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 /COUNT=@{ASIS,CASE,CELL@}
602 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
603 KAPPA,ETA,CORR,ALL,NONE@}
607 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
610 The @cmd{CROSSTABS} procedure displays crosstabulation
611 tables requested by the user. It can calculate several statistics for
612 each cell in the crosstabulation tables. In addition, a number of
613 statistics can be calculated for each table itself.
615 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
616 number of dimensions is permitted, and any number of variables per
617 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
618 times as needed. This is the only required subcommand in @dfn{general
621 Occasionally, one may want to invoke a special mode called @dfn{integer
622 mode}. Normally, in general mode, @pspp{} automatically determines
623 what values occur in the data. In integer mode, the user specifies the
624 range of values that the data assumes. To invoke this mode, specify the
625 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
626 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
627 the range are truncated to the nearest integer, then assigned to that
628 value. If values occur outside this range, they are discarded. When it
629 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
632 In general mode, numeric and string variables may be specified on
633 TABLES. In integer mode, only numeric variables are allowed.
635 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
636 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
637 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
638 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
639 integer mode, user-missing values are included in tables but marked with
640 an @samp{M} (for ``missing'') and excluded from statistical
643 Currently the @subcmd{WRITE} subcommand is ignored.
645 The @subcmd{FORMAT} subcommand controls the characteristics of the
646 crosstabulation tables to be displayed. It has a number of possible
651 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
652 @subcmd{NOTABLES} suppresses them.
655 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
656 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
660 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
661 @subcmd{DVALUE} asserts a descending sort order.
664 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
667 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
670 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
671 crosstabulation table. The possible settings are:
687 Standardized residual.
689 Adjusted standardized residual.
693 Suppress cells entirely.
696 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
697 @subcmd{COLUMN}, and @subcmd{TOTAL}.
698 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
701 By default, crosstabulation and statistics use raw case weights,
702 without rounding. Use the @subcmd{/COUNT} subcommand to perform
703 rounding: CASE rounds the weights of individual weights as cases are
704 read, CELL rounds the weights of cells within each crosstabulation
705 table after it has been constructed, and ASIS explicitly specifies the
706 default non-rounding behavior. When rounding is requested, ROUND, the
707 default, rounds to the nearest integer and TRUNCATE rounds toward
710 The @subcmd{STATISTICS} subcommand selects statistics for computation:
717 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
718 correction, linear-by-linear association.
722 Contingency coefficient.
726 Uncertainty coefficient.
742 Spearman correlation, Pearson's r.
749 Selected statistics are only calculated when appropriate for the
750 statistic. Certain statistics require tables of a particular size, and
751 some statistics are calculated only in integer mode.
753 @samp{/STATISTICS} without any settings selects CHISQ. If the
754 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
757 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
758 variables on each table.
759 If a table has more than two variables, the counts for the third and subsequent levels
760 will be aggregated and the chart will be produces as if there were only two variables.
763 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
764 following limitations:
768 Significance of some symmetric and directional measures is not calculated.
770 Asymptotic standard error is not calculated for
771 Goodman and Kruskal's tau or symmetric Somers' d.
773 Approximate T is not calculated for symmetric uncertainty coefficient.
776 Fixes for any of these deficiencies would be welcomed.
782 @cindex factor analysis
783 @cindex principal components analysis
784 @cindex principal axis factoring
785 @cindex data reduction
789 VARIABLES=@var{var_list},
790 MATRIX IN (@{CORR,COV@}=@{*,@var{file_spec}@})
793 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
795 [ /ANALYSIS=@var{var_list} ]
797 [ /EXTRACTION=@{PC, PAF@}]
799 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
801 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [AIC] [SIG] [ALL] [DEFAULT] ]
805 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
807 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
809 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
812 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
813 common factors in the data or for data reduction purposes.
815 The @subcmd{VARIABLES} subcommand is required (unless the @subcmd{MATRIX IN}
817 It lists the variables which are to partake in the analysis. (The @subcmd{ANALYSIS}
818 subcommand may optionally further limit the variables that
819 participate; it is useful primarily in conjunction with @subcmd{MATRIX IN}.)
821 If @subcmd{MATRIX IN} instead of @subcmd{VARIABLES} is specified, then the analysis
822 is performed on a pre-prepared correlation or covariance matrix file instead of on
823 individual data cases. Typically the matrix file will have been generated by
824 @cmd{MATRIX DATA} (@pxref{MATRIX DATA}) or provided by a third party.
