1 @c PSPP - a program for statistical analysis.
2 @c Copyright (C) 2017, 2020 Free Software Foundation, Inc.
3 @c Permission is granted to copy, distribute and/or modify this document
4 @c under the terms of the GNU Free Documentation License, Version 1.3
5 @c or any later version published by the Free Software Foundation;
6 @c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
7 @c A copy of the license is included in the section entitled "GNU
8 @c Free Documentation License".
13 This chapter documents the statistical procedures that @pspp{} supports so
17 * DESCRIPTIVES:: Descriptive statistics.
18 * FREQUENCIES:: Frequency tables.
19 * EXAMINE:: Testing data for normality.
21 * CORRELATIONS:: Correlation tables.
22 * CROSSTABS:: Crosstabulation tables.
23 * CTABLES:: Custom tables.
24 * FACTOR:: Factor analysis and Principal Components analysis.
25 * GLM:: Univariate Linear Models.
26 * LOGISTIC REGRESSION:: Bivariate Logistic Regression.
27 * MEANS:: Average values and other statistics.
28 * NPAR TESTS:: Nonparametric tests.
29 * T-TEST:: Test hypotheses about means.
30 * ONEWAY:: One way analysis of variance.
31 * QUICK CLUSTER:: K-Means clustering.
32 * RANK:: Compute rank scores.
33 * RELIABILITY:: Reliability analysis.
34 * ROC:: Receiver Operating Characteristic.
43 /VARIABLES=@var{var_list}
44 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
45 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
47 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
48 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
49 SESKEWNESS,SEKURTOSIS@}
50 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
51 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
55 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
56 linear descriptive statistics requested by the user. In addition, it can optionally
59 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
60 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
62 All other subcommands are optional:
64 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
65 @subcmd{INCLUDE} is set, then user-missing values are included in the
66 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
67 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
68 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
69 the entire case is excluded whenever any value in that case has a
70 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
72 The @subcmd{FORMAT} subcommand has no effect. It is accepted for
73 backward compatibility.
75 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
76 the specified variables. The Z scores are saved to new variables.
77 Variable names are generated by trying first the original variable name
78 with Z prepended and truncated to a maximum of 8 characters, then the
79 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
80 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
81 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
82 list by enclosing them in parentheses after each variable.
83 When Z scores are calculated, @pspp{} ignores @cmd{TEMPORARY},
84 treating temporary transformations as permanent.
86 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
90 All of the statistics below.
94 Standard error of the mean.
97 @item @subcmd{VARIANCE}
99 @item @subcmd{KURTOSIS}
100 Kurtosis and standard error of the kurtosis.
101 @item @subcmd{SKEWNESS}
102 Skewness and standard error of the skewness.
112 Mean, standard deviation of the mean, minimum, maximum.
114 Standard error of the kurtosis.
116 Standard error of the skewness.
119 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
120 of the possible values should be self-explanatory. @subcmd{NAME} causes the
121 statistics to be sorted by name. By default, the statistics are listed
122 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
123 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
124 sort order, respectively.
126 @subsection Descriptives Example
128 The @file{physiology.sav} file contains various physiological data for a sample
129 of persons. Running the @cmd{DESCRIPTIVES} command on the variables @exvar{height}
130 and @exvar{temperature} with the default options allows one to see simple linear
131 statistics for these two variables. In @ref{descriptives:ex}, these variables
132 are specfied on the @subcmd{VARIABLES} subcommand and the @subcmd{SAVE} option
133 has been used, to request that Z scores be calculated.
135 After the command has completed, this example runs @cmd{DESCRIPTIVES} again, this
136 time on the @exvar{zheight} and @exvar{ztemperature} variables,
137 which are the two normalized (Z-score) variables generated by the
138 first @cmd{DESCRIPTIVES} command.
140 @float Example, descriptives:ex
141 @psppsyntax {descriptives.sps}
142 @caption {Running two @cmd{DESCRIPTIVES} commands, one with the @subcmd{SAVE} subcommand}
145 @float Screenshot, descriptives:scr
146 @psppimage {descriptives}
147 @caption {The Descriptives dialog box with two variables and Z-Scores option selected}
150 In @ref{descriptives:res}, we can see that there are 40 valid data for each of the variables
151 and no missing values. The mean average of the height and temperature is 16677.12
152 and 37.02 respectively. The descriptive statistics for temperature seem reasonable.
153 However there is a very high standard deviation for @exvar{height} and a suspiciously
154 low minimum. This is due to a data entry error in the
155 data (@pxref{Identifying incorrect data}).
157 In the second Descriptive Statistics command, one can see that the mean and standard
158 deviation of both Z score variables is 0 and 1 respectively. All Z score statistics
159 should have these properties since they are normalized versions of the original scores.
161 @float Result, descriptives:res
162 @psppoutput {descriptives}
163 @caption {Descriptives statistics including two normalized variables (Z-scores)}
172 /VARIABLES=@var{var_list}
173 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
174 @{AVALUE,DVALUE,AFREQ,DFREQ@}
175 /MISSING=@{EXCLUDE,INCLUDE@}
176 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
177 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
178 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
180 /PERCENTILES=percent@dots{}
181 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
182 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
183 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
184 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
185 /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
187 /ORDER=@{ANALYSIS,VARIABLE@}
190 (These options are not currently implemented.)
195 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
197 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
198 (including median and mode) and percentiles, and various graphical representations
199 of the frequency distribution.
201 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
202 variables to be analyzed.
204 The @subcmd{FORMAT} subcommand controls the output format. It has several
209 @subcmd{TABLE}, the default, causes a frequency table to be output for every
210 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
211 with a numeric argument causes them to be output except when there are
212 more than the specified number of values in the table.
215 Normally frequency tables are sorted in ascending order by value. This
216 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
217 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
218 respectively, by frequency count.
221 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
222 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
223 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
224 are included. System-missing values are never included in statistics,
225 but are listed in frequency tables.
227 The available @subcmd{STATISTICS} are the same as available
228 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
229 of @subcmd{MEDIAN}, the data's median
230 value, and MODE, the mode. (If there are multiple modes, the smallest
231 value is reported.) By default, the mean, standard deviation of the
232 mean, minimum, and maximum are reported for each variable.
235 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
236 The percentiles should be presented at a list of numbers between 0
238 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
239 boundaries of the data set divided into the specified number of ranges.
240 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
243 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
244 each specified numeric variable. The X axis by default ranges from
245 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
246 and @subcmd{MAXIMUM} keywords can set an explicit range.
247 @footnote{The number of
248 bins is chosen according to the Freedman-Diaconis rule:
249 @math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x}
250 and @math{n} is the number of samples. Note that
251 @cmd{EXAMINE} uses a different algorithm to determine bin sizes.}
252 Histograms are not created for string variables.
254 Specify @subcmd{NORMAL} to superimpose a normal curve on the
258 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
259 slice represents one value, with the size of the slice proportional to
260 the value's frequency. By default, all non-missing values are given
262 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
263 displayed slices to a given range of values.
264 The keyword @subcmd{NOMISSING} causes missing values to be omitted from the
265 piechart. This is the default.
266 If instead, @subcmd{MISSING} is specified, then the pie chart includes
267 a single slice representing all system missing and user-missing cases.
270 The @subcmd{BARCHART} subcommand produces a bar chart for each variable.
271 The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit
272 categories whose counts which lie outside the specified limits.
273 The @subcmd{FREQ} option (default) causes the ordinate to display the frequency
274 of each category, whereas the @subcmd{PERCENT} option displays relative
277 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and
278 @subcmd{PIECHART} are accepted but not currently honoured.
280 The @subcmd{ORDER} subcommand is accepted but ignored.
282 @subsection Frequencies Example
284 @ref{frequencies:ex} runs a frequency analysis on the @exvar{sex}
285 and @exvar{occupation} variables from the @file{personnel.sav} file.
286 This is useful to get an general idea of the way in which these nominal
287 variables are distributed.
