMIRNOV
1397 @cindex Kolmogorov-Smirnov test
1400 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1403 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1404 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1405 Normal, Uniform, Poisson and Exponential.
1407 Ideally you should provide the parameters of the distribution against which you wish to test
1408 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1409 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1411 However, if the parameters are omitted they will be imputed from the data. Imputing the
1412 parameters reduces the power of the test so should be avoided if possible.
1414 In the following example, two variables @var{score} and @var{age} are tested to see if
1415 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1418 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1420 If the variables need to be tested against different distributions, then a separate
1421 subcommand must be used. For example the following syntax tests @var{score} against
1422 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1423 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1426 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1427 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1430 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1432 @node KRUSKAL-WALLIS
1433 @subsection Kruskal-Wallis Test
1434 @vindex KRUSKAL-WALLIS
1436 @cindex Kruskal-Wallis test
1439 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1442 The Kruskal-Wallis test is used to compare data from an
1443 arbitrary number of populations. It does not assume normality.
1444 The data to be compared are specified by @var{var_list}.
1445 The categorical variable determining the groups to which the
1446 data belongs is given by @var{var}. The limits @var{lower} and
1447 @var{upper} specify the valid range of @var{var}. Any cases for
1448 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1451 The mean rank of each group as well as the chi-squared value and significance
1452 of the test will be printed.
1453 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1457 @subsection Mann-Whitney U Test
1458 @vindex MANN-WHITNEY
1460 @cindex Mann-Whitney U test
1461 @cindex U, Mann-Whitney U
1464 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1467 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1468 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}.
1469 @var{Var} may be either a string or an alpha variable.
1470 @var{Group1} and @var{group2} specify the
1471 two values of @var{var} which determine the groups of the test data.
1472 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1474 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1475 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1478 @subsection McNemar Test
1480 @cindex McNemar test
1483 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1486 Use McNemar's test to analyse the significance of the difference between
1487 pairs of correlated proportions.
1489 If the @code{WITH} keyword is omitted, then tests for all
1490 combinations of the listed variables are performed.
1491 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1492 is also given, then the number of variables preceding @code{WITH}
1493 must be the same as the number following it.
1494 In this case, tests for each respective pair of variables are
1496 If the @code{WITH} keyword is given, but the
1497 @code{(PAIRED)} keyword is omitted, then tests for each combination
1498 of variable preceding @code{WITH} against variable following
1499 @code{WITH} are performed.
1501 The data in each variable must be dichotomous. If there are more
1502 than two distinct variables an error will occur and the test will
1506 @subsection Median Test
1511 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1514 The median test is used to test whether independent samples come from
1515 populations with a common median.
1516 The median of the populations against which the samples are to be tested
1517 may be given in parentheses immediately after the
1518 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1519 union of all the samples.
1521 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1522 keyword @code{BY} must come next, and then the grouping variable. Two values
1523 in parentheses should follow. If the first value is greater than the second,
1524 then a 2 sample test is performed using these two values to determine the groups.
1525 If however, the first variable is less than the second, then a @i{k} sample test is
1526 conducted and the group values used are all values encountered which lie in the
1527 range [@var{value1},@var{value2}].
1531 @subsection Runs Test
1536 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1539 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1541 It works by examining the number of times a variable's value crosses a given threshold.
1542 The desired threshold must be specified within parentheses.
1543 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1544 Following the threshold specification comes the list of variables whose values are to be
1547 The subcommand shows the number of runs, the asymptotic significance based on the
1551 @subsection Sign Test
1556 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1559 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1561 The test does not make any assumptions about the
1562 distribution of the data.
1564 If the @code{WITH} keyword is omitted, then tests for all
1565 combinations of the listed variables are performed.
1566 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1567 is also given, then the number of variables preceding @code{WITH}
1568 must be the same as the number following it.
1569 In this case, tests for each respective pair of variables are
1571 If the @code{WITH} keyword is given, but the
1572 @code{(PAIRED)} keyword is omitted, then tests for each combination
1573 of variable preceding @code{WITH} against variable following
1574 @code{WITH} are performed.