825 If specified, @subcmd{MATRIX IN} must be followed by @samp{COV} or @samp{CORR},
826 then by @samp{=} and @var{file_spec} all in parentheses.
827 @var{file_spec} may either be an asterisk, which indicates the currently loaded
828 dataset, or it may be a filename to be loaded. @xref{MATRIX DATA} for the expected
831 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
832 If @subcmd{PC} is specified, then Principal Components Analysis is used.
833 If @subcmd{PAF} is specified, then Principal Axis Factoring is
834 used. By default Principal Components Analysis will be used.
836 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
837 Three orthogonal rotation methods are available:
838 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
839 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
840 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
841 The default value of @var{k} is 5.
842 If you don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
843 rotation on the data.
845 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
846 to be analysed. By default, the correlation matrix is analysed.
848 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
851 @item @subcmd{UNIVARIATE}
852 A table of mean values, standard deviations and total weights are printed.
853 @item @subcmd{INITIAL}
854 Initial communalities and eigenvalues are printed.
855 @item @subcmd{EXTRACTION}
856 Extracted communalities and eigenvalues are printed.
857 @item @subcmd{ROTATION}
858 Rotated communalities and eigenvalues are printed.
859 @item @subcmd{CORRELATION}
860 The correlation matrix is printed.
861 @item @subcmd{COVARIANCE}
862 The covariance matrix is printed.
864 The determinant of the correlation or covariance matrix is printed.
866 The anti-image covariance and anti-image correlation matrices are printed.
868 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
870 The significance of the elements of correlation matrix is printed.
872 All of the above are printed.
873 @item @subcmd{DEFAULT}
874 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
877 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
878 which factors (components) should be retained.
880 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
881 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
882 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
883 performed, and all coefficients will be printed.
885 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
886 If @subcmd{FACTORS(@var{n})} is
887 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
889 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
890 The default value of @var{l} is 1.
891 The @subcmd{ECONVERGE} setting has effect only when iterative algorithms for factor
892 extraction (such as Principal Axis Factoring) are used.
893 @subcmd{ECONVERGE(@var{delta})} specifies that
894 iteration should cease when
895 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
896 default value of @var{delta} is 0.001.
897 The @subcmd{ITERATE(@var{m})} may appear any number of times and is used for two different purposes.
898 It is used to set the maximum number of iterations (@var{m}) for convergence and also to set the maximum number of iterations
900 Whether it affects convergence or rotation depends upon which subcommand follows the @subcmd{ITERATE} subcommand.
901 If @subcmd{EXTRACTION} follows, it affects convergence.
902 If @subcmd{ROTATION} follows, it affects rotation.
903 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a @subcmd{ITERATE} subcommand it will be ignored.
904 The default value of @var{m} is 25.
906 The @cmd{MISSING} subcommand determines the handling of missing variables.
907 If @subcmd{INCLUDE} is set, then user-missing values are included in the
908 calculations, but system-missing values are not.
909 If @subcmd{EXCLUDE} is set, which is the default, user-missing
910 values are excluded as well as system-missing values.
912 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
913 whenever any variable specified in the @cmd{VARIABLES} subcommand
914 contains a missing value.
915 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
916 values for the particular coefficient are missing.
917 The default is @subcmd{LISTWISE}.
923 @cindex univariate analysis of variance
924 @cindex fixed effects
925 @cindex factorial anova
926 @cindex analysis of variance
931 GLM @var{dependent_vars} BY @var{fixed_factors}
932 [/METHOD = SSTYPE(@var{type})]
933 [/DESIGN = @var{interaction_0} [@var{interaction_1} [... @var{interaction_n}]]]
934 [/INTERCEPT = @{INCLUDE|EXCLUDE@}]
935 [/MISSING = @{INCLUDE|EXCLUDE@}]
938 The @cmd{GLM} procedure can be used for fixed effects factorial Anova.
940 The @var{dependent_vars} are the variables to be analysed.
941 You may analyse several variables in the same command in which case they should all
942 appear before the @code{BY} keyword.
944 The @var{fixed_factors} list must be one or more categorical variables. Normally it
945 will not make sense to enter a scalar variable in the @var{fixed_factors} and doing
946 so may cause @pspp{} to do a lot of unnecessary processing.
948 The @subcmd{METHOD} subcommand is used to change the method for producing the sums of
949 squares. Available values of @var{type} are 1, 2 and 3. The default is type 3.