289 @float Example, frequencies:ex
290 @psppsyntax {frequencies.sps}
291 @caption {Running frequencies on the @exvar{sex} and @exvar{occupation} variables}
294 If you are using the graphic user interface, the dialog box is set up such that
295 by default, several statistics are calculated. Some are not particularly useful
296 for categorical variables, so you may want to disable those.
298 @float Screenshot, frequencies:scr
299 @psppimage {frequencies}
300 @caption {The frequencies dialog box with the @exvar{sex} and @exvar{occupation} variables selected}
303 From @ref{frequencies:res} it is evident that there are 33 males, 21 females and
304 2 persons for whom their sex has not been entered.
306 One can also see how many of each occupation there are in the data.
307 When dealing with string variables used as nominal values, running a frequency
308 analysis is useful to detect data input entries. Notice that
309 one @exvar{occupation} value has been mistyped as ``Scrientist''. This entry should
310 be corrected, or marked as missing before using the data.
312 @float Result, frequencies:res
313 @psppoutput {frequencies}
314 @caption {The relative frequencies of @exvar{sex} and @exvar{occupation}}
321 @cindex Exploratory data analysis
322 @cindex normality, testing
326 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
327 [BY @var{factor1} [BY @var{subfactor1}]
328 [ @var{factor2} [BY @var{subfactor2}]]
330 [ @var{factor3} [BY @var{subfactor3}]]
332 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
333 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
335 /COMPARE=@{GROUPS,VARIABLES@}
336 /ID=@var{identity_variable}
338 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
339 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
340 [@{NOREPORT,REPORT@}]
344 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
345 In particular, it is useful for testing how closely a distribution follows a
346 normal distribution, and for finding outliers and extreme values.
348 The @subcmd{VARIABLES} subcommand is mandatory.
349 It specifies the dependent variables and optionally variables to use as
350 factors for the analysis.
351 Variables listed before the first @subcmd{BY} keyword (if any) are the
353 The dependent variables may optionally be followed by a list of
354 factors which tell @pspp{} how to break down the analysis for each
357 Following the dependent variables, factors may be specified.
358 The factors (if desired) should be preceded by a single @subcmd{BY} keyword.
359 The format for each factor is
361 @var{factorvar} [BY @var{subfactorvar}].
363 Each unique combination of the values of @var{factorvar} and
364 @var{subfactorvar} divide the dataset into @dfn{cells}.
365 Statistics are calculated for each cell
366 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
368 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
369 @subcmd{DESCRIPTIVES} produces a table showing some parametric and
370 non-parametrics statistics.
371 @subcmd{EXTREME} produces a table showing the extremities of each cell.
372 A number in parentheses, @var{n} determines
373 how many upper and lower extremities to show.
374 The default number is 5.
376 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
377 If @subcmd{TOTAL} appears, then statistics for the entire dataset
378 as well as for each cell are produced.
379 If @subcmd{NOTOTAL} appears, then statistics are produced only for the cells
380 (unless no factor variables have been given).
381 These subcommands have no effect if there have been no factor variables
387 @cindex spreadlevel plot
388 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
389 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
390 @subcmd{SPREADLEVEL}.
391 The first three can be used to visualise how closely each cell conforms to a
392 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
393 how the variance differs between factors.
394 Boxplots show you the outliers and extreme values.
395 @footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of
396 bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples.
397 Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.}
399 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
400 median. It takes an optional parameter @var{t}, which specifies how the data
401 should be transformed prior to plotting.
402 The given value @var{t} is a power to which the data are raised. For example, if
403 @var{t} is given as 2, then the square of the data is used.
404 Zero, however is a special value. If @var{t} is 0 or
405 is omitted, then data are transformed by taking its natural logarithm instead of
406 raising to the power of @var{t}.
409 When one or more plots are requested, @subcmd{EXAMINE} also performs the
410 Shapiro-Wilk test for each category.
411 There are however a number of provisos:
413 @item All weight values must be integer.
414 @item The cumulative weight value must be in the range [3, 5000]
417 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
418 useful there is more than one dependent variable and at least one factor.
420 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
421 each of which contain boxplots for all the cells.
422 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
423 each containing one boxplot per dependent variable.
424 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
425 @subcmd{/COMPARE=GROUPS} were given.
427 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
428 @subcmd{/STATISTICS=EXTREME} has been given.
429 If given, it should provide the name of a variable which is to be used
430 to labels extreme values and outliers.
431 Numeric or string variables are permissible.
432 If the @subcmd{ID} subcommand is not given, then the case number is used for
435 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
436 calculation of the descriptives command. The default is 95%.
439 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
440 and which algorithm to use for calculating them. The default is to
441 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
442 @subcmd{HAVERAGE} algorithm.
444 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
445 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
446 then statistics for the unfactored dependent variables are
447 produced in addition to the factored variables. If there are no
448 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
451 The following example generates descriptive statistics and histograms for
452 two variables @var{score1} and @var{score2}.
453 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
454 Therefore, the descriptives and histograms are generated for each
456 of @var{gender} @emph{and} for each distinct combination of the values
457 of @var{gender} and @var{race}.
458 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
459 @var{score1} and @var{score2} covering the whole dataset are not produced.
461 EXAMINE @var{score1} @var{score2} BY
463 @var{gender} BY @var{culture}
464 /STATISTICS = DESCRIPTIVES
469 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
471 EXAMINE @var{height} @var{weight} BY
473 /STATISTICS = EXTREME (3)
478 In this example, we look at the height and weight of a sample of individuals and
479 how they differ between male and female.
480 A table showing the 3 largest and the 3 smallest values of @exvar{height} and
481 @exvar{weight} for each gender, and for the whole dataset as are shown.
482 In addition, the @subcmd{/PLOT} subcommand requests boxplots.
483 Because @subcmd{/COMPARE = GROUPS} was specified, boxplots for male and female are
484 shown in juxtaposed in the same graphic, allowing us to easily see the difference between
486 Since the variable @var{name} was specified on the @subcmd{ID} subcommand,
487 values of the @var{name} variable are used to label the extreme values.
490 If you specify many dependent variables or factor variables
491 for which there are many distinct values, then @cmd{EXAMINE} will produce a very
492 large quantity of output.
498 @cindex Exploratory data analysis
499 @cindex normality, testing
503 /HISTOGRAM [(NORMAL)]= @var{var}
504 /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}]
505 /BAR = @{@var{summary-function}(@var{var1}) | @var{count-function}@} BY @var{var2} [BY @var{var3}]
506 [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ]
507 [@{NOREPORT,REPORT@}]
511 The @cmd{GRAPH} command produces graphical plots of data. Only one of the subcommands
512 @subcmd{HISTOGRAM}, @subcmd{BAR} or @subcmd{SCATTERPLOT} can be specified, @i{i.e.} only one plot
513 can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional.
516 * SCATTERPLOT:: Cartesian Plots
517 * HISTOGRAM:: Histograms
518 * BAR CHART:: Bar Charts
522 @subsection Scatterplot
525 The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the
527 @cmd{GRAPH} uses the third variable @var{var3}, if specified, to determine
528 the colours and/or markers for the plot.
529 The following is an example for producing a scatterplot.
533 /SCATTERPLOT = @var{height} WITH @var{weight} BY @var{gender}.
536 This example produces a scatterplot where @var{height} is plotted versus @var{weight}. Depending
537 on the value of the @var{gender} variable, the colour of the datapoint is different. With
538 this plot it is possible to analyze gender differences for @var{height} versus @var{weight} relation.
541 @subsection Histogram
544 The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for
546 The keyword @subcmd{NORMAL} may be specified in parentheses, to indicate that the ideal normal curve
547 should be superimposed over the histogram.
548 For an alternative method to produce histograms @pxref{EXAMINE}. The
549 following example produces a histogram plot for the variable @var{weight}.
553 /HISTOGRAM = @var{weight}.
557 @subsection Bar Chart
560 The subcommand @subcmd{BAR} produces a bar chart.
561 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.
562 Following the summary or count function, the keyword @subcmd{BY} should be specified and then a catagorical variable, @var{var2}.
563 The values of the variable @var{var2} determine the labels of the bars to be plotted.
564 Optionally a second categorical variable @var{var3} may be specified in which case a clustered (grouped) bar chart is produced.
