4 This chapter documents the statistical procedures that @pspp{} supports so
8 * DESCRIPTIVES:: Descriptive statistics.
9 * FREQUENCIES:: Frequency tables.
10 * EXAMINE:: Testing data for normality.
12 * CORRELATIONS:: Correlation tables.
13 * CROSSTABS:: Crosstabulation tables.
14 * FACTOR:: Factor analysis and Principal Components analysis.
15 * GLM:: Univariate Linear Models.
16 * LOGISTIC REGRESSION:: Bivariate Logistic Regression.
17 * MEANS:: Average values and other statistics.
18 * NPAR TESTS:: Nonparametric tests.
19 * T-TEST:: Test hypotheses about means.
20 * ONEWAY:: One way analysis of variance.
21 * QUICK CLUSTER:: K-Means clustering.
22 * RANK:: Compute rank scores.
23 * REGRESSION:: Linear regression.
24 * RELIABILITY:: Reliability analysis.
25 * ROC:: Receiver Operating Characteristic.
34 /VARIABLES=@var{var_list}
35 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
36 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
38 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
39 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
40 SESKEWNESS,SEKURTOSIS@}
41 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
42 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
46 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
48 statistics requested by the user. In addition, it can optionally
51 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
52 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
54 All other subcommands are optional:
56 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
57 @subcmd{INCLUDE} is set, then user-missing values are included in the
58 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
59 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
60 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
61 the entire case is excluded whenever any value in that case has a
62 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
64 The @subcmd{FORMAT} subcommand affects the output format. Currently the
65 @subcmd{LABELS/NOLABELS} and @subcmd{NOINDEX/INDEX} settings are not used.
66 When @subcmd{SERIAL} is
67 set, both valid and missing number of cases are listed in the output;
68 when @subcmd{NOSERIAL} is set, only valid cases are listed.
70 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
71 the specified variables. The Z scores are saved to new variables.
72 Variable names are generated by trying first the original variable name
73 with Z prepended and truncated to a maximum of 8 characters, then the
74 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
75 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
76 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
77 list by enclosing them in parentheses after each variable.
78 When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
79 treating temporary transformations as permanent.
81 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
85 All of the statistics below.
89 Standard error of the mean.
92 @item @subcmd{VARIANCE}
94 @item @subcmd{KURTOSIS}
95 Kurtosis and standard error of the kurtosis.
96 @item @subcmd{SKEWNESS}
97 Skewness and standard error of the skewness.
107 Mean, standard deviation of the mean, minimum, maximum.
109 Standard error of the kurtosis.
111 Standard error of the skewness.
114 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
115 of the possible values should be self-explanatory. @subcmd{NAME} causes the
116 statistics to be sorted by name. By default, the statistics are listed
117 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
118 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
119 sort order, respectively.
127 /VARIABLES=@var{var_list}
128 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
129 @{AVALUE,DVALUE,AFREQ,DFREQ@}
130 /MISSING=@{EXCLUDE,INCLUDE@}
131 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
132 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
133 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
135 /PERCENTILES=percent@dots{}
136 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
137 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
138 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
139 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
140 /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
142 /ORDER=@{ANALYSIS,VARIABLE@}
145 (These options are not currently implemented.)
150 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
152 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
153 (including median and mode) and percentiles, and various graphical representations
154 of the frequency distribution.
156 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
157 variables to be analyzed.
159 The @subcmd{FORMAT} subcommand controls the output format. It has several
164 @subcmd{TABLE}, the default, causes a frequency table to be output for every
165 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
166 with a numeric argument causes them to be output except when there are
167 more than the specified number of values in the table.
170 Normally frequency tables are sorted in ascending order by value. This
171 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
172 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
173 respectively, by frequency count.
176 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
177 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
178 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
179 are included. System-missing values are never included in statistics,
180 but are listed in frequency tables.
182 The available @subcmd{STATISTICS} are the same as available
183 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
184 of @subcmd{MEDIAN}, the data's median
185 value, and MODE, the mode. (If there are multiple modes, the smallest
186 value is reported.) By default, the mean, standard deviation of the
187 mean, minimum, and maximum are reported for each variable.
190 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
191 The percentiles should be presented at a list of numbers between 0
193 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
194 boundaries of the data set divided into the specified number of ranges.
195 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
198 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
199 each specified numeric variable. The X axis by default ranges from
200 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
201 and @subcmd{MAXIMUM} keywords can set an explicit range.
202 @footnote{The number of
203 bins is chosen according to the Freedman-Diaconis rule:
204 @math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
205 and @math{n} is the number of samples. Note that
206 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
207 Histograms are not created for string variables.
209 Specify @subcmd{NORMAL} to superimpose a normal curve on the
213 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
214 slice represents one value, with the size of the slice proportional to
215 the value's frequency. By default, all non-missing values are given
217 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
218 displayed slices to a given range of values.
219 The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
220 piechart. This is the default.
221 If instead, @subcmd{MISSING} is specified, then a single slice
222 will be included representing all system missing and user-missing cases.
225 The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
226 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
227 categories whose counts which lie outside the specified limits.
228 The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
229 of each category, whereas the @subcmd{PERCENT} option will display relative
232 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
233 @subcmd{PIECHART} are accepted but not currently honoured.
235 The @subcmd{ORDER} subcommand is accepted but ignored.
241 @cindex Exploratory data analysis
242 @cindex normality, testing
246 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
247 [BY @var{factor1} [BY @var{subfactor1}]
248 [ @var{factor2} [BY @var{subfactor2}]]
250 [ @var{factor3} [BY @var{subfactor3}]]
252 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
253 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
255 /COMPARE=@{GROUPS,VARIABLES@}
256 /ID=@var{identity_variable}
258 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
259 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
260 [@{NOREPORT,REPORT@}]
264 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
265 In particular, it is useful for testing how closely a distribution follows a
266 normal distribution, and for finding outliers and extreme values.