951 You may specify a custom design using the @subcmd{DESIGN} subcommand.
952 The design comprises a list of interactions where each interaction is a
953 list of variables separated by a @samp{*}. For example the command
955 GLM subject BY sex age_group race
956 /DESIGN = age_group sex group age_group*sex age_group*race
958 @noindent specifies the model @math{subject = age_group + sex + race + age_group*sex + age_group*race}.
959 If no @subcmd{DESIGN} subcommand is specified, then the default is all possible combinations
960 of the fixed factors. That is to say
962 GLM subject BY sex age_group race
965 @math{subject = age_group + sex + race + age_group*sex + age_group*race + sex*race + age_group*sex*race}.
968 The @subcmd{MISSING} subcommand determines the handling of missing
970 If @subcmd{INCLUDE} is set then, for the purposes of GLM analysis,
971 only system-missing values are considered
972 to be missing; user-missing values are not regarded as missing.
973 If @subcmd{EXCLUDE} is set, which is the default, then user-missing
974 values are considered to be missing as well as system-missing values.
975 A case for which any dependent variable or any factor
976 variable has a missing value is excluded from the analysis.
978 @node LOGISTIC REGRESSION
979 @section LOGISTIC REGRESSION
981 @vindex LOGISTIC REGRESSION
982 @cindex logistic regression
983 @cindex bivariate logistic regression
986 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
988 [/CATEGORICAL = @var{categorical_predictors}]
990 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
992 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
994 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
995 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
996 [CUT(@var{cut_point})]]
998 [/MISSING = @{INCLUDE|EXCLUDE@}]
1001 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
1002 variable in terms of one or more predictor variables.
1004 The minimum command is
1006 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
1008 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
1009 are the predictor variables whose coefficients the procedure estimates.
1011 By default, a constant term is included in the model.
1012 Hence, the full model is
1015 = b_0 + b_1 {\bf x_1}
1021 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
1022 Simple variables as well as interactions between variables may be listed here.
1024 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
1025 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
1027 An iterative Newton-Raphson procedure is used to fit the model.
1028 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
1029 and other parameters.
1030 The value of @var{cut_point} is used in the classification table. It is the
1031 threshold above which predicted values are considered to be 1. Values
1032 of @var{cut_point} must lie in the range [0,1].
1033 During iterations, if any one of the stopping criteria are satisfied, the procedure is
1034 considered complete.
1035 The stopping criteria are:
1037 @item The number of iterations exceeds @var{max_iterations}.
1038 The default value of @var{max_iterations} is 20.
1039 @item The change in the all coefficient estimates are less than @var{min_delta}.
1040 The default value of @var{min_delta} is 0.001.
1041 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
1042 The default value of @var{min_delta} is zero.
1043 This means that this criterion is disabled.
1044 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
1045 In other words, the probabilities are close to zero or one.
1046 The default value of @var{min_epsilon} is 0.00000001.
1050 The @subcmd{PRINT} subcommand controls the display of optional statistics.
1051 Currently there is one such option, @subcmd{CI}, which indicates that the
1052 confidence interval of the odds ratio should be displayed as well as its value.
1053 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
1054 confidence level of the desired confidence interval.
1056 The @subcmd{MISSING} subcommand determines the handling of missing
1058 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1059 calculations, but system-missing values are not.
1060 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1061 values are excluded as well as system-missing values.
1062 This is the default.
1073 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
1075 [ /@{@var{var_list}@}
1076 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
1078 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
1079 [VARIANCE] [KURT] [SEKURT]
1080 [SKEW] [SESKEW] [FIRST] [LAST]
1081 [HARMONIC] [GEOMETRIC]
1086 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
1089 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
1090 statistics, either for the dataset as a whole or for categories of data.
1092 The simplest form of the command is
1096 @noindent which calculates the mean, count and standard deviation for @var{v}.
1097 If you specify a grouping variable, for example
1099 MEANS @var{v} BY @var{g}.
1101 @noindent then the means, counts and standard deviations for @var{v} after having
1102 been grouped by @var{g} will be calculated.
1103 Instead of the mean, count and standard deviation, you could specify the statistics
1104 in which you are interested:
1106 MEANS @var{x} @var{y} BY @var{g}
1107 /CELLS = HARMONIC SUM MIN.