566 Valid count functions are
569 The weighted counts of the cases in each category.
571 The weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
573 The cumulative weighted counts of the cases in each category.
575 The cumulative weighted counts of the cases in each category expressed as a percentage of the total weights of the cases.
578 The summary function is applied to @var{var1} across all cases in each category.
579 The recognised summary functions are:
591 The following examples assume a dataset which is the results of a survey.
592 Each respondent has indicated annual income, their sex and city of residence.
593 One could create a bar chart showing how the mean income varies between of residents of different cities, thus:
595 GRAPH /BAR = MEAN(@var{income}) BY @var{city}.
598 This can be extended to also indicate how income in each city differs between the sexes.
600 GRAPH /BAR = MEAN(@var{income}) BY @var{city} BY @var{sex}.
603 One might also want to see how many respondents there are from each city. This can be achieved as follows:
605 GRAPH /BAR = COUNT BY @var{city}.
608 Bar charts can also be produced using the @ref{FREQUENCIES} and @ref{CROSSTABS} commands.
611 @section CORRELATIONS
616 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
621 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
622 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
625 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
626 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
627 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
631 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
632 for a set of variables. The significance of the coefficients are also given.
634 At least one @subcmd{VARIABLES} subcommand is required. If you specify the @subcmd{WITH}
635 keyword, then a non-square correlation table is produced.
636 The variables preceding @subcmd{WITH}, are used as the rows of the table,
637 and the variables following @subcmd{WITH} are used as the columns of the table.
638 If no @subcmd{WITH} subcommand is specified, then @cmd{CORRELATIONS} produces a
639 square, symmetrical table using all variables.
641 The @cmd{MISSING} subcommand determines the handling of missing variables.
642 If @subcmd{INCLUDE} is set, then user-missing values are included in the
643 calculations, but system-missing values are not.
644 If @subcmd{EXCLUDE} is set, which is the default, user-missing
645 values are excluded as well as system-missing values.
647 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
648 whenever any variable specified in any @cmd{/VARIABLES} subcommand
649 contains a missing value.
650 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
651 values for the particular coefficient are missing.
652 The default is @subcmd{PAIRWISE}.
654 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
655 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
656 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
657 The default is @subcmd{TWOTAIL}.
659 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
660 0.05 are highlighted.
661 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
664 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
665 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
666 estimator of the standard deviation are displayed.
667 These statistics are displayed in a separated table, for all the variables listed
668 in any @subcmd{/VARIABLES} subcommand.
669 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
670 be displayed for each pair of variables.
671 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
679 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
680 /MISSING=@{TABLE,INCLUDE,REPORT@}
681 /FORMAT=@{TABLES,NOTABLES@}
683 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
684 ASRESIDUAL,ALL,NONE@}
685 /COUNT=@{ASIS,CASE,CELL@}
687 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
688 KAPPA,ETA,CORR,ALL,NONE@}
692 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
695 The @cmd{CROSSTABS} procedure displays crosstabulation
696 tables requested by the user. It can calculate several statistics for
697 each cell in the crosstabulation tables. In addition, a number of
698 statistics can be calculated for each table itself.
700 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
701 number of dimensions is permitted, and any number of variables per
702 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
703 times as needed. This is the only required subcommand in @dfn{general
706 Occasionally, one may want to invoke a special mode called @dfn{integer
707 mode}. Normally, in general mode, @pspp{} automatically determines
708 what values occur in the data. In integer mode, the user specifies the
709 range of values that the data assumes. To invoke this mode, specify the
710 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
711 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
712 the range are truncated to the nearest integer, then assigned to that
713 value. If values occur outside this range, they are discarded. When it
714 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
717 In general mode, numeric and string variables may be specified on
718 TABLES. In integer mode, only numeric variables are allowed.
720 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
721 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
722 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
723 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
724 integer mode, user-missing values are included in tables but marked with
725 a footnote and excluded from statistical calculations.
727 The @subcmd{FORMAT} subcommand controls the characteristics of the
728 crosstabulation tables to be displayed. It has a number of possible
733 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
734 @subcmd{NOTABLES}, which is equivalent to @code{CELLS=NONE}, suppresses them.
737 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
738 @subcmd{DVALUE} asserts a descending sort order.
741 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
742 crosstabulation table. The possible settings are:
758 Standardized residual.
760 Adjusted standardized residual.
764 Suppress cells entirely.
767 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
768 @subcmd{COLUMN}, and @subcmd{TOTAL}.
769 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
772 By default, crosstabulation and statistics use raw case weights,
773 without rounding. Use the @subcmd{/COUNT} subcommand to perform
774 rounding: CASE rounds the weights of individual weights as cases are
775 read, CELL rounds the weights of cells within each crosstabulation
776 table after it has been constructed, and ASIS explicitly specifies the
777 default non-rounding behavior. When rounding is requested, ROUND, the
778 default, rounds to the nearest integer and TRUNCATE rounds toward
781 The @subcmd{STATISTICS} subcommand selects statistics for computation:
787 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
788 correction, linear-by-linear association.
792 Contingency coefficient.
796 Uncertainty coefficient.
812 Spearman correlation, Pearson's r.
819 Selected statistics are only calculated when appropriate for the
820 statistic. Certain statistics require tables of a particular size, and
821 some statistics are calculated only in integer mode.
823 @samp{/STATISTICS} without any settings selects CHISQ. If the
824 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
827 The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two
828 variables on each table.
829 If a table has more than two variables, the counts for the third and subsequent levels
830 are aggregated and the chart is produced as if there were only two variables.
833 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
834 following limitations:
838 Significance of some symmetric and directional measures is not calculated.
840 Asymptotic standard error is not calculated for
841 Goodman and Kruskal's tau or symmetric Somers' d.
843 Approximate T is not calculated for symmetric uncertainty coefficient.
846 Fixes for any of these deficiencies would be welcomed.
848 @subsection Crosstabs Example
850 @cindex chi-square test of independence
852 A researcher wishes to know if, in an industry, a person's sex is related to
853 the person's occupation. To investigate this, she has determined that the
854 @file{personnel.sav} is a representative, randomly selected sample of persons.
855 The researcher's null hypothesis is that a person's sex has no relation to a
856 person's occupation. She uses a chi-squared test of independence to investigate
859 @float Example, crosstabs:ex
860 @psppsyntax {crosstabs.sps}
861 @caption {Running crosstabs on the @exvar{sex} and @exvar{occupation} variables}
864 The syntax in @ref{crosstabs:ex} conducts a chi-squared test of independence.
865 The line @code{/tables = occupation by sex} indicates that @exvar{occupation}
866 and @exvar{sex} are the variables to be tabulated. To do this using the @gui{}
867 you must place these variable names respectively in the @samp{Row} and
868 @samp{Column} fields as shown in @ref{crosstabs:scr}.
870 @float Screenshot, crosstabs:scr
871 @psppimage {crosstabs}
872 @caption {The Crosstabs dialog box with the @exvar{sex} and @exvar{occupation} variables selected}
875 Similarly, the @samp{Cells} button shows a dialog box to select the @code{count}
876 and @code{expected} options. All other cell options can be deselected for this
879 You would use the @samp{Format} and @samp{Statistics} buttons to select options
880 for the @subcmd{FORMAT} and @subcmd{STATISTICS} subcommands. In this example,
881 the @samp{Statistics} requires only the @samp{Chisq} option to be checked. All
882 other options should be unchecked. No special settings are required from the
883 @samp{Format} dialog.
885 As shown in @ref{crosstabs:res} @cmd{CROSSTABS} generates a contingency table
886 containing the observed count and the expected count of each sex and each
887 occupation. The expected count is the count which would be observed if the
888 null hypothesis were true.
890 The significance of the Pearson Chi-Square value is very much larger than the
891 normally accepted value of 0.05 and so one cannot reject the null hypothesis.