1577 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1579 @cindex wilcoxon matched pairs signed ranks test
1582 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1585 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1587 The test does not make any assumptions about the variances of the samples.
1588 It does however assume that the distribution is symmetrical.
1590 If the @subcmd{WITH} keyword is omitted, then tests for all
1591 combinations of the listed variables are performed.
1592 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1593 is also given, then the number of variables preceding @subcmd{WITH}
1594 must be the same as the number following it.
1595 In this case, tests for each respective pair of variables are
1597 If the @subcmd{WITH} keyword is given, but the
1598 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1599 of variable preceding @subcmd{WITH} against variable following
1600 @subcmd{WITH} are performed.
1609 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1610 /CRITERIA=CI(@var{confidence})
1614 TESTVAL=@var{test_value}
1615 /VARIABLES=@var{var_list}
1618 (Independent Samples mode.)
1619 GROUPS=var(@var{value1} [, @var{value2}])
1620 /VARIABLES=@var{var_list}
1623 (Paired Samples mode.)
1624 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1629 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1631 It operates in one of three modes:
1633 @item One Sample mode.
1634 @item Independent Groups mode.
1639 Each of these modes are described in more detail below.
1640 There are two optional subcommands which are common to all modes.
1642 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1643 in the tests. The default value is 0.95.
1646 The @cmd{MISSING} subcommand determines the handling of missing
1648 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1649 calculations, but system-missing values are not.
1650 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1651 values are excluded as well as system-missing values.
1652 This is the default.
1654 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1655 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1656 @subcmd{/GROUPS} subcommands contains a missing value.
1657 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1658 which they would be needed. This is the default.
1662 * One Sample Mode:: Testing against a hypothesized mean
1663 * Independent Samples Mode:: Testing two independent groups for equal mean
1664 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1667 @node One Sample Mode
1668 @subsection One Sample Mode
1670 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1671 This mode is used to test a population mean against a hypothesized
1673 The value given to the @subcmd{TESTVAL} subcommand is the value against
1674 which you wish to test.
1675 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1676 tell @pspp{} which variables you wish to test.
1678 @node Independent Samples Mode
1679 @subsection Independent Samples Mode
1681 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1683 This mode is used to test whether two groups of values have the
1684 same population mean.
1685 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1686 tell @pspp{} the dependent variables you wish to test.
1688 The variable given in the @subcmd{GROUPS} subcommand is the independent
1689 variable which determines to which group the samples belong.
1690 The values in parentheses are the specific values of the independent
1691 variable for each group.
1692 If the parentheses are omitted and no values are given, the default values
1693 of 1.0 and 2.0 are assumed.
1695 If the independent variable is numeric,
1696 it is acceptable to specify only one value inside the parentheses.
1697 If you do this, cases where the independent variable is
1698 greater than or equal to this value belong to the first group, and cases
1699 less than this value belong to the second group.
1700 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1701 the independent variable are excluded on a listwise basis, regardless
1702 of whether @subcmd{/MISSING=LISTWISE} was specified.
1705 @node Paired Samples Mode
1706 @subsection Paired Samples Mode
1708 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1709 Use this mode when repeated measures have been taken from the same
1711 If the @subcmd{WITH} keyword is omitted, then tables for all
1712 combinations of variables given in the @cmd{PAIRS} subcommand are
1714 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1715 is also given, then the number of variables preceding @subcmd{WITH}
1716 must be the same as the number following it.
1717 In this case, tables for each respective pair of variables are
1719 In the event that the @subcmd{WITH} keyword is given, but the
1720 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1721 of variable preceding @subcmd{WITH} against variable following
1722 @subcmd{WITH} are generated.
1729 @cindex analysis of variance
1734 [/VARIABLES = ] @var{var_list} BY @var{var}
1735 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1736 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1737 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1738 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1741 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1742 variables factored by a single independent variable.
1743 It is used to compare the means of a population
1744 divided into more than two groups.
1746 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1748 The list of variables must be followed by the @subcmd{BY} keyword and
1749 the name of the independent (or factor) variable.