1109 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
1112 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
1116 @cindex arithmetic mean
1117 The arithmetic mean.
1118 @item @subcmd{COUNT}
1119 The count of the values.
1120 @item @subcmd{STDDEV}
1121 The standard deviation.
1122 @item @subcmd{SEMEAN}
1123 The standard error of the mean.
1125 The sum of the values.
1130 @item @subcmd{RANGE}
1131 The difference between the maximum and minimum values.
1132 @item @subcmd{VARIANCE}
1134 @item @subcmd{FIRST}
1135 The first value in the category.
1137 The last value in the category.
1140 @item @subcmd{SESKEW}
1141 The standard error of the skewness.
1144 @item @subcmd{SEKURT}
1145 The standard error of the kurtosis.
1146 @item @subcmd{HARMONIC}
1147 @cindex harmonic mean
1149 @item @subcmd{GEOMETRIC}
1150 @cindex geometric mean
1154 In addition, three special keywords are recognized:
1156 @item @subcmd{DEFAULT}
1157 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
1159 All of the above statistics will be calculated.
1161 No statistics will be calculated (only a summary will be shown).
1165 More than one @dfn{table} can be specified in a single command.
1166 Each table is separated by a @samp{/}. For
1170 @var{c} @var{d} @var{e} BY @var{x}
1171 /@var{a} @var{b} BY @var{x} @var{y}
1172 /@var{f} BY @var{y} BY @var{z}.
1174 has three tables (the @samp{TABLE =} is optional).
1175 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1176 and a single categorical variable @var{x}.
1177 The second table has two dependent variables @var{a} and @var{b},
1178 and two categorical variables @var{x} and @var{y}.
1179 The third table has a single dependent variables @var{f}
1180 and a categorical variable formed by the combination of @var{y} and @var{z}.
1183 By default values are omitted from the analysis only if missing values
1184 (either system missing or user missing)
1185 for any of the variables directly involved in their calculation are
1187 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1188 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1190 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
1191 in the table specification currently being processed, regardless of
1192 whether it is needed to calculate the statistic.
1194 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1195 variables or in the categorical variables should be taken at their face
1196 value, and not excluded.
1198 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1199 variables should be taken at their face value, however cases which
1200 have user missing values for the categorical variables should be omitted
1201 from the calculation.
1207 @cindex nonparametric tests
1212 nonparametric test subcommands
1217 [ /STATISTICS=@{DESCRIPTIVES@} ]
1219 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1221 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1224 @cmd{NPAR TESTS} performs nonparametric tests.
1225 Non parametric tests make very few assumptions about the distribution of the
1227 One or more tests may be specified by using the corresponding subcommand.
1228 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1229 produces for each variable that is the subject of any test.
1231 Certain tests may take a long time to execute, if an exact figure is required.
1232 Therefore, by default asymptotic approximations are used unless the
1233 subcommand @subcmd{/METHOD=EXACT} is specified.
1234 Exact tests give more accurate results, but may take an unacceptably long
1235 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1236 after which the test will be abandoned, and a warning message printed.
1237 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1238 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1243 * BINOMIAL:: Binomial Test
1244 * CHISQUARE:: Chisquare Test
1245 * COCHRAN:: Cochran Q Test
1246 * FRIEDMAN:: Friedman Test
1247 * KENDALL:: Kendall's W Test
1248 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1249 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1250 * MANN-WHITNEY:: Mann Whitney U Test
1251 * MCNEMAR:: McNemar Test
1252 * MEDIAN:: Median Test
1254 * SIGN:: The Sign Test
1255 * WILCOXON:: Wilcoxon Signed Ranks Test
1260 @subsection Binomial test
1262 @cindex binomial test
1265 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1268 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1269 variable with that of a binomial distribution.
1270 The variable @var{p} specifies the test proportion of the binomial
1272 The default value of 0.5 is assumed if @var{p} is omitted.
1274 If a single value appears after the variable list, then that value is
1275 used as the threshold to partition the observed values. Values less
1276 than or equal to the threshold value form the first category. Values
1277 greater than the threshold form the second category.
1279 If two values appear after the variable list, then they will be used
1280 as the values which a variable must take to be in the respective
1282 Cases for which a variable takes a value equal to neither of the specified
1283 values, take no part in the test for that variable.
1285 If no values appear, then the variable must assume dichotomous
1287 If more than two distinct, non-missing values for a variable
1288 under test are encountered then an error occurs.
1290 If the test proportion is equal to 0.5, then a two tailed test is
1291 reported. For any other test proportion, a one tailed test is
1293 For one tailed tests, if the test proportion is less than
1294 or equal to the observed proportion, then the significance of
1295 observing the observed proportion or more is reported.