892 Thus the researcher must conclude that a person's sex has no relation to the
895 @float Results, crosstabs:res
896 @psppoutput {crosstabs}
897 @caption {The results of a test of independence between @exvar{sex} and @exvar{occupation}}
904 @cindex custom tables
905 @cindex tables, custom
907 @code{CTABLES} has the following overall syntax. At least one
908 @code{TABLE} subcommand is required:
912 @dots{}@i{global subcommands}@dots{}
913 [@t{/TABLE} @i{axis} [@t{BY} @i{axis} [@t{BY} @i{axis}]]
914 @dots{}@i{per-table subcommands}@dots{}]@dots{}
918 where each @i{axis} may be empty or take one of the following forms:
922 @i{variable} @t{[}@{@t{C} @math{|} @t{S}@}@t{]}
926 @i{axis} @t{[}@i{summary} [@i{string}] [@i{format}]@t{]}
929 The following subcommands precede the first @code{TABLE} subcommand
930 and apply to all of the output tables. All of these subcommands are
935 [@t{MINCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
936 [@t{MAXCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
937 [@t{UNITS=}@{@t{POINTS} @math{|} @t{INCHES} @math{|} @t{CM}@}]
938 [@t{EMPTY=}@{@t{ZERO} @math{|} @t{BLANK} @math{|} @i{string}@}]
939 [@t{MISSING=}@i{string}]
941 @t{VARIABLES=}@i{variables}
942 @t{DISPLAY}=@{@t{DEFAULT} @math{|} @t{NAME} @math{|} @t{LABEL} @math{|} @t{BOTH} @math{|} @t{NONE}@}
943 @ignore @c not yet implemented
944 @t{/MRSETS COUNTDUPLICATES=}@{@t{YES} @math{|} @t{NO}@}
946 @t{/SMISSING} @{@t{VARIABLE} @math{|} @t{LISTWISE}@}
947 @t{/PCOMPUTE} @t{&}@i{postcompute}@t{=EXPR(}@i{expression}@t{)}
948 @t{/PPROPERTIES} @t{&}@i{postcompute}@dots{}
949 [@t{LABEL=}@i{string}]
950 [@t{FORMAT=}[@i{summary} @i{format}]@dots{}]
951 [@t{HIDESOURCECATS=}@{@t{NO} @math{|} @t{YES}@}
952 @t{/WEIGHT VARIABLE=}@i{variable}
953 @t{/HIDESMALLCOUNTS COUNT=@i{count}}
956 The following subcommands follow @code{TABLE} and apply only to the
957 previous @code{TABLE}. All of these subcommands are optional:
961 [@t{POSITION=}@{@t{COLUMN} @math{|} @t{ROW} @math{|} @t{LAYER}@}]
962 [@t{VISIBLE=}@{@t{YES} @math{|} @t{NO}@}]
963 @t{/CLABELS} @{@t{AUTO} @math{|} @{@t{ROWLABELS}@math{|}@t{COLLABELS}@}@t{=}@{@t{OPPOSITE}@math{|}@t{LAYER}@}@}
964 @t{/CATEGORIES} @t{VARIABLES=}@i{variables}
965 @{@t{[}@i{value}@t{,} @i{value}@dots{}@t{]}
966 @math{|} [@t{ORDER=}@{@t{A} @math{|} @t{D}@}]
967 [@t{KEY=}@{@t{VALUE} @math{|} @t{LABEL} @math{|} @i{summary}@t{(}@i{variable}@t{)}@}]
968 [@t{MISSING=}@{@t{EXCLUDE} @math{|} @t{INCLUDE}@}]@}
969 [@t{TOTAL=}@{@t{NO} @math{|} @t{YES}@} [@t{LABEL=}@i{string}] [@t{POSITION=}@{@t{AFTER} @math{|} @t{BEFORE}@}]]
970 [@t{EMPTY=}@{@t{INCLUDE} @math{|} @t{EXCLUDE}@}]
972 [@t{TITLE=}@i{string}@dots{}]
973 [@t{CAPTION=}@i{string}@dots{}]
974 [@t{CORNER=}@i{string}@dots{}]
975 @ignore @c not yet implemented
976 @t{/CRITERIA CILEVEL=}@i{percentage}
977 @t{/SIGTEST TYPE=CHISQUARE}
978 [@t{ALPHA=}@i{siglevel}]
979 [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
980 [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
981 @t{/COMPARETEST TYPE=}@{@t{PROP} @math{|} @t{MEAN}@}
982 [@t{ALPHA=}@i{value}[@t{,} @i{value}]]
983 [@t{ADJUST=}@{@t{BONFERRONI} @math{|} @t{BH} @math{|} @t{NONE}@}]
984 [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
985 [@t{MEANSVARIANCE=}@{@t{ALLCATS} @math{|} @t{TESTEDCATS}@}]
986 [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
987 [@t{MERGE=}@{@t{NO} @math{|} @t{YES}@}]
988 [@t{STYLE=}@{@t{APA} @math{|} @t{SIMPLE}@}]
989 [@t{SHOWSIG=}@{@t{NO} @math{|} @t{YES}@}]
993 The @code{CTABLES} (aka ``custom tables'') command produces
994 multi-dimensional tables from categorical and scale data. It offers
995 many options for data summarization and formatting.
997 This section's examples use data from the 2008 (USA) National Survey
998 of Drinking and Driving Attitudes and Behaviors, a public domain data
999 set from the (USA) National Highway Traffic Administration and
1000 available at @url{https://data.transportation.gov}. @pspp{} includes
1001 this data set, with a slightly modified dictionary, as
1002 @file{examples/nhtsa.sav}.
1004 @node CTABLES Basics
1007 The only required subcommand is @code{TABLE}, which specifies the
1008 variables to include along each axis:
1010 @t{/TABLE} @i{rows} [@t{BY} @i{columns} [@t{BY} @i{layers}]]
1013 In @code{TABLE}, each of @var{rows}, @var{columns}, and @var{layers}
1014 is either empty or an axis expression that specifies one or more
1015 variables. At least one must specify an axis expression.
1018 * CTABLES Categorical Variable Basics::
1019 * CTABLES Scalar Variable Basics::
1020 * CTABLES Overriding Measurement Level::
1023 @node CTABLES Categorical Variable Basics
1024 @subsubsection Categorical Variables
1026 An axis expression that names a categorical variable divides the data
1027 into cells according to the values of that variable. When all the
1028 variables named on @code{TABLE} are categorical, by default each cell
1029 displays the number of cases that it contains, so specifying a single
1030 variable yields a frequency table, much like the output of the
1031 @code{FREQUENCIES} command (@pxref{FREQUENCIES}):
1034 CTABLES /TABLE=AgeGroup.
1036 @psppoutput {ctables1}
1039 Specifying a row and a column categorical variable yields a
1040 crosstabulation, much like the output of the @code{CROSSTABS} command
1041 (@pxref{CROSSTABS}):
1044 CTABLES /TABLE=AgeGroup BY qns3a.
1046 @psppoutput {ctables2}
1049 The @samp{>} ``nesting'' operator nests multiple variables on a single
1053 CTABLES /TABLE qn105ba BY AgeGroup > qns3a.
1055 @psppoutput {ctables3}
1058 The @samp{+} ``stacking'' operator allows a single output table to
1059 include multiple data analyses. With @samp{+}, @code{CTABLES} divides
1060 the output table into multiple @dfn{sections}, each of which includes
1061 an analysis of the full data set. For example, the following command
1062 separately tabulates age group and driving frequency by gender:
1065 CTABLES /TABLE AgeGroup + qn1 BY qns3a.
1067 @psppoutput {ctables4}
1070 When @samp{+} and @samp{>} are used together, @samp{>} binds more
1071 tightly. Use parentheses to override operator precedence. Thus:
1074 CTABLES /TABLE qn26 + qn27 > qns3a.
1075 CTABLES /TABLE (qn26 + qn27) > qns3a.
1077 @psppoutput {ctables5}
1079 @node CTABLES Scalar Variable Basics
1080 @subsubsection Scalar Variables
1082 For a categorical variable, @code{CTABLES} divides the table into a
1083 cell per category. For a scalar variable, @code{CTABLES} instead
1084 calculates a summary measure, by default the mean, of the values that
1085 fall into a cell. For example, if the only variable specified is a
1086 scalar variable, then the output is a single cell that holds the mean
1090 CTABLES /TABLE qnd1.
1092 @psppoutput {ctables6}
1094 A scalar variable may nest with categorical variables. The following
1095 example shows the mean age of survey respondents across gender and
1099 CTABLES /TABLE qns3a > qnd1 BY region.
1101 @psppoutput {ctables7}
1103 The order of nesting of scalar and categorical variables affects table
1104 labeling, but it does not affect the data displayed in the table. The
1105 following example shows how the output changes when the nesting order
1106 of the scalar and categorical variable are interchanged:
1109 CTABLES /TABLE qnd1 > qns3a BY region.
1111 @psppoutput {ctables8}
1113 Only a single scalar variable may appear in each section; that is, a
1114 scalar variable may not nest inside a scalar variable directly or
1115 indirectly. Scalar variables may only appear on one axis within
1118 @node CTABLES Overriding Measurement Level
1119 @subsubsection Overriding Measurement Level
1121 By default, @code{CTABLES} uses a variable's measurement level to
1122 decide whether to treat it as categorical or scalar. Variables
1123 assigned the nominal or ordinal measurement level are treated as
1124 categorical, and scalar variables are treated as scalar.
1126 When @pspp{} reads data from a file in an external format, such as a
1127 text file, variables' measurement levels are often unknown. If
1128 @code{CTABLES} runs when a variable has an unknown measurement level,
1129 it makes an initial pass through the data to guess measurement levels
1130 using the rules described earlier in this manual (@pxref{Measurement
1131 Level}). Use the @code{VARIABLE LEVEL} command to set or change a
1132 variable's measurement level (@pxref{VARIABLE LEVEL}).
1134 To treat a variable as categorical or scalar only for one use on
1135 @code{CTABLES}, add @samp{[C]} or @samp{[S]}, respectively, after the
1136 variable name. The following example shows the output when variable
1137 @code{qn20} is analyzed as scalar (the default for its measurement
1138 level) and as categorical:
1142 /TABLE qn20 BY qns3a
1143 /TABLE qn20 [C] BY qns3a.
1145 @psppoutput {ctables9}
1148 @node CTABLES Multiple Response Sets
1149 @subsubheading Multiple Response Sets
1151 The @code{CTABLES} command does not yet support multiple response
1155 @node CTABLES Data Summarization
1156 @subsection Data Summarization
1158 @c TODO Summary function default formats
1160 The @code{CTABLES} command allows the user to control how the data are
1161 summarized with @dfn{summary specifications}, syntax that lists one or
1162 more summary function names, optionally separated by commas, and which
1163 are enclosed in square brackets following a variable name on the
1164 @code{TABLE} subcommand. When all the variables are categorical,
1165 summary specifications can be given for the innermost nested variables
1166 on any one axis. When a scalar variable is present, only the scalar
1167 variable may have summary specifications.
1169 The following example includes a summary specification for column and
1170 row percentages for categorical variables, and mean and median for a
1175 /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a
1176 /TABLE=AgeGroup [COLPCT, ROWPCT] BY qns3a.
1178 @psppoutput {ctables10}
1180 A summary specification may override the default label and format by
1181 appending a string or format specification or both (in that order) to
1182 the summary function name. For example:
1185 CTABLES /TABLE=AgeGroup [COLPCT 'Gender %' PCT5.0,
1186 ROWPCT 'Age Group %' PCT5.0]
1189 @psppoutput {ctables11}
1191 Parentheses provide a shorthand to apply summary specifications to
1192 multiple variables. For example, both of these commands:
1195 CTABLES /TABLE=AgeGroup[COLPCT] + qns1[COLPCT] BY qns3a.
1196 CTABLES /TABLE=(AgeGroup + qns1)[COLPCT] BY qns3a.
1200 produce the same output shown below:
1202 @psppoutput {ctables12}
1204 The following sections list the available summary functions.
1207 * CTABLES Summary Functions for Individual Cells::
1208 * CTABLES Summary Functions for Groups of Cells::
1209 * CTABLES Summary Functions for Adjusted Weights::
1210 * CTABLES Unweighted Summary Functions::
1213 @node CTABLES Summary Functions for Individual Cells
1214 @subsubsection Summary Functions for Individual Cells
1216 This section lists the summary functions that consider only an
1217 individual cell in @code{CTABLES}. Only one such summary function,
1218 @code{COUNT}, may be applied to both categorical and scale variables:
1221 @item @code{COUNT} (``Count'')
1222 The sum of weights in a cell.
1224 If @code{CATEGORIES} for one or more of the variables in a table
1225 include missing values (@pxref{CTABLES Per-Variable Category
1226 Options}), then some or all of the categories for a cell might be
1227 missing values. @code{COUNT} counts data included in a cell
1228 regardless of whether its categories are missing.
1231 The following summary functions apply only to scale variables or
1232 totals and subtotals for categorical variables. Be cautious about
1233 interpreting the summary value in the latter case, because it is not
1234 necessarily meaningful; however, the mean of a Likert scale, etc.@:
1235 may have a straightforward interpreation.
1238 @item @code{MAXIMUM} (``Maximum'')
1241 @item @code{MEAN} (``Mean'')
1244 @item @code{MEDIAN} (``Median'')
1247 @item @code{MINIMUM} (``Minimum'')
1250 @item @code{MISSING} (``Missing'')
1251 Sum of weights of user- and system-missing values.
1253 @item @code{MODE} (``Mode'')
1254 The highest-frequency value. Ties are broken by taking the smallest mode.
1256 @item @code{PTILE} @i{n} (``Percentile @i{n}'')
1257 The @var{n}th percentile, where @math{0 @leq{} @var{n} @leq{} 100}.
1259 @item @code{RANGE} (``Range'')
1260 The maximum minus the minimum.
1262 @item @code{SEMEAN} (``Std Error of Mean'')
1263 The standard error of the mean.
1265 @item @code{STDDEV} (``Std Deviation'')
1266 The standard deviation.
1268 @item @code{SUM} (``Sum'')
1271 @item @code{TOTALN} (``Total N'')
1272 The sum of weights in a cell.
1274 For scale data, @code{COUNT} and @code{TOTALN} are the same.
1276 For categorical data, @code{TOTALN} counts missing values in excluded
1277 categories, that is, user-missing values not in an explicit category
1278 list on @code{CATEGORIES} (@pxref{CTABLES Per-Variable Category
1279 Options}), or user-missing values excluded because
1280 @code{MISSING=EXCLUDE} is in effect on @code{CATEGORIES}, or
1281 system-missing values. @code{COUNT} does not count these.
1283 @item @code{VALIDN} (``Valid N'')
1284 The sum of valid count weights in included categories.
1286 @code{VALIDN} does not count missing values regardless of whether they
1287 are in included categories via @code{CATEGORIES}. @code{VALIDN} does
1288 not count valid values that are in excluded categories.
1290 @item @code{VARIANCE} (``Variance'')
1294 @node CTABLES Summary Functions for Groups of Cells
1295 @subsubsection Summary Functions for Groups of Cells
1297 These summary functions summarize over multiple cells within an area
1298 of the output chosen by the user and specified as part of the function
1299 name. The following basic @var{area}s are supported, in decreasing
1304 A @dfn{section}. Stacked variables divide sections of the output from
1305 each other. sections may span multiple layers.
1308 A section within a single layer.
1311 A @dfn{subtable}, whose contents are the cells that pair an innermost
1312 row variable and an innermost column variable within a single layer.
1315 The following shows how the output for the table expression @code{qn61
1316 > qn57 BY qnd7a > qn86 + qn64b BY qns3a}@footnote{This is not
1317 necessarily a meaningful table, so for clarity variable labels are
1318 omitted.} is divided up into @code{TABLE}, @code{LAYER}, and
1319 @code{SUBTABLE} areas. Each unique value for Table ID is one section,
1320 and similarly for Layer ID and Subtable ID. Thus, this output has two
1321 @code{TABLE} areas (one for @code{qnd7a} and one for @code{qn64b}),
1322 four @code{LAYER} areas (for those two variables, per layer), and 12
1323 @code{SUBTABLE} areas.