268 The @subcmd{VARIABLES} subcommand is mandatory.
269 It specifies the dependent variables and optionally variables to use as
270 factors for the analysis.
271 Variables listed before the first @subcmd{BY} keyword (if any) are the
273 The dependent variables may optionally be followed by a list of
274 factors which tell @pspp{} how to break down the analysis for each
277 Following the dependent variables, factors may be specified.
278 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
279 The format for each factor is
281 @var{factorvar} [BY @var{subfactorvar}].
283 Each unique combination of the values of @var{factorvar} and
284 @var{subfactorvar} divide the dataset into @dfn{cells}.
285 Statistics will be calculated for each cell
286 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
288 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
289 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
290 non-parametrics statistics.
291 @subcmd{EXTREME} produces a table showing the extremities of each cell.
292 A number in parentheses, @var{n} determines
293 how many upper and lower extremities to show.
294 The default number is 5.
296 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
297 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
298 as well as for each cell.
299 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
300 (unless no factor variables have been given).
301 These subcommands have no effect if there have been no factor variables
307 @cindex spreadlevel plot
308 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
309 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
310 @subcmd{SPREADLEVEL}.
311 The first three can be used to visualise how closely each cell conforms to a
312 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
313 how the variance of differs between factors.
314 Boxplots will also show you the outliers and extreme values.
315 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
316 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
317 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
319 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
320 median. It takes an optional parameter @var{t}, which specifies how the data
321 should be transformed prior to plotting.
322 The given value @var{t} is a power to which the data is raised. For example, if
323 @var{t} is given as 2, then the data will be squared.
324 Zero, however is a special value. If @var{t} is 0 or
325 is omitted, then data will be transformed by taking its natural logarithm instead of
326 raising to the power of @var{t}.
328 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
329 useful there is more than one dependent variable and at least one factor.
331 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
332 each of which contain boxplots for all the cells.
333 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
334 each containing one boxplot per dependent variable.
335 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
336 @subcmd{/COMPARE=GROUPS} were given.
338 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
339 @subcmd{/STATISTICS=EXTREME} has been given.
340 If given, it should provide the name of a variable which is to be used
341 to labels extreme values and outliers.
342 Numeric or string variables are permissible.
343 If the @subcmd{ID} subcommand is not given, then the case number will be used for
346 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
347 calculation of the descriptives command. The default is 95%.
350 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
351 and which algorithm to use for calculating them. The default is to
352 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
353 @subcmd{HAVERAGE} algorithm.
355 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
356 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
357 then then statistics for the unfactored dependent variables are
358 produced in addition to the factored variables. If there are no
359 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
362 The following example will generate descriptive statistics and histograms for
363 two variables @var{score1} and @var{score2}.
364 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
365 Therefore, the descriptives and histograms will be generated for each
367 of @var{gender} @emph{and} for each distinct combination of the values
368 of @var{gender} and @var{race}.
369 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
370 @var{score1} and @var{score2} covering the whole dataset are not produced.
372 EXAMINE @var{score1} @var{score2} BY
374 @var{gender} BY @var{culture}
375 /STATISTICS = DESCRIPTIVES
380 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
382 EXAMINE @var{height} @var{weight} BY
384 /STATISTICS = EXTREME (3)
389 In this example, we look at the height and weight of a sample of individuals and
390 how they differ between male and female.
391 A table showing the 3 largest and the 3 smallest values of @var{height} and
392 @var{weight} for each gender, and for the whole dataset will be shown.
393 Boxplots will also be produced.
394 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
395 shown in the same graphic, allowing us to easily see the difference between
397 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
398 used to label the extreme values.
401 If many dependent variables are specified, or if factor variables are
403 there are many distinct values, then @cmd{EXAMINE} will produce a very
404 large quantity of output.
410 @cindex Exploratory data analysis
411 @cindex normality, testing
415 /HISTOGRAM [(NORMAL)]= @var{var}
416 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
417 /BAR = @{@var{summary-function}(@var{var1}) | @var{count-function}@} BY @var{var2} [BY @var{var3}]
418 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
419 [@{NOREPORT,REPORT@}]
423 The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands
424 @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot
425 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
428 * SCATTERPLOT:: Cartesian Plots
429 * HISTOGRAM:: Histograms
430 * BAR CHART:: Bar Charts
434 @subsection Scatterplot
437 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the
438 data. The different values of the optional third variable @var{var3}
439 will result in different colours and/or markers for the plot. The
440 following is an example for producing a scatterplot.
444 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
447 This example will produce a scatterplot where @var{height} is plotted versus @var{weight}. Depending
448 on the value of the @var{gender} variable, the colour of the datapoint is different. With
449 this plot it is possible to analyze gender differences for @var{height} vs.@: @var{weight} relation.
452 @subsection Histogram
455 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
457 The keyword @subcmd{NORMAL} may be specified in parentheses, to indicate that the ideal normal curve
458 should be superimposed over the histogram.
459 For an alternative method to produce histograms @pxref{EXAMINE}. The
460 following example produces a histogram plot for the variable @var{weight}.
464 /HISTOGRAM = @var{weight}.
468 @subsection Bar Chart
471 The subcommand @subcmd{BAR} produces a bar chart.
472 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.
473 Following the summary or count function, the keyword @subcmd{BY} should be specified and then a catagorical variable, @var{var2}.
474 The values of the variable @var{var2} determine the labels of the bars to be plotted.
475 Optionally a second categorical variable @var{var3} may be specified in which case a clustered (grouped) bar chart is produced.