1296 If the test proportion is more than the observed proportion, then the
1297 significance of observing the observed proportion or less is reported.
1298 That is to say, the test is always performed in the observed
1301 @pspp{} uses a very precise approximation to the gamma function to
1302 compute the binomial significance. Thus, exact results are reported
1303 even for very large sample sizes.
1308 @subsection Chisquare Test
1310 @cindex chisquare test
1314 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1318 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1319 between the expected and observed frequencies of the categories of a variable.
1320 Optionally, a range of values may appear after the variable list.
1321 If a range is given, then non integer values are truncated, and values
1322 outside the specified range are excluded from the analysis.
1324 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1326 There must be exactly one non-zero expected value, for each observed
1327 category, or the @subcmd{EQUAL} keyword must be specified.
1328 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1329 consecutive expected categories all taking a frequency of @var{f}.
1330 The frequencies given are proportions, not absolute frequencies. The
1331 sum of the frequencies need not be 1.
1332 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1337 @subsection Cochran Q Test
1339 @cindex Cochran Q test
1340 @cindex Q, Cochran Q
1343 [ /COCHRAN = @var{var_list} ]
1346 The Cochran Q test is used to test for differences between three or more groups.
1347 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1349 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1352 @subsection Friedman Test
1354 @cindex Friedman test
1357 [ /FRIEDMAN = @var{var_list} ]
1360 The Friedman test is used to test for differences between repeated measures when
1361 there is no indication that the distributions are normally distributed.
1363 A list of variables which contain the measured data must be given. The procedure
1364 prints the sum of ranks for each variable, the test statistic and its significance.
1367 @subsection Kendall's W Test
1369 @cindex Kendall's W test
1370 @cindex coefficient of concordance
1373 [ /KENDALL = @var{var_list} ]
1376 The Kendall test investigates whether an arbitrary number of related samples come from the
1378 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1379 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1380 unity indicates complete agreement.
1383 @node KOLMOGOROV-SMIRNOV
1384 @subsection Kolmogorov-Smirnov Test
1385 @vindex KOLMOGOROV-SMIRNOV
1387 @cindex Kolmogorov-Smirnov test
1390 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1393 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1394 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1395 Normal, Uniform, Poisson and Exponential.
1397 Ideally you should provide the parameters of the distribution against which you wish to test
1398 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1399 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1401 However, if the parameters are omitted they will be imputed from the data. Imputing the
1402 parameters reduces the power of the test so should be avoided if possible.
1404 In the following example, two variables @var{score} and @var{age} are tested to see if
1405 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1408 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1410 If the variables need to be tested against different distributions, then a separate
1411 subcommand must be used. For example the following syntax tests @var{score} against
1412 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1413 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1416 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1417 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1420 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1422 @node KRUSKAL-WALLIS
1423 @subsection Kruskal-Wallis Test
1424 @vindex KRUSKAL-WALLIS
1426 @cindex Kruskal-Wallis test
1429 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1432 The Kruskal-Wallis test is used to compare data from an
1433 arbitrary number of populations. It does not assume normality.
1434 The data to be compared are specified by @var{var_list}.
1435 The categorical variable determining the groups to which the
1436 data belongs is given by @var{var}. The limits @var{lower} and
1437 @var{upper} specify the valid range of @var{var}. Any cases for
1438 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1441 The mean rank of each group as well as the chi-squared value and significance
1442 of the test will be printed.
1443 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1447 @subsection Mann-Whitney U Test
1448 @vindex MANN-WHITNEY
1450 @cindex Mann-Whitney U test
1451 @cindex U, Mann-Whitney U
1454 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1457 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1458 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}.
1459 @var{Var} may be either a string or an alpha variable.
1460 @var{Group1} and @var{group2} specify the
1461 two values of @var{var} which determine the groups of the test data.
1462 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1464 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1465 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1468 @subsection McNemar Test
1470 @cindex McNemar test
1473 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1476 Use McNemar's test to analyse the significance of the difference between
1477 pairs of correlated proportions.
1479 If the @code{WITH} keyword is omitted, then tests for all
1480 combinations of the listed variables are performed.
1481 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1482 is also given, then the number of variables preceding @code{WITH}
1483 must be the same as the number following it.
1484 In this case, tests for each respective pair of variables are
1486 If the @code{WITH} keyword is given, but the
1487 @code{(PAIRED)} keyword is omitted, then tests for each combination
1488 of variable preceding @code{WITH} against variable following
1489 @code{WITH} are performed.