1324 @psppoutput {ctables22}
1326 @code{CTABLES} also supports the following @var{area}s that further
1327 divide a subtable or a layer within a section:
1332 A row or column, respectively, in one layer of a section.
1336 A row or column, respectively, in a subtable.
1339 The following summary functions for groups of cells are available for
1340 each @var{area} described above, for both categorical and scale
1344 @item @code{@i{area}PCT} or @code{@i{area}PCT.COUNT} (``@i{Area} %'')
1345 A percentage of total counts within @var{area}.
1347 @item @code{@i{area}PCT.VALIDN} (``@i{Area} Valid N %'')
1348 A percentage of total counts for valid values within @var{area}.
1350 @item @code{@i{area}PCT.TOTALN} (``@i{Area} Total N %'')
1351 A percentage of total counts for all values within @var{area}.
1354 Scale variables and totals and subtotals for categorical variables may
1355 use the following additional group cell summary function:
1358 @item @code{@i{area}PCT.SUM} (``@i{Area} Sum %'')
1359 Percentage of the sum of the values within @var{area}.
1362 @node CTABLES Summary Functions for Adjusted Weights
1363 @subsubsection Summary Functions for Adjusted Weights
1365 If the @code{WEIGHT} subcommand specified an adjustment weight
1366 variable, then the following summary functions use its value instead
1367 of the dictionary weight variable. Otherwise, they are equivalent to
1368 the summary function without the @samp{E}-prefix:
1372 @code{ECOUNT} (``Adjusted Count'')
1375 @code{ETOTALN} (``Adjusted Total N'')
1378 @code{EVALIDN} (``Adjusted Valid N'')
1381 @node CTABLES Unweighted Summary Functions
1382 @subsubsection Unweighted Summary Functions
1384 The following summary functions with a @samp{U}-prefix are equivalent
1385 to the same ones without the prefix, except that they use unweighted
1390 @code{UCOUNT} (``Unweighted Count'')
1393 @code{U@i{area}PCT} or @code{U@i{area}PCT.COUNT} (``Unweighted @i{Area} %'')
1396 @code{U@i{area}PCT.VALIDN} (``Unweighted @i{Area} Valid N %'')
1399 @code{U@i{area}PCT.TOTALN} (``Unweighted @i{Area} Total N %'')
1402 @code{UMEAN} (``Unweighted Mean'')
1405 @code{UMEDIAN} (``Unweighted Median'')
1408 @code{UMISSING} (``Unweighted Missing'')
1411 @code{UMODE} (``Unweight Mode'')
1414 @code{U@i{area}PCT.SUM} (``Unweighted @i{Area} Sum %'')
1417 @code{UPTILE} @i{n} (``Unweighted Percentile @i{n}'')
1420 @code{USEMEAN} (``Unweighted Std Error of Mean'')
1423 @code{USTDDEV} (``Unweighted Std Deviation'')
1426 @code{USUM} (``Unweighted Sum'')
1429 @code{UTOTALN} (``Unweighted Total N'')
1432 @code{UVALIDN} (``Unweighted Valid N'')
1435 @code{UVARIANCE} (``Unweighted Variance'')
1438 @node CTABLES Statistics Positions and Labels
1439 @subsection Statistics Positions and Labels
1443 [@t{POSITION=}@{@t{COLUMN} @math{|} @t{ROW} @math{|} @t{LAYER}@}]
1444 [@t{VISIBLE=}@{@t{YES} @math{|} @t{NO}@}]
1447 The @code{SLABELS} subcommand controls the position and visibility of
1448 summary statistics for the @code{TABLE} subcommand that it follows.
1450 @code{POSITION} sets the axis on which summary statistics appear.
1451 With @t{POSITION=COLUMN}, which is the default, each summary statistic
1452 appears in a column. For example:
1455 CTABLES /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a.
1457 @psppoutput {ctables13}
1460 With @t{POSITION=ROW}, each summary statistic appears in a row, as
1464 CTABLES /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a /SLABELS POSITION=ROW.
1466 @psppoutput {ctables14}
1469 @t{POSITION=LAYER} is also available to place each summary statistic in
1472 Labels for summary statistics are shown by default. Use
1473 @t{VISIBLE=NO} to suppress them. Because unlabeled data can cause
1474 confusion, it should only be considered if the meaning of the data is
1475 evident, as in a simple case like this:
1478 CTABLES /TABLE=AgeGroup [TABLEPCT] /SLABELS VISIBLE=NO.
1480 @psppoutput {ctables15}
1482 @node CTABLES Category Label Positions
1483 @subsection Category Label Positions
1486 @t{/CLABELS} @{@t{AUTO} @math{|} @{@t{ROWLABELS}@math{|}@t{COLLABELS}@}@t{=}@{@t{OPPOSITE}@math{|}@t{LAYER}@}@}
1489 The @code{CLABELS} subcommand controls the position of category labels
1490 for the @code{TABLE} subcommand that it follows. By default, or if
1491 @t{AUTO} is specified, category labels for a given variable nest
1492 inside the variable's label on the same axis. For example, the
1493 command below results in age categories nesting within the age group
1494 variable on the rows axis and gender categories within the gender
1495 variable on the columns axis:
1498 CTABLES /TABLE AgeGroup BY qns3a.
1500 @psppoutput {ctables16}
1502 @t{ROWLABELS=OPPOSITE} or @t{COLLABELS=OPPOSITE} move row or column
1503 variable category labels, respectively, to the opposite axis. The
1504 setting affects only the innermost variable on the given axis. For
1508 CTABLES /TABLE AgeGroup BY qns3a /CLABELS ROWLABELS=OPPOSITE.
1509 CTABLES /TABLE AgeGroup BY qns3a /CLABELS COLLABELS=OPPOSITE.
1511 @psppoutput {ctables17}
1513 @t{ROWLABELS=LAYER} or @t{COLLABELS=LAYER} move the innermost row or
1514 column variable category labels, respectively, to the layer axis.
1516 Only one axis's labels may be moved, whether to the opposite axis or
1519 @c TODO Moving category labels for stacked variables
1521 @subsubheading Effect on Summary Statistics
1523 @code{CLABELS} primarily affects the appearance of tables, not the
1524 data displayed in them. However, @code{CTABLES} can affect the values
1525 displayed for statistics that summarize areas of a table, since it can
1526 change the definitions of these areas.
1528 For example, consider the following syntax and output:
1531 CTABLES /TABLE AgeGroup BY qns3a [ROWPCT, COLPCT].
1533 @psppoutput {ctables23}
1536 Using @code{COLLABELS=OPPOSITE} changes the definitions of rows and
1537 columns, so that column percentages display what were previously row
1538 percentages and the new row percentages become meaningless (because
1539 there is only one cell per row):
1543 /TABLE AgeGroup BY qns3a [ROWPCT, COLPCT]
1544 /CLABELS COLLABELS=OPPOSITE.
1546 @psppoutput {ctables24}
1548 @node CTABLES Per-Variable Category Options
1549 @subsection Per-Variable Category Options
1552 @t{/CATEGORIES} @t{VARIABLES=}@i{variables}
1553 @{@t{[}@i{value}@t{,} @i{value}@dots{}@t{]}
1554 @math{|} [@t{ORDER=}@{@t{A} @math{|} @t{D}@}]
1555 [@t{KEY=}@{@t{VALUE} @math{|} @t{LABEL} @math{|} @i{summary}@t{(}@i{variable}@t{)}@}]
1556 [@t{MISSING=}@{@t{EXCLUDE} @math{|} @t{INCLUDE}@}]@}
1557 [@t{TOTAL=}@{@t{NO} @math{|} @t{YES}@} [@t{LABEL=}@i{string}] [@t{POSITION=}@{@t{AFTER} @math{|} @t{BEFORE}@}]]
1558 [@t{EMPTY=}@{@t{INCLUDE} @math{|} @t{EXCLUDE}@}]
1561 The @code{CATEGORIES} subcommand specifies, for one or more
1562 categorical variables, the categories to include and exclude, the sort
1563 order for included categories, and treatment of missing values. It
1564 also controls the totals and subtotals to display. It may be
1565 specified any number of times, each time for a different set of
1566 variables. @code{CATEGORIES} applies to the table produced by the
1567 @code{TABLE} subcommand that it follows.