477 Valid count functions are
480 The weighted counts of the cases in each category.
482 The weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
484 The cumulative weighted counts of the cases in each category.
486 The cumulative weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
489 The summary function is applied to @var{var1} across all cases in each category.
490 The recognised summary functions are:
502 The following examples assume a dataset which is the results of a survey.
503 Each respondent has indicated annual income, their sex and city of residence.
504 One could create a bar chart showing how the mean income varies between of residents of different cities, thus:
506 GRAPH /BAR = MEAN(@var{income}) BY @var{city}.
509 This can be extended to also indicate how income in each city differs between the sexes.
511 GRAPH /BAR = MEAN(@var{income}) BY @var{city} BY @var{sex}.
514 One might also want to see how many respondents there are from each city. This can be achieved as follows:
516 GRAPH /BAR = COUNT BY @var{city}.
519 Bar charts can also be produced using the @ref{FREQUENCIES} and @ref{CROSSTABS} commands.
522 @section CORRELATIONS
527 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
532 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
533 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
536 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
537 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
538 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
542 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
543 for a set of variables. The significance of the coefficients are also given.
545 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
546 keyword is used, then a non-square correlation table will be produced.
547 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
548 and the variables following will be the columns of the table.
549 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
552 The @cmd{MISSING} subcommand determines the handling of missing variables.
553 If @subcmd{INCLUDE} is set, then user-missing values are included in the
554 calculations, but system-missing values are not.
555 If @subcmd{EXCLUDE} is set, which is the default, user-missing
556 values are excluded as well as system-missing values.
558 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
559 whenever any variable specified in any @cmd{/VARIABLES} subcommand
560 contains a missing value.
561 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
562 values for the particular coefficient are missing.
563 The default is @subcmd{PAIRWISE}.
565 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
566 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
567 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
568 The default is @subcmd{TWOTAIL}.
570 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
571 0.05 are highlighted.
572 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
575 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
576 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
577 estimator of the standard deviation are displayed.
578 These statistics will be displayed in a separated table, for all the variables listed
579 in any @subcmd{/VARIABLES} subcommand.
580 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
581 be displayed for each pair of variables.
582 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
590 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
591 /MISSING=@{TABLE,INCLUDE,REPORT@}
592 /WRITE=@{NONE,CELLS,ALL@}
593 /FORMAT=@{TABLES,NOTABLES@}
598 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
599 ASRESIDUAL,ALL,NONE@}
600 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
601 KAPPA,ETA,CORR,ALL,NONE@}
605 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
608 The @cmd{CROSSTABS} procedure displays crosstabulation
609 tables requested by the user. It can calculate several statistics for
610 each cell in the crosstabulation tables. In addition, a number of
611 statistics can be calculated for each table itself.
613 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
614 number of dimensions is permitted, and any number of variables per
615 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
616 times as needed. This is the only required subcommand in @dfn{general
619 Occasionally, one may want to invoke a special mode called @dfn{integer
620 mode}. Normally, in general mode, @pspp{} automatically determines
621 what values occur in the data. In integer mode, the user specifies the
622 range of values that the data assumes. To invoke this mode, specify the
623 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
624 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
625 the range are truncated to the nearest integer, then assigned to that
626 value. If values occur outside this range, they are discarded. When it
627 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
630 In general mode, numeric and string variables may be specified on
631 TABLES. In integer mode, only numeric variables are allowed.
633 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
634 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
635 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
636 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
637 integer mode, user-missing values are included in tables but marked with
638 an @samp{M} (for ``missing'') and excluded from statistical
641 Currently the @subcmd{WRITE} subcommand is ignored.
643 The @subcmd{FORMAT} subcommand controls the characteristics of the
644 crosstabulation tables to be displayed. It has a number of possible
649 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
650 @subcmd{NOTABLES} suppresses them.
653 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
654 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
658 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
659 @subcmd{DVALUE} asserts a descending sort order.
662 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
665 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
668 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
669 crosstabulation table. The possible settings are:
685 Standardized residual.
687 Adjusted standardized residual.
691 Suppress cells entirely.
694 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
695 @subcmd{COLUMN}, and @subcmd{TOTAL}.
696 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
699 The @subcmd{STATISTICS} subcommand selects statistics for computation:
706 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
707 correction, linear-by-linear association.
711 Contingency coefficient.
715 Uncertainty coefficient.
731 Spearman correlation, Pearson's r.
738 Selected statistics are only calculated when appropriate for the
739 statistic. Certain statistics require tables of a particular size, and
740 some statistics are calculated only in integer mode.
742 @samp{/STATISTICS} without any settings selects CHISQ. If the
743 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
746 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
747 variables on each table.
748 If a table has more than two variables, the counts for the third and subsequent levels
749 will be aggregated and the chart will be produces as if there were only two variables.
752 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
753 following limitations:
757 Significance of some symmetric and directional measures is not calculated.
759 Asymptotic standard error is not calculated for
760 Goodman and Kruskal's tau or symmetric Somers' d.
762 Approximate T is not calculated for symmetric uncertainty coefficient.
765 Fixes for any of these deficiencies would be welcomed.
771 @cindex factor analysis
772 @cindex principal components analysis
773 @cindex principal axis factoring
774 @cindex data reduction
777 FACTOR VARIABLES=@var{var_list}
779 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
781 [ /ANALYSIS=@var{var_list} ]
783 [ /EXTRACTION=@{PC, PAF@}]
785 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
787 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
791 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
793 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
795 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
798 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
799 common factors in the data or for data reduction purposes.
801 The @subcmd{VARIABLES} subcommand is required. It lists the variables
802 which are to partake in the analysis. (The @subcmd{ANALYSIS}
803 subcommand may optionally further limit the variables that
804 participate; it is not useful and implemented only for compatibility.)
806 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
807 If @subcmd{PC} is specified, then Principal Components Analysis is used.
808 If @subcmd{PAF} is specified, then Principal Axis Factoring is
809 used. By default Principal Components Analysis will be used.
811 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
812 Three orthogonal rotation methods are available:
813 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
814 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
815 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
816 The default value of @var{k} is 5.
817 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
818 rotation on the data.
820 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
821 to be analysed. By default, the correlation matrix is analysed.