1751 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1752 ancillary information. The options accepted are:
1755 Displays descriptive statistics about the groups factored by the independent
1758 Displays the Levene test of Homogeneity of Variance for the
1759 variables and their groups.
1762 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1763 differences between the groups.
1764 The subcommand must be followed by a list of numerals which are the
1765 coefficients of the groups to be tested.
1766 The number of coefficients must correspond to the number of distinct
1767 groups (or values of the independent variable).
1768 If the total sum of the coefficients are not zero, then @pspp{} will
1769 display a warning, but will proceed with the analysis.
1770 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1771 to specify different contrast tests.
1772 The @subcmd{MISSING} subcommand defines how missing values are handled.
1773 If @subcmd{LISTWISE} is specified then cases which have missing values for
1774 the independent variable or any dependent variable will be ignored.
1775 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1776 variable is missing or if the dependent variable currently being
1777 analysed is missing. The default is @subcmd{ANALYSIS}.
1778 A setting of @subcmd{EXCLUDE} means that variables whose values are
1779 user-missing are to be excluded from the analysis. A setting of
1780 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1782 Using the @code{POSTHOC} subcommand you can perform multiple
1783 pairwise comparisons on the data. The following comparison methods
1787 Least Significant Difference.
1788 @item @subcmd{TUKEY}
1789 Tukey Honestly Significant Difference.
1790 @item @subcmd{BONFERRONI}
1792 @item @subcmd{SCHEFFE}
1794 @item @subcmd{SIDAK}
1797 The Games-Howell test.
1801 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1802 that @var{value} should be used as the
1803 confidence level for which the posthoc tests will be performed.
1804 The default is 0.05.
1807 @section QUICK CLUSTER
1808 @vindex QUICK CLUSTER
1810 @cindex K-means clustering
1814 QUICK CLUSTER @var{var_list}
1815 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
1816 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1817 [/PRINT=@{INITIAL@} @{CLUSTER@}]
1818 [/SAVE[=[CLUSTER[(@var{membership_var})]] [DISTANCE[(@var{distance_var})]]]
1821 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1822 dataset. This is useful when you wish to allocate cases into clusters
1823 of similar values and you already know the number of clusters.
1825 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1826 of the variables which contain the cluster data. Normally you will also
1827 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1828 number of clusters. If this is not specified, then @var{k} defaults to 2.
1830 If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
1831 the initial clusters is used. This will provide for faster execution but
1832 less well separated initial clusters and hence possibly an inferior final
1836 @cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
1837 The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
1838 During classification, @pspp{} will continue iterating until until @var{max_iter}
1839 iterations have been done or the convergence criterion (see below) is fulfilled.
1840 The default value of @var{max_iter} is 2.
1842 If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
1843 no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
1846 The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
1847 to set the convergence criterion. The value of convergence criterion is @var{epsilon}
1848 times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
1849 the mean cluster distance between one iteration and the next
1850 is less than the convergence criterion. The default value of @var{epsilon} is zero.
1852 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1853 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1854 value and not as missing values.
1855 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1856 values are excluded as well as system-missing values.
1858 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1859 whenever any of the clustering variables contains a missing value.
1860 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1861 clustering variables contain missing values. Otherwise it is clustered
1862 on the basis of the non-missing values.
1863 The default is @subcmd{LISTWISE}.
1865 The @subcmd{PRINT} subcommand requests additional output to be printed.
1866 If @subcmd{INITIAL} is set, then the initial cluster memberships will
1868 If @subcmd{CLUSTER} is set, the cluster memberships of the individual
1869 cases will be displayed (potentially generating lengthy output).
1871 You can specify the subcommand @subcmd{SAVE} to ask that each case's cluster membership
1872 and the euclidean distance between the case and its cluster center be saved to
1873 a new variable in the active dataset. To save the cluster membership use the
1874 @subcmd{CLUSTER} keyword and to save the distance use the @subcmd{DISTANCE} keyword.
1875 Each keyword may optionally be followed by a variable name in parentheses to specify
1876 the new variable which is to contain the saved parameter. If no variable name is specified,
1877 then PSPP will create one.