1569 @code{CATEGORIES} does not apply to scalar variables.
1571 @t{VARIABLES} is required and must list the variables for the subcommand
1574 There are two way to specify the Categories to include and their sort
1578 @item Explicit categories.
1579 @anchor{CTABLES Explicit Category List}
1580 To explicitly specify categories to include, list the categories
1581 within square brackets in the desired sort order. Use spaces or
1582 commas to separate values. Categories not covered by the list are
1583 excluded from analysis.
1585 Each element of the list takes one of the following forms:
1590 A numeric or string category value, for variables that have the
1595 A date or time category value, for variables that have a date or time
1598 @item @i{min} THRU @i{max}
1599 @itemx LO THRU @i{max}
1600 @itemx @i{min} THRU HI
1601 A range of category values, where @var{min} and @var{max} each takes
1602 one of the forms above, in increasing order.
1605 All user-missing values. (To match individual user-missing values,
1606 specify their category values.)
1609 Any non-missing value not covered by any other element of the list
1610 (regardless of where @t{OTHERNM} is placed in the list).
1612 @item &@i{postcompute}
1613 A computed category name (@pxref{CTABLES Computed Categories}).
1616 Additional forms, described later, allow for subtotals.
1617 If multiple elements of the list cover a given category, the last one
1618 in the list takes precedence.
1620 @item Implicit categories.
1621 Without an explicit list of categories, @pspp{} sorts
1622 categories automatically.
1624 The @code{KEY} setting specifies the sort key. By default, or with
1625 @code{KEY=VALUE}, categories are sorted by default. Categories may
1626 also be sorted by value label, with @code{KEY=LABEL}, or by the value
1627 of a summary function, e.g.@: @code{KEY=COUNT}.
1628 @ignore @c Not yet implemented
1629 For summary functions, a variable name may be specified in
1630 parentheses, e.g.@: @code{KEY=MAXIUM(qnd1)}, and this is required for
1631 functions that apply only to scalar variables. The @code{PTILE}
1632 function also requires a percentage argument, e.g.@:
1633 @code{KEY=PTILE(qnd1, 90)}. Only summary functions used in the table
1634 may be used, except that @code{COUNT} is always allowed.
1637 By default, or with @code{ORDER=A}, categories are sorted in ascending
1638 order. Specify @code{ORDER=D} to sort in descending order.
1640 User-missing values are excluded by default, or with
1641 @code{MISSING=EXCLUDE}. Specify @code{MISSING=INCLUDE} to include
1642 user-missing values. The system-missing value is always excluded.
1645 @subsubheading Totals and Subtotals
1647 @code{CATEGORIES} also controls display of totals and subtotals.
1648 Totals are not displayed with @code{TOTAL=NO}, which is also the
1649 default. Specify @code{TOTAL=YES} to display a total. By default,
1650 the total is labeled ``Total''; use @code{LABEL="@i{label}"} to
1653 Subtotals are also not displayed by default. To add one or more
1654 subtotals, use an explicit category list and insert @code{SUBTOTAL} or
1655 @code{HSUBTOTAL} in the position or positions where the subtotal
1656 should appear. With @code{SUBTOTAL}, the subtotal becomes an extra
1657 row or column or layer; @code{HSUBTOTAL} additionally hides the
1658 categories that make up the subtotal. Either way, the default label
1659 is ``Subtotal'', use @code{SUBTOTAL="@i{label}"} or
1660 @code{HSUBTOTAL="@i{label}"} to specify a custom label.
1662 By default, or with @code{POSITION=AFTER}, totals are displayed in the
1663 output after the last category and subtotals apply to categories that
1664 precede them. With @code{POSITION=BEFORE}, totals come before the
1665 first category and subtotals apply to categories that follow them.
1667 Only categorical variables may have totals and subtotals. Scalar
1668 variables may be ``totaled'' indirectly by enabling totals and
1669 subtotals on a categorical variable within which the scalar variable is
1672 @c TODO Specifying summaries for totals and subtotals
1674 @subsubheading Categories Without Values
1676 Some categories might not be included in the data set being analyzed.
1677 For example, our example data set has no cases in the ``15 or
1678 younger'' age group. By default, or with @code{EMPTY=INCLUDE},
1679 @pspp{} includes these empty categories in output tables. To exclude
1680 them, specify @code{EMPTY=EXCLUDE}.
1682 For implicit categories, empty categories potentially include all the
1683 values with value labels for a given variable; for explicit
1684 categories, they include all the values listed individually and all
1685 values with value labels that are covered by ranges or @code{MISSING}
1688 @node CTABLES Titles
1693 [@t{TITLE=}@i{string}@dots{}]
1694 [@t{CAPTION=}@i{string}@dots{}]
1695 [@t{CORNER=}@i{string}@dots{}]
1698 @c TODO Describe substitution variables
1700 The @code{TITLES} subcommand sets the title, caption, and corner text
1701 for the table output for the previous @code{TABLE} subcommand. The
1702 title appears above the table, the caption below the table, and the
1703 corner text appears in the table's upper left corner. By default, the
1704 title is ``Custom Tables'' and the caption and corner text are empty.
1705 With some table output styles, the corner text is not displayed.
1707 @node CTABLES Table Formatting
1708 @subsection Table Formatting
1712 [@t{MINCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
1713 [@t{MAXCOLWIDTH=}@{@t{DEFAULT} @math{|} @i{width}@}]
1714 [@t{UNITS=}@{@t{POINTS} @math{|} @t{INCHES} @math{|} @t{CM}@}]
1715 [@t{EMPTY=}@{@t{ZERO} @math{|} @t{BLANK} @math{|} @i{string}@}]
1716 [@t{MISSING=}@i{string}]
1719 The @code{FORMAT} subcommand, which must precede the first
1720 @code{TABLE} subcommand, controls formatting for all the output
1721 tables. @code{FORMAT} and all of its settings are optional.
1723 Use @code{MINCOLWIDTH} and @code{MAXCOLWIDTH} to control the minimum
1724 or maximum width of columns in output tables. By default, with
1725 @code{DEFAULT}, column width varies based on content. Otherwise,
1726 specify a number for either or both of these settings. If both are
1727 specified, @code{MAXCOLWIDTH} must be greater than or equal to
1728 @code{MINCOLWIDTH}. The default unit, or with @code{UNITS=POINTS}, is
1729 points (1/72 inch), or specify @code{UNITS=INCHES} to use inches or
1730 @code{UNITS=CM} for centimeters.
1732 By default, or with @code{EMPTY=ZERO}, zero values are displayed in
1733 their usual format. Use @code{EMPTY=BLANK} to use an empty cell
1734 instead, or @code{EMPTY="@i{string}"} to use the specified string.
1736 By default, missing values are displayed as @samp{.}, the same as in
1737 other tables. Specify @code{MISSING="@i{string}"} to instead use a
1740 @node CTABLES Display of Variable Labels
1741 @subsection Display of Variable Labels
1745 @t{VARIABLES=}@i{variables}
1746 @t{DISPLAY}=@{@t{DEFAULT} @math{|} @t{NAME} @math{|} @t{LABEL} @math{|} @t{BOTH} @math{|} @t{NONE}@}
1749 The @code{VLABELS} subcommand, which must precede the first
1750 @code{TABLE} subcommand, controls display of variable labels in all
1751 the output tables. @code{VLABELS} is optional. It may appear
1752 multiple times to adjust settings for different variables.