823 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
826 @item @subcmd{UNIVARIATE}
827 A table of mean values, standard deviations and total weights are printed.
828 @item @subcmd{INITIAL}
829 Initial communalities and eigenvalues are printed.
830 @item @subcmd{EXTRACTION}
831 Extracted communalities and eigenvalues are printed.
832 @item @subcmd{ROTATION}
833 Rotated communalities and eigenvalues are printed.
834 @item @subcmd{CORRELATION}
835 The correlation matrix is printed.
836 @item @subcmd{COVARIANCE}
837 The covariance matrix is printed.
839 The determinant of the correlation or covariance matrix is printed.
841 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
843 The significance of the elements of correlation matrix is printed.
845 All of the above are printed.
846 @item @subcmd{DEFAULT}
847 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
850 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
851 which factors (components) should be retained.
853 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
854 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
855 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
856 performed, and all coefficients will be printed.
858 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
859 If @subcmd{FACTORS(@var{n})} is
860 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
862 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
863 The default value of @var{l} is 1.
864 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
865 extraction (such as Principal Axis Factoring) are used.
866 @subcmd{ECONVERGE(@var{delta})} specifies that
867 iteration should cease when
868 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
869 default value of @var{delta} is 0.001.
870 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
871 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
873 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
874 If @subcmd{EXTRACTION} follows, it affects convergence.
875 If @subcmd{ROTATION} follows, it affects rotation.
876 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
877 The default value of @var{m} is 25.
879 The @cmd{MISSING} subcommand determines the handling of missing variables.
880 If @subcmd{INCLUDE} is set, then user-missing values are included in the
881 calculations, but system-missing values are not.
882 If @subcmd{EXCLUDE} is set, which is the default, user-missing
883 values are excluded as well as system-missing values.
885 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
886 whenever any variable specified in the @cmd{VARIABLES} subcommand
887 contains a missing value.
888 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
889 values for the particular coefficient are missing.
890 The default is @subcmd{LISTWISE}.
896 @cindex univariate analysis of variance
897 @cindex fixed effects
898 @cindex factorial anova
899 @cindex analysis of variance
904 GLM @var{dependent_vars} BY @var{fixed_factors}
905 [/METHOD = SSTYPE(@var{type})]
906 [/DESIGN = @var{interaction_0} [@var{interaction_1} [... @var{interaction_n}]]]
907 [/INTERCEPT = @{INCLUDE|EXCLUDE@}]
908 [/MISSING = @{INCLUDE|EXCLUDE@}]
911 The @cmd{GLM} procedure can be used for fixed effects factorial Anova.
913 The @var{dependent_vars} are the variables to be analysed.
914 You may analyse several variables in the same command in which case they should all
915 appear before the @code{BY} keyword.
917 The @var{fixed_factors} list must be one or more categorical variables. Normally it
918 will not make sense to enter a scalar variable in the @var{fixed_factors} and doing
919 so may cause @pspp{} to do a lot of unnecessary processing.
921 The @subcmd{METHOD} subcommand is used to change the method for producing the sums of
922 squares. Available values of @var{type} are 1, 2 and 3. The default is type 3.
924 You may specify a custom design using the @subcmd{DESIGN} subcommand.
925 The design comprises a list of interactions where each interaction is a
926 list of variables separated by a @samp{*}. For example the command
928 GLM subject BY sex age_group race
929 /DESIGN = age_group sex group age_group*sex age_group*race
931 @noindent specifies the model @math{subject = age_group + sex + race + age_group*sex + age_group*race}.
932 If no @subcmd{DESIGN} subcommand is specified, then the default is all possible combinations
933 of the fixed factors. That is to say
935 GLM subject BY sex age_group race
938 @math{subject = age_group + sex + race + age_group*sex + age_group*race + sex*race + age_group*sex*race}.
941 The @subcmd{MISSING} subcommand determines the handling of missing
943 If @subcmd{INCLUDE} is set, then user-missing values are included in the
944 calculations, but system-missing values are not.
945 If @subcmd{EXCLUDE} is set, which is the default, user-missing
946 values are excluded as well as system-missing values.
950 @node LOGISTIC REGRESSION
951 @section LOGISTIC REGRESSION
953 @vindex LOGISTIC REGRESSION
954 @cindex logistic regression
955 @cindex bivariate logistic regression
958 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
960 [/CATEGORICAL = @var{categorical_predictors}]
962 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
964 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
966 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
967 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
968 [CUT(@var{cut_point})]]
970 [/MISSING = @{INCLUDE|EXCLUDE@}]
973 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
974 variable in terms of one or more predictor variables.
976 The minimum command is
978 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
980 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
981 are the predictor variables whose coefficients the procedure estimates.
983 By default, a constant term is included in the model.
984 Hence, the full model is
987 = b_0 + b_1 {\bf x_1}
993 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
994 Simple variables as well as interactions between variables may be listed here.
996 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
997 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
999 An iterative Newton-Raphson procedure is used to fit the model.
1000 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
1001 and other parameters.
1002 The value of @var{cut_point} is used in the classification table. It is the
1003 threshold above which predicted values are considered to be 1. Values
1004 of @var{cut_point} must lie in the range [0,1].
1005 During iterations, if any one of the stopping criteria are satisfied, the procedure is
1006 considered complete.
1007 The stopping criteria are:
1009 @item The number of iterations exceeds @var{max_iterations}.
1010 The default value of @var{max_iterations} is 20.
1011 @item The change in the all coefficient estimates are less than @var{min_delta}.
1012 The default value of @var{min_delta} is 0.001.
1013 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
1014 The default value of @var{min_delta} is zero.
1015 This means that this criterion is disabled.
1016 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
1017 In other words, the probabilities are close to zero or one.
1018 The default value of @var{min_epsilon} is 0.00000001.
1022 The @subcmd{PRINT} subcommand controls the display of optional statistics.
1023 Currently there is one such option, @subcmd{CI}, which indicates that the
1024 confidence interval of the odds ratio should be displayed as well as its value.