1491 The data in each variable must be dichotomous. If there are more
1492 than two distinct variables an error will occur and the test will
1496 @subsection Median Test
1501 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1504 The median test is used to test whether independent samples come from
1505 populations with a common median.
1506 The median of the populations against which the samples are to be tested
1507 may be given in parentheses immediately after the
1508 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1509 union of all the samples.
1511 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1512 keyword @code{BY} must come next, and then the grouping variable. Two values
1513 in parentheses should follow. If the first value is greater than the second,
1514 then a 2 sample test is performed using these two values to determine the groups.
1515 If however, the first variable is less than the second, then a @i{k} sample test is
1516 conducted and the group values used are all values encountered which lie in the
1517 range [@var{value1},@var{value2}].
1521 @subsection Runs Test
1526 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1529 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1531 It works by examining the number of times a variable's value crosses a given threshold.
1532 The desired threshold must be specified within parentheses.
1533 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1534 Following the threshold specification comes the list of variables whose values are to be
1537 The subcommand shows the number of runs, the asymptotic significance based on the
1541 @subsection Sign Test
1546 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1549 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1551 The test does not make any assumptions about the
1552 distribution of the data.
1554 If the @code{WITH} keyword is omitted, then tests for all
1555 combinations of the listed variables are performed.
1556 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1557 is also given, then the number of variables preceding @code{WITH}
1558 must be the same as the number following it.
1559 In this case, tests for each respective pair of variables are
1561 If the @code{WITH} keyword is given, but the
1562 @code{(PAIRED)} keyword is omitted, then tests for each combination
1563 of variable preceding @code{WITH} against variable following
1564 @code{WITH} are performed.
1567 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1569 @cindex wilcoxon matched pairs signed ranks test
1572 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1575 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1577 The test does not make any assumptions about the variances of the samples.
1578 It does however assume that the distribution is symmetrical.
1580 If the @subcmd{WITH} keyword is omitted, then tests for all
1581 combinations of the listed variables are performed.
1582 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1583 is also given, then the number of variables preceding @subcmd{WITH}
1584 must be the same as the number following it.
1585 In this case, tests for each respective pair of variables are
1587 If the @subcmd{WITH} keyword is given, but the
1588 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1589 of variable preceding @subcmd{WITH} against variable following
1590 @subcmd{WITH} are performed.
1599 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1600 /CRITERIA=CI(@var{confidence})
1604 TESTVAL=@var{test_value}
1605 /VARIABLES=@var{var_list}
1608 (Independent Samples mode.)
1609 GROUPS=var(@var{value1} [, @var{value2}])
1610 /VARIABLES=@var{var_list}
1613 (Paired Samples mode.)
1614 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1619 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1621 It operates in one of three modes:
1623 @item One Sample mode.
1624 @item Independent Groups mode.
1629 Each of these modes are described in more detail below.
1630 There are two optional subcommands which are common to all modes.
1632 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1633 in the tests. The default value is 0.95.
1636 The @cmd{MISSING} subcommand determines the handling of missing
1638 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1639 calculations, but system-missing values are not.
1640 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1641 values are excluded as well as system-missing values.
1642 This is the default.
1644 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1645 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1646 @subcmd{/GROUPS} subcommands contains a missing value.
1647 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1648 which they would be needed. This is the default.
1652 * One Sample Mode:: Testing against a hypothesized mean
1653 * Independent Samples Mode:: Testing two independent groups for equal mean
1654 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1657 @node One Sample Mode
1658 @subsection One Sample Mode
1660 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1661 This mode is used to test a population mean against a hypothesized
1663 The value given to the @subcmd{TESTVAL} subcommand is the value against
1664 which you wish to test.
1665 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1666 tell @pspp{} which variables you wish to test.
1668 @node Independent Samples Mode
1669 @subsection Independent Samples Mode
1671 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1673 This mode is used to test whether two groups of values have the
1674 same population mean.
1675 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1676 tell @pspp{} the dependent variables you wish to test.
1678 The variable given in the @subcmd{GROUPS} subcommand is the independent
1679 variable which determines to which group the samples belong.
1680 The values in parentheses are the specific values of the independent
1681 variable for each group.
1682 If the parentheses are omitted and no values are given, the default values
1683 of 1.0 and 2.0 are assumed.
1685 If the independent variable is numeric,
1686 it is acceptable to specify only one value inside the parentheses.