1885 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1886 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1887 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1889 /MISSING=@{EXCLUDE,INCLUDE@}
1891 /RANK [INTO @var{var_list}]
1892 /NTILES(k) [INTO @var{var_list}]
1893 /NORMAL [INTO @var{var_list}]
1894 /PERCENT [INTO @var{var_list}]
1895 /RFRACTION [INTO @var{var_list}]
1896 /PROPORTION [INTO @var{var_list}]
1897 /N [INTO @var{var_list}]
1898 /SAVAGE [INTO @var{var_list}]
1901 The @cmd{RANK} command ranks variables and stores the results into new
1904 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1905 more variables whose values are to be ranked.
1906 After each variable, @samp{A} or @samp{D} may appear, indicating that
1907 the variable is to be ranked in ascending or descending order.
1908 Ascending is the default.
1909 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1910 which are to serve as group variables.
1911 In this case, the cases are gathered into groups, and ranks calculated
1914 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1915 default is to take the mean value of all the tied cases.
1917 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1918 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1919 functions are requested.
1921 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1922 variables created should appear in the output.
1924 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1925 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1926 If none are given, then the default is RANK.
1927 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1928 partitions into which values should be ranked.
1929 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1930 variables which are the variables to be created and receive the rank
1931 scores. There may be as many variables specified as there are
1932 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1933 then the variable names are automatically created.
1935 The @subcmd{MISSING} subcommand determines how user missing values are to be
1936 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1937 user-missing are to be excluded from the rank scores. A setting of
1938 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1940 @include regression.texi
1944 @section RELIABILITY
1949 /VARIABLES=@var{var_list}
1950 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1951 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1952 /SUMMARY=@{TOTAL,ALL@}
1953 /MISSING=@{EXCLUDE,INCLUDE@}
1956 @cindex Cronbach's Alpha
1957 The @cmd{RELIABILITY} command performs reliability analysis on the data.
1959 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1960 upon which analysis is to be performed.
1962 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1963 calculated for. If it is omitted, then analysis for all variables named
1964 in the @subcmd{VARIABLES} subcommand will be used.
1965 Optionally, the @var{name} parameter may be specified to set a string name
1968 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1969 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1970 then the variables are divided into 2 subsets. An optional parameter
1971 @var{n} may be given, to specify how many variables to be in the first subset.
1972 If @var{n} is omitted, then it defaults to one half of the variables in the
1973 scale, or one half minus one if there are an odd number of variables.
1974 The default model is @subcmd{ALPHA}.
1976 By default, any cases with user missing, or system missing values for
1978 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1979 The @subcmd{MISSING} subcommand determines whether user missing values are to
1980 be included or excluded in the analysis.
1982 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1983 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1984 analysis tested against the totals.
1992 @cindex Receiver Operating Characteristic
1993 @cindex Area under curve
1996 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1997 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1998 /PRINT = [ SE ] [ COORDINATES ]
1999 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
2000 [ TESTPOS (@{LARGE,SMALL@}) ]
2001 [ CI (@var{confidence}) ]
2002 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
2003 /MISSING=@{EXCLUDE,INCLUDE@}
2007 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
2008 of a dataset, and to estimate the area under the curve.
2009 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
2011 The mandatory @var{var_list} is the list of predictor variables.
2012 The variable @var{state_var} is the variable whose values represent the actual states,
2013 and @var{state_value} is the value of this variable which represents the positive state.
2015 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
2016 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
2017 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
2018 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
2019 By default, the curve is drawn with no reference line.
2021 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
2022 Two additional tables are available.
2023 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
2025 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
2027 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
2029 The @subcmd{CRITERIA} subcommand has four optional parameters:
2031 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
2032 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
2033 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
2035 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
2036 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
2038 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
2040 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
2041 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
2042 exponential distribution estimate.
2043 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
2044 equal to the number of negative actual states.
2045 The default is @subcmd{FREE}.
2047 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
2050 The @subcmd{MISSING} subcommand determines whether user missing values are to
2051 be included or excluded in the analysis. The default behaviour is to
2053 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
2054 or if the variable @var{state_var} is missing, then the entire case will be
2057 @c LocalWords: subcmd subcommand