1025 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
1026 confidence level of the desired confidence interval.
1028 The @subcmd{MISSING} subcommand determines the handling of missing
1030 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1031 calculations, but system-missing values are not.
1032 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1033 values are excluded as well as system-missing values.
1034 This is the default.
1045 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
1047 [ /@{@var{var_list}@}
1048 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
1050 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
1051 [VARIANCE] [KURT] [SEKURT]
1052 [SKEW] [SESKEW] [FIRST] [LAST]
1053 [HARMONIC] [GEOMETRIC]
1058 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
1061 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
1062 statistics, either for the dataset as a whole or for categories of data.
1064 The simplest form of the command is
1068 @noindent which calculates the mean, count and standard deviation for @var{v}.
1069 If you specify a grouping variable, for example
1071 MEANS @var{v} BY @var{g}.
1073 @noindent then the means, counts and standard deviations for @var{v} after having
1074 been grouped by @var{g} will be calculated.
1075 Instead of the mean, count and standard deviation, you could specify the statistics
1076 in which you are interested:
1078 MEANS @var{x} @var{y} BY @var{g}
1079 /CELLS = HARMONIC SUM MIN.
1081 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
1084 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
1088 @cindex arithmetic mean
1089 The arithmetic mean.
1090 @item @subcmd{COUNT}
1091 The count of the values.
1092 @item @subcmd{STDDEV}
1093 The standard deviation.
1094 @item @subcmd{SEMEAN}
1095 The standard error of the mean.
1097 The sum of the values.
1102 @item @subcmd{RANGE}
1103 The difference between the maximum and minimum values.
1104 @item @subcmd{VARIANCE}
1106 @item @subcmd{FIRST}
1107 The first value in the category.
1109 The last value in the category.
1112 @item @subcmd{SESKEW}
1113 The standard error of the skewness.
1116 @item @subcmd{SEKURT}
1117 The standard error of the kurtosis.
1118 @item @subcmd{HARMONIC}
1119 @cindex harmonic mean
1121 @item @subcmd{GEOMETRIC}
1122 @cindex geometric mean
1126 In addition, three special keywords are recognized:
1128 @item @subcmd{DEFAULT}
1129 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
1131 All of the above statistics will be calculated.
1133 No statistics will be calculated (only a summary will be shown).
1137 More than one @dfn{table} can be specified in a single command.
1138 Each table is separated by a @samp{/}. For
1142 @var{c} @var{d} @var{e} BY @var{x}
1143 /@var{a} @var{b} BY @var{x} @var{y}
1144 /@var{f} BY @var{y} BY @var{z}.
1146 has three tables (the @samp{TABLE =} is optional).
1147 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1148 and a single categorical variable @var{x}.
1149 The second table has two dependent variables @var{a} and @var{b},
1150 and two categorical variables @var{x} and @var{y}.
1151 The third table has a single dependent variables @var{f}
1152 and a categorical variable formed by the combination of @var{y} and @var{z}.
1155 By default values are omitted from the analysis only if missing values
1156 (either system missing or user missing)
1157 for any of the variables directly involved in their calculation are
1159 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1160 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1162 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1163 in the table specification currently being processed, regardless of
1164 whether it is needed to calculate the statistic.
1166 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1167 variables or in the categorical variables should be taken at their face
1168 value, and not excluded.
1170 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1171 variables should be taken at their face value, however cases which
1172 have user missing values for the categorical variables should be omitted
1173 from the calculation.
1179 @cindex nonparametric tests
1184 nonparametric test subcommands
1189 [ /STATISTICS=@{DESCRIPTIVES@} ]
1191 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1193 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1196 @cmd{NPAR TESTS} performs nonparametric tests.
1197 Non parametric tests make very few assumptions about the distribution of the
1199 One or more tests may be specified by using the corresponding subcommand.
1200 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1201 produces for each variable that is the subject of any test.
1203 Certain tests may take a long time to execute, if an exact figure is required.
1204 Therefore, by default asymptotic approximations are used unless the
1205 subcommand @subcmd{/METHOD=EXACT} is specified.
1206 Exact tests give more accurate results, but may take an unacceptably long
1207 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1208 after which the test will be abandoned, and a warning message printed.
1209 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1210 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1215 * BINOMIAL:: Binomial Test
1216 * CHISQUARE:: Chisquare Test
1217 * COCHRAN:: Cochran Q Test
1218 * FRIEDMAN:: Friedman Test
1219 * KENDALL:: Kendall's W Test
1220 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1221 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1222 * MANN-WHITNEY:: Mann Whitney U Test
1223 * MCNEMAR:: McNemar Test
1224 * MEDIAN:: Median Test
1226 * SIGN:: The Sign Test
1227 * WILCOXON:: Wilcoxon Signed Ranks Test
1232 @subsection Binomial test
1234 @cindex binomial test
1237 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1240 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1241 variable with that of a binomial distribution.
1242 The variable @var{p} specifies the test proportion of the binomial
1244 The default value of 0.5 is assumed if @var{p} is omitted.
1246 If a single value appears after the variable list, then that value is
1247 used as the threshold to partition the observed values. Values less
1248 than or equal to the threshold value form the first category. Values
1249 greater than the threshold form the second category.
1251 If two values appear after the variable list, then they will be used
1252 as the values which a variable must take to be in the respective
1254 Cases for which a variable takes a value equal to neither of the specified
1255 values, take no part in the test for that variable.
1257 If no values appear, then the variable must assume dichotomous
1259 If more than two distinct, non-missing values for a variable
1260 under test are encountered then an error occurs.
1262 If the test proportion is equal to 0.5, then a two tailed test is
1263 reported. For any other test proportion, a one tailed test is
1265 For one tailed tests, if the test proportion is less than
1266 or equal to the observed proportion, then the significance of
1267 observing the observed proportion or more is reported.