1687 If you do this, cases where the independent variable is
1688 greater than or equal to this value belong to the first group, and cases
1689 less than this value belong to the second group.
1690 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1691 the independent variable are excluded on a listwise basis, regardless
1692 of whether @subcmd{/MISSING=LISTWISE} was specified.
1695 @node Paired Samples Mode
1696 @subsection Paired Samples Mode
1698 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1699 Use this mode when repeated measures have been taken from the same
1701 If the @subcmd{WITH} keyword is omitted, then tables for all
1702 combinations of variables given in the @cmd{PAIRS} subcommand are
1704 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1705 is also given, then the number of variables preceding @subcmd{WITH}
1706 must be the same as the number following it.
1707 In this case, tables for each respective pair of variables are
1709 In the event that the @subcmd{WITH} keyword is given, but the
1710 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1711 of variable preceding @subcmd{WITH} against variable following
1712 @subcmd{WITH} are generated.
1719 @cindex analysis of variance
1724 [/VARIABLES = ] @var{var_list} BY @var{var}
1725 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1726 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1727 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1728 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1731 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1732 variables factored by a single independent variable.
1733 It is used to compare the means of a population
1734 divided into more than two groups.
1736 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1738 The list of variables must be followed by the @subcmd{BY} keyword and
1739 the name of the independent (or factor) variable.
1741 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1742 ancillary information. The options accepted are:
1745 Displays descriptive statistics about the groups factored by the independent
1748 Displays the Levene test of Homogeneity of Variance for the
1749 variables and their groups.
1752 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1753 differences between the groups.
1754 The subcommand must be followed by a list of numerals which are the
1755 coefficients of the groups to be tested.
1756 The number of coefficients must correspond to the number of distinct
1757 groups (or values of the independent variable).
1758 If the total sum of the coefficients are not zero, then @pspp{} will
1759 display a warning, but will proceed with the analysis.
1760 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1761 to specify different contrast tests.
1762 The @subcmd{MISSING} subcommand defines how missing values are handled.
1763 If @subcmd{LISTWISE} is specified then cases which have missing values for
1764 the independent variable or any dependent variable will be ignored.
1765 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1766 variable is missing or if the dependent variable currently being
1767 analysed is missing. The default is @subcmd{ANALYSIS}.
1768 A setting of @subcmd{EXCLUDE} means that variables whose values are
1769 user-missing are to be excluded from the analysis. A setting of
1770 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1772 Using the @code{POSTHOC} subcommand you can perform multiple
1773 pairwise comparisons on the data. The following comparison methods
1777 Least Significant Difference.
1778 @item @subcmd{TUKEY}
1779 Tukey Honestly Significant Difference.
1780 @item @subcmd{BONFERRONI}
1782 @item @subcmd{SCHEFFE}
1784 @item @subcmd{SIDAK}
1787 The Games-Howell test.
1791 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1792 that @var{value} should be used as the
1793 confidence level for which the posthoc tests will be performed.
1794 The default is 0.05.
1797 @section QUICK CLUSTER
1798 @vindex QUICK CLUSTER
1800 @cindex K-means clustering
1804 QUICK CLUSTER @var{var_list}
1805 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
1806 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1807 [/PRINT=@{INITIAL@} @{CLUSTER@}]
1810 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1811 dataset. This is useful when you wish to allocate cases into clusters
1812 of similar values and you already know the number of clusters.
1814 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1815 of the variables which contain the cluster data. Normally you will also
1816 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1817 number of clusters. If this is not specified, then @var{k} defaults to 2.
1819 If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
1820 the initial clusters is used. This will provide for faster execution but
1821 less well separated initial clusters and hence possibly an inferior final
1825 @cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
1826 The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
1827 During classification, @pspp{} will continue iterating until until @var{max_iter}
1828 iterations have been done or the convergence criterion (see below) is fulfilled.
1829 The default value of @var{max_iter} is 2.
1831 If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
1832 no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
1835 The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
1836 to set the convergence criterion. The value of convergence criterion is @var{epsilon}
1837 times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
1838 the mean cluster distance between one iteration and the next
1839 is less than the convergence criterion. The default value of @var{epsilon} is zero.
1841 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1842 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1843 value and not as missing values.
1844 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1845 values are excluded as well as system-missing values.
1847 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1848 whenever any of the clustering variables contains a missing value.
1849 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1850 clustering variables contain missing values. Otherwise it is clustered
1851 on the basis of the non-missing values.