1268 If the test proportion is more than the observed proportion, then the
1269 significance of observing the observed proportion or less is reported.
1270 That is to say, the test is always performed in the observed
1273 @pspp{} uses a very precise approximation to the gamma function to
1274 compute the binomial significance. Thus, exact results are reported
1275 even for very large sample sizes.
1280 @subsection Chisquare Test
1282 @cindex chisquare test
1286 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1290 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1291 between the expected and observed frequencies of the categories of a variable.
1292 Optionally, a range of values may appear after the variable list.
1293 If a range is given, then non integer values are truncated, and values
1294 outside the specified range are excluded from the analysis.
1296 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1298 There must be exactly one non-zero expected value, for each observed
1299 category, or the @subcmd{EQUAL} keyword must be specified.
1300 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1301 consecutive expected categories all taking a frequency of @var{f}.
1302 The frequencies given are proportions, not absolute frequencies. The
1303 sum of the frequencies need not be 1.
1304 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1309 @subsection Cochran Q Test
1311 @cindex Cochran Q test
1312 @cindex Q, Cochran Q
1315 [ /COCHRAN = @var{var_list} ]
1318 The Cochran Q test is used to test for differences between three or more groups.
1319 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1321 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1324 @subsection Friedman Test
1326 @cindex Friedman test
1329 [ /FRIEDMAN = @var{var_list} ]
1332 The Friedman test is used to test for differences between repeated measures when
1333 there is no indication that the distributions are normally distributed.
1335 A list of variables which contain the measured data must be given. The procedure
1336 prints the sum of ranks for each variable, the test statistic and its significance.
1339 @subsection Kendall's W Test
1341 @cindex Kendall's W test
1342 @cindex coefficient of concordance
1345 [ /KENDALL = @var{var_list} ]
1348 The Kendall test investigates whether an arbitrary number of related samples come from the
1350 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1351 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1352 unity indicates complete agreement.
1355 @node KOLMOGOROV-SMIRNOV
1356 @subsection Kolmogorov-Smirnov Test
1357 @vindex KOLMOGOROV-SMIRNOV
1359 @cindex Kolmogorov-Smirnov test
1362 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1365 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1366 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1367 Normal, Uniform, Poisson and Exponential.
1369 Ideally you should provide the parameters of the distribution against which you wish to test
1370 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1371 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1373 However, if the parameters are omitted they will be imputed from the data. Imputing the
1374 parameters reduces the power of the test so should be avoided if possible.
1376 In the following example, two variables @var{score} and @var{age} are tested to see if
1377 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1380 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1382 If the variables need to be tested against different distributions, then a separate
1383 subcommand must be used. For example the following syntax tests @var{score} against
1384 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1385 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1388 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1389 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1392 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1394 @node KRUSKAL-WALLIS
1395 @subsection Kruskal-Wallis Test
1396 @vindex KRUSKAL-WALLIS
1398 @cindex Kruskal-Wallis test
1401 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1404 The Kruskal-Wallis test is used to compare data from an
1405 arbitrary number of populations. It does not assume normality.
1406 The data to be compared are specified by @var{var_list}.
1407 The categorical variable determining the groups to which the
1408 data belongs is given by @var{var}. The limits @var{lower} and
1409 @var{upper} specify the valid range of @var{var}. Any cases for
1410 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1413 The mean rank of each group as well as the chi-squared value and significance
1414 of the test will be printed.
1415 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1419 @subsection Mann-Whitney U Test
1420 @vindex MANN-WHITNEY
1422 @cindex Mann-Whitney U test
1423 @cindex U, Mann-Whitney U
1426 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1429 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1430 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}.
1431 @var{Var} may be either a string or an alpha variable.
1432 @var{Group1} and @var{group2} specify the
1433 two values of @var{var} which determine the groups of the test data.
1434 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1436 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1437 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1440 @subsection McNemar Test
1442 @cindex McNemar test
1445 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1448 Use McNemar's test to analyse the significance of the difference between
1449 pairs of correlated proportions.
1451 If the @code{WITH} keyword is omitted, then tests for all
1452 combinations of the listed variables are performed.
1453 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1454 is also given, then the number of variables preceding @code{WITH}
1455 must be the same as the number following it.
1456 In this case, tests for each respective pair of variables are
1458 If the @code{WITH} keyword is given, but the
1459 @code{(PAIRED)} keyword is omitted, then tests for each combination
1460 of variable preceding @code{WITH} against variable following
1461 @code{WITH} are performed.
1463 The data in each variable must be dichotomous. If there are more
1464 than two distinct variables an error will occur and the test will
1468 @subsection Median Test
1473 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1476 The median test is used to test whether independent samples come from
1477 populations with a common median.
1478 The median of the populations against which the samples are to be tested
1479 may be given in parentheses immediately after the
1480 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1481 union of all the samples.
1483 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1484 keyword @code{BY} must come next, and then the grouping variable. Two values
1485 in parentheses should follow. If the first value is greater than the second,
1486 then a 2 sample test is performed using these two values to determine the groups.
1487 If however, the first variable is less than the second, then a @i{k} sample test is
1488 conducted and the group values used are all values encountered which lie in the
1489 range [@var{value1},@var{value2}].
1493 @subsection Runs Test
1498 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1501 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1503 It works by examining the number of times a variable's value crosses a given threshold.
1504 The desired threshold must be specified within parentheses.
1505 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1506 Following the threshold specification comes the list of variables whose values are to be
1509 The subcommand shows the number of runs, the asymptotic significance based on the
1513 @subsection Sign Test
1518 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1521 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1523 The test does not make any assumptions about the
1524 distribution of the data.
1526 If the @code{WITH} keyword is omitted, then tests for all
1527 combinations of the listed variables are performed.
1528 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1529 is also given, then the number of variables preceding @code{WITH}
1530 must be the same as the number following it.
1531 In this case, tests for each respective pair of variables are
1533 If the @code{WITH} keyword is given, but the
1534 @code{(PAIRED)} keyword is omitted, then tests for each combination
1535 of variable preceding @code{WITH} against variable following
1536 @code{WITH} are performed.
1539 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1541 @cindex wilcoxon matched pairs signed ranks test
1544 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1547 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1549 The test does not make any assumptions about the variances of the samples.
1550 It does however assume that the distribution is symmetrical.
1552 If the @subcmd{WITH} keyword is omitted, then tests for all
1553 combinations of the listed variables are performed.
1554 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1555 is also given, then the number of variables preceding @subcmd{WITH}
1556 must be the same as the number following it.
1557 In this case, tests for each respective pair of variables are
1559 If the @subcmd{WITH} keyword is given, but the
1560 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1561 of variable preceding @subcmd{WITH} against variable following
1562 @subcmd{WITH} are performed.
1571 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1572 /CRITERIA=CI(@var{confidence})
1576 TESTVAL=@var{test_value}
1577 /VARIABLES=@var{var_list}
1580 (Independent Samples mode.)
1581 GROUPS=var(@var{value1} [, @var{value2}])
1582 /VARIABLES=@var{var_list}
1585 (Paired Samples mode.)
1586 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1591 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1593 It operates in one of three modes:
1595 @item One Sample mode.
1596 @item Independent Groups mode.
1601 Each of these modes are described in more detail below.
1602 There are two optional subcommands which are common to all modes.
1604 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1605 in the tests. The default value is 0.95.
1608 The @cmd{MISSING} subcommand determines the handling of missing
1610 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1611 calculations, but system-missing values are not.
1612 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1613 values are excluded as well as system-missing values.
1614 This is the default.
1616 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1617 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1618 @subcmd{/GROUPS} subcommands contains a missing value.
1619 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1620 which they would be needed. This is the default.
1624 * One Sample Mode:: Testing against a hypothesized mean
1625 * Independent Samples Mode:: Testing two independent groups for equal mean
1626 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1629 @node One Sample Mode
1630 @subsection One Sample Mode
1632 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1633 This mode is used to test a population mean against a hypothesized
1635 The value given to the @subcmd{TESTVAL} subcommand is the value against
1636 which you wish to test.
1637 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1638 tell @pspp{} which variables you wish to test.
1640 @node Independent Samples Mode
1641 @subsection Independent Samples Mode
1643 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1645 This mode is used to test whether two groups of values have the
1646 same population mean.
1647 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1648 tell @pspp{} the dependent variables you wish to test.
1650 The variable given in the @subcmd{GROUPS} subcommand is the independent
1651 variable which determines to which group the samples belong.
1652 The values in parentheses are the specific values of the independent
1653 variable for each group.
1654 If the parentheses are omitted and no values are given, the default values
1655 of 1.0 and 2.0 are assumed.
1657 If the independent variable is numeric,
1658 it is acceptable to specify only one value inside the parentheses.
1659 If you do this, cases where the independent variable is
1660 greater than or equal to this value belong to the first group, and cases
1661 less than this value belong to the second group.
1662 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1663 the independent variable are excluded on a listwise basis, regardless
1664 of whether @subcmd{/MISSING=LISTWISE} was specified.
1667 @node Paired Samples Mode
1668 @subsection Paired Samples Mode
1670 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1671 Use this mode when repeated measures have been taken from the same
1673 If the @subcmd{WITH} keyword is omitted, then tables for all
1674 combinations of variables given in the @cmd{PAIRS} subcommand are
1676 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1677 is also given, then the number of variables preceding @subcmd{WITH}
1678 must be the same as the number following it.
1679 In this case, tables for each respective pair of variables are
1681 In the event that the @subcmd{WITH} keyword is given, but the
1682 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1683 of variable preceding @subcmd{WITH} against variable following
1684 @subcmd{WITH} are generated.
1691 @cindex analysis of variance
1696 [/VARIABLES = ] @var{var_list} BY @var{var}
1697 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1698 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1699 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1700 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1703 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1704 variables factored by a single independent variable.
1705 It is used to compare the means of a population
1706 divided into more than two groups.
1708 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1710 The list of variables must be followed by the @subcmd{BY} keyword and
1711 the name of the independent (or factor) variable.
1713 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1714 ancillary information. The options accepted are:
1717 Displays descriptive statistics about the groups factored by the independent
1720 Displays the Levene test of Homogeneity of Variance for the
1721 variables and their groups.
1724 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1725 differences between the groups.
1726 The subcommand must be followed by a list of numerals which are the
1727 coefficients of the groups to be tested.
1728 The number of coefficients must correspond to the number of distinct
1729 groups (or values of the independent variable).
1730 If the total sum of the coefficients are not zero, then @pspp{} will
1731 display a warning, but will proceed with the analysis.
1732 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1733 to specify different contrast tests.
1734 The @subcmd{MISSING} subcommand defines how missing values are handled.
1735 If @subcmd{LISTWISE} is specified then cases which have missing values for
1736 the independent variable or any dependent variable will be ignored.
1737 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1738 variable is missing or if the dependent variable currently being
1739 analysed is missing. The default is @subcmd{ANALYSIS}.
1740 A setting of @subcmd{EXCLUDE} means that variables whose values are
1741 user-missing are to be excluded from the analysis. A setting of
1742 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1744 Using the @code{POSTHOC} subcommand you can perform multiple
1745 pairwise comparisons on the data. The following comparison methods
1749 Least Significant Difference.
1750 @item @subcmd{TUKEY}
1751 Tukey Honestly Significant Difference.
1752 @item @subcmd{BONFERRONI}
1754 @item @subcmd{SCHEFFE}
1756 @item @subcmd{SIDAK}
1759 The Games-Howell test.
1763 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1764 that @var{value} should be used as the
1765 confidence level for which the posthoc tests will be performed.