1852 The default is @subcmd{LISTWISE}.
1854 The @subcmd{PRINT} subcommand requests additional output to be printed.
1855 If @subcmd{INITIAL} is set, then the initial cluster memberships will
1857 If @subcmd{CLUSTER} is set, the cluster memberships of the individual
1858 cases will be displayed (potentially generating lengthy output).
1867 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1868 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1869 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1871 /MISSING=@{EXCLUDE,INCLUDE@}
1873 /RANK [INTO @var{var_list}]
1874 /NTILES(k) [INTO @var{var_list}]
1875 /NORMAL [INTO @var{var_list}]
1876 /PERCENT [INTO @var{var_list}]
1877 /RFRACTION [INTO @var{var_list}]
1878 /PROPORTION [INTO @var{var_list}]
1879 /N [INTO @var{var_list}]
1880 /SAVAGE [INTO @var{var_list}]
1883 The @cmd{RANK} command ranks variables and stores the results into new
1886 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1887 more variables whose values are to be ranked.
1888 After each variable, @samp{A} or @samp{D} may appear, indicating that
1889 the variable is to be ranked in ascending or descending order.
1890 Ascending is the default.
1891 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1892 which are to serve as group variables.
1893 In this case, the cases are gathered into groups, and ranks calculated
1896 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1897 default is to take the mean value of all the tied cases.
1899 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1900 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1901 functions are requested.
1903 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1904 variables created should appear in the output.
1906 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1907 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1908 If none are given, then the default is RANK.
1909 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1910 partitions into which values should be ranked.
1911 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1912 variables which are the variables to be created and receive the rank
1913 scores. There may be as many variables specified as there are
1914 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1915 then the variable names are automatically created.
1917 The @subcmd{MISSING} subcommand determines how user missing values are to be
1918 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1919 user-missing are to be excluded from the rank scores. A setting of
1920 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1922 @include regression.texi
1926 @section RELIABILITY
1931 /VARIABLES=@var{var_list}
1932 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1933 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1934 /SUMMARY=@{TOTAL,ALL@}
1935 /MISSING=@{EXCLUDE,INCLUDE@}
1938 @cindex Cronbach's Alpha
1939 The @cmd{RELIABILITY} command performs reliability analysis on the data.
1941 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1942 upon which analysis is to be performed.
1944 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1945 calculated for. If it is omitted, then analysis for all variables named
1946 in the @subcmd{VARIABLES} subcommand will be used.
1947 Optionally, the @var{name} parameter may be specified to set a string name
1950 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1951 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1952 then the variables are divided into 2 subsets. An optional parameter
1953 @var{n} may be given, to specify how many variables to be in the first subset.
1954 If @var{n} is omitted, then it defaults to one half of the variables in the
1955 scale, or one half minus one if there are an odd number of variables.
1956 The default model is @subcmd{ALPHA}.
1958 By default, any cases with user missing, or system missing values for
1960 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1961 The @subcmd{MISSING} subcommand determines whether user missing values are to
1962 be included or excluded in the analysis.
1964 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1965 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1966 analysis tested against the totals.
1974 @cindex Receiver Operating Characteristic
1975 @cindex Area under curve
1978 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1979 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1980 /PRINT = [ SE ] [ COORDINATES ]
1981 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1982 [ TESTPOS (@{LARGE,SMALL@}) ]
1983 [ CI (@var{confidence}) ]
1984 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1985 /MISSING=@{EXCLUDE,INCLUDE@}
1989 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1990 of a dataset, and to estimate the area under the curve.
1991 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1993 The mandatory @var{var_list} is the list of predictor variables.
1994 The variable @var{state_var} is the variable whose values represent the actual states,
1995 and @var{state_value} is the value of this variable which represents the positive state.
1997 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1998 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1999 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
2000 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
2001 By default, the curve is drawn with no reference line.
2003 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
2004 Two additional tables are available.
2005 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
2007 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
2009 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
2011 The @subcmd{CRITERIA} subcommand has four optional parameters:
2013 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
2014 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
2015 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
2017 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
2018 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
2020 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
2022 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
2023 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
2024 exponential distribution estimate.
2025 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
2026 equal to the number of negative actual states.
2027 The default is @subcmd{FREE}.
2029 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
2032 The @subcmd{MISSING} subcommand determines whether user missing values are to
2033 be included or excluded in the analysis. The default behaviour is to
2035 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
2036 or if the variable @var{state_var} is missing, then the entire case will be
2039 @c LocalWords: subcmd subcommand