1766 The default is 0.05.
1769 @section QUICK CLUSTER
1770 @vindex QUICK CLUSTER
1772 @cindex K-means clustering
1776 QUICK CLUSTER @var{var_list}
1777 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
1778 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1779 [/PRINT=@{INITIAL@} @{CLUSTER@}]
1782 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1783 dataset. This is useful when you wish to allocate cases into clusters
1784 of similar values and you already know the number of clusters.
1786 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1787 of the variables which contain the cluster data. Normally you will also
1788 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1789 number of clusters. If this is not specified, then @var{k} defaults to 2.
1791 If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
1792 the initial clusters is used. This will provide for faster execution but
1793 less well separated initial clusters and hence possibly an inferior final
1797 @cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
1798 The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
1799 During classification, @pspp{} will continue iterating until until @var{max_iter}
1800 iterations have been done or the convergence criterion (see below) is fulfilled.
1801 The default value of @var{max_iter} is 2.
1803 If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
1804 no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
1807 The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
1808 to set the convergence criterion. The value of convergence criterion is @var{epsilon}
1809 times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
1810 the mean cluster distance between one iteration and the next
1811 is less than the convergence criterion. The default value of @var{epsilon} is zero.
1813 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1814 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1815 value and not as missing values.
1816 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1817 values are excluded as well as system-missing values.
1819 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1820 whenever any of the clustering variables contains a missing value.
1821 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1822 clustering variables contain missing values. Otherwise it is clustered
1823 on the basis of the non-missing values.
1824 The default is @subcmd{LISTWISE}.
1826 The @subcmd{PRINT} subcommand requests additional output to be printed.
1827 If @subcmd{INITIAL} is set, then the initial cluster memberships will
1829 If @subcmd{CLUSTER} is set, the cluster memberships of the individual
1830 cases will be displayed (potentially generating lengthy output).
1839 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1840 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1841 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1843 /MISSING=@{EXCLUDE,INCLUDE@}
1845 /RANK [INTO @var{var_list}]
1846 /NTILES(k) [INTO @var{var_list}]
1847 /NORMAL [INTO @var{var_list}]
1848 /PERCENT [INTO @var{var_list}]
1849 /RFRACTION [INTO @var{var_list}]
1850 /PROPORTION [INTO @var{var_list}]
1851 /N [INTO @var{var_list}]
1852 /SAVAGE [INTO @var{var_list}]
1855 The @cmd{RANK} command ranks variables and stores the results into new
1858 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1859 more variables whose values are to be ranked.
1860 After each variable, @samp{A} or @samp{D} may appear, indicating that
1861 the variable is to be ranked in ascending or descending order.
1862 Ascending is the default.
1863 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1864 which are to serve as group variables.
1865 In this case, the cases are gathered into groups, and ranks calculated
1868 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1869 default is to take the mean value of all the tied cases.
1871 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1872 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1873 functions are requested.
1875 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1876 variables created should appear in the output.
1878 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1879 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1880 If none are given, then the default is RANK.
1881 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1882 partitions into which values should be ranked.
1883 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1884 variables which are the variables to be created and receive the rank
1885 scores. There may be as many variables specified as there are
1886 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1887 then the variable names are automatically created.
1889 The @subcmd{MISSING} subcommand determines how user missing values are to be
1890 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1891 user-missing are to be excluded from the rank scores. A setting of
1892 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1894 @include regression.texi
1898 @section RELIABILITY
1903 /VARIABLES=@var{var_list}
1904 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1905 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1906 /SUMMARY=@{TOTAL,ALL@}
1907 /MISSING=@{EXCLUDE,INCLUDE@}
1910 @cindex Cronbach's Alpha
1911 The @cmd{RELIABILITY} command performs reliability analysis on the data.
1913 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1914 upon which analysis is to be performed.
1916 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1917 calculated for. If it is omitted, then analysis for all variables named
1918 in the @subcmd{VARIABLES} subcommand will be used.
1919 Optionally, the @var{name} parameter may be specified to set a string name
1922 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1923 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1924 then the variables are divided into 2 subsets. An optional parameter
1925 @var{n} may be given, to specify how many variables to be in the first subset.
1926 If @var{n} is omitted, then it defaults to one half of the variables in the
1927 scale, or one half minus one if there are an odd number of variables.
1928 The default model is @subcmd{ALPHA}.
1930 By default, any cases with user missing, or system missing values for
1932 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1933 The @subcmd{MISSING} subcommand determines whether user missing values are to
1934 be included or excluded in the analysis.
1936 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1937 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1938 analysis tested against the totals.
1946 @cindex Receiver Operating Characteristic
1947 @cindex Area under curve
1950 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1951 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1952 /PRINT = [ SE ] [ COORDINATES ]
1953 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1954 [ TESTPOS (@{LARGE,SMALL@}) ]
1955 [ CI (@var{confidence}) ]
1956 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1957 /MISSING=@{EXCLUDE,INCLUDE@}
1961 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1962 of a dataset, and to estimate the area under the curve.
1963 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1965 The mandatory @var{var_list} is the list of predictor variables.
1966 The variable @var{state_var} is the variable whose values represent the actual states,
1967 and @var{state_value} is the value of this variable which represents the positive state.
1969 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1970 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1971 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1972 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1973 By default, the curve is drawn with no reference line.
1975 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1976 Two additional tables are available.
1977 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1979 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1981 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1983 The @subcmd{CRITERIA} subcommand has four optional parameters:
1985 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1986 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1987 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1989 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1990 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1992 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1994 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1995 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1996 exponential distribution estimate.
1997 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1998 equal to the number of negative actual states.
1999 The default is @subcmd{FREE}.
2001 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
2004 The @subcmd{MISSING} subcommand determines whether user missing values are to
2005 be included or excluded in the analysis. The default behaviour is to
2007 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
2008 or if the variable @var{state_var} is missing, then the entire case will be
2011 @c LocalWords: subcmd subcommand