1754 @code{VARIABLES} and @code{DISPLAY} are required. The value of
1755 @code{DISPLAY} controls how variable labels are displayed for the
1756 variables listed on @code{VARIABLES}. The supported values are:
1760 Use the setting from @code{SET TVARS} (@pxref{SET TVARS}).
1763 Show only a variable name.
1766 Show only a variable label.
1769 Show variable name and label.
1775 @node CTABLES Missing Value Treatment
1776 @subsection Missing Value Treatment
1779 @t{/SMISSING} @{@t{VARIABLE} @math{|} @t{LISTWISE}@}
1782 The @code{SMISSING} subcommand, which must precede the first
1783 @code{TABLE} subcommand, controls treatment of missing values for
1784 scalar variables in producing all the output tables. @code{SMISSING}
1787 With @code{SMISSING=VARIABLE}, which is the default, missing values
1788 are excluded on a variable-by-variable basis. With
1789 @code{SMISSING=LISTWISE}, when stacked scalar variables are nested
1790 together with a categorical variable, a missing value for any of the
1791 scalar variables causes the case to be excluded for all of them.
1793 As an example, consider the following dataset, in which @samp{x} is a
1794 categorical variable and @samp{y} and @samp{z} are scale:
1796 @psppoutput{ctables18}
1799 With the default missing-value treatment, @samp{x}'s mean is 20, based
1800 on the values 10, 20, and 30, and @samp{y}'s mean is 50, based on 40,
1804 CTABLES /TABLE (y + z) > x.
1806 @psppoutput{ctables19}
1809 By adding @code{SMISSING=LISTWISE}, only cases where @samp{y} and
1810 @samp{z} are both non-missing are considered, so @samp{x}'s mean
1811 becomes 15, as the average of 10 and 20, and @samp{y}'s mean becomes
1812 55, the average of 50 and 60:
1815 CTABLES /SMISSING LISTWISE /TABLE (y + z) > x.
1817 @psppoutput{ctables20}
1820 Even with @code{SMISSING=LISTWISE}, if @samp{y} and @samp{z} are
1821 separately nested with @samp{x}, instead of using a single @samp{>}
1822 operator, missing values revert to being considered on a
1823 variable-by-variable basis:
1826 CTABLES /SMISSING LISTWISE /TABLE (y > x) + (z > x).
1828 @psppoutput{ctables21}
1830 @node CTABLES Computed Categories
1831 @subsection Computed Categories
1834 @t{/PCOMPUTE} @t{&}@i{postcompute}@t{=EXPR(}@i{expression}@t{)}
1837 @dfn{Computed categories}, also called @dfn{postcomputes}, are
1838 categories created using arithmetic on categories obtained from the
1839 data. The @code{PCOMPUTE} subcommand defines computed categories,
1840 which can then be used in two places: on @code{CATEGORIES} within an
1841 explicit category list (@pxref{CTABLES Explicit Category List}), and on
1842 the @code{PPROPERTIES} subcommand to define further properties for a
1845 @code{PCOMPUTE} must precede the first @code{TABLE} command. It is
1846 optional and it may be used any number of times to define multiple
1849 Each @code{PCOMPUTE} defines one postcompute. Its syntax consists of
1850 a name to identify the postcompute as a @pspp{} identifier prefixed by
1851 @samp{&}, followed by @samp{=} and a postcompute expression enclosed
1852 in @code{EXPR(@dots{})}. A postcompute expression consists of:
1855 @item [@i{category}]
1856 This form evaluates to the summary statistic for @i{category}, e.g.@:
1857 @code{[1]} evaluates to the value of the summary statistic associated
1858 with category 1. The @i{category} may be a number, a quoted string,
1859 or a quoted time or date value. All of the categories for a given
1860 postcompute must have the same form. The category must appear in all
1861 the @code{CATEGORIES} list in which the postcompute is used.
1863 @item [@i{min} THRU @i{max}]
1864 @itemx [LO THRU @i{max}]
1865 @itemx [@i{min} THRU HI]
1868 These forms evaluate to the summary statistics for a category
1869 specified with the same syntax, as described in previous section
1870 (@pxref{CTABLES Explicit Category List}). The category must appear in
1871 all the @code{CATEGORIES} list in which the postcompute is used.
1874 The summary statistic for the subtotal category. This form is allowed
1875 only if the @code{CATEGORIES} lists that include this postcompute have
1876 exactly one subtotal.
1878 @item SUBTOTAL[@i{index}]
1879 The summary statistic for subtotal category @i{index}, where 1 is the
1880 first subtotal, 2 is the second, and so on. This form may be used for
1881 @code{CATEGORIES} lists with any number of subtotals.
1884 The summary statistic for the total. The @code{CATEGORIES} lsits that
1885 include this postcompute must have a total enabled.
1888 @itemx @i{a} - @i{b}
1889 @itemx @i{a} * @i{b}
1890 @itemx @i{a} / @i{b}
1891 @itemx @i{a} ** @i{b}
1892 These forms perform arithmetic on the values of postcompute
1893 expressions @i{a} and @i{b}. The usual operator precedence rules
1897 Numeric constants may be used in postcompute expressions.
1900 Parentheses override operator precedence.
1903 A postcompute is not associated with any particular variable.
1904 Instead, it may be referenced within @code{CATEGORIES} for any
1905 suitable variable (e.g.@: only a string variable is suitable for a
1906 postcompute expression that refers to a string category, only a
1907 variable with subtotals for an expression that refers to subtotals,
1910 Normally a named postcompute is defined only once, but if a later
1911 @code{PCOMPUTE} redefines a postcompute with the same name as an
1912 earlier one, the later one take precedence.
1914 @node CTABLES Computed Category Properties
1915 @subsection Computed Category Properties
1918 @t{/PPROPERTIES} @t{&}@i{postcompute}@dots{}
1919 [@t{LABEL=}@i{string}]
1920 [@t{FORMAT=}[@i{summary} @i{format}]@dots{}]
1921 [@t{HIDESOURCECATS=}@{@t{NO} @math{|} @t{YES}@}
1924 The @code{PPROPERTIES} subcommand, which must appear before
1925 @code{TABLE}, sets properties for one or more postcomputes defined on
1926 prior @code{PCOMPUTE} subcommands. The subcommand syntax begins with
1927 the list of postcomputes, each prefixed with @samp{&} as specified on
1930 All of the settings on @code{PPROPERTIES} are optional. Use
1931 @code{LABEL} to set the label shown for the postcomputes in table
1932 output. The default label for a postcompute is the expression used to
1935 The @code{FORMAT} setting sets summary statistics and display formats
1936 for the postcomputes.
1938 By default, or with @code{HIDESOURCECATS=NO}, categories referred to
1939 by computed categories are displayed like other categories. Use
1940 @code{HIDESOURCECATS=YES} to hide them.
1942 @node CTABLES Base Weight
1943 @subsection Base Weight
1946 @t{/WEIGHT VARIABLE=}@i{variable}
1949 The @code{WEIGHT} subcommand is optional and must appear before
1950 @code{TABLE}. If it appears, it must name a numeric variable, known
1951 as the @dfn{effective base weight} or @dfn{adjustment weight}. The
1952 effective base weight variable stands in for the dictionary's weight
1953 variable (@pxref{WEIGHT}), if any, in most calculations in
1954 @code{CTABLES}. The only exceptions are the @code{COUNT},
1955 @code{TOTALN}, and @code{VALIDN} summary functions, which use the
1956 dictionary weight instead.
1958 Weights obtained from the @pspp{} dictionary are rounded to the
1959 nearest integer at the case level. Effective base weights are not
1960 rounded. Regardless of the weighting source, @pspp{} does not analyze
1961 cases with zero, missing, or negative effective weights.
1963 @node CTABLES Hiding Small Counts
1964 @subsection Hiding Small Counts
1967 @t{/HIDESMALLCOUNTS COUNT=@i{count}}
1970 The @code{HIDESMALLCOUNTS} subcommand is optional. If it specified,
1971 then count values in output tables less than the value of @i{count}
1972 are shown as @code{<@i{count}} instead of their true values. The
1973 value of @i{count} must be an integer and must be at least 2. Case
1974 weights are considered for deciding whether to hide a count.
1980 @cindex factor analysis
1981 @cindex principal components analysis
1982 @cindex principal axis factoring
1983 @cindex data reduction
1987 VARIABLES=@var{var_list},
1988 MATRIX IN (@{CORR,COV@}=@{*,@var{file_spec}@})
1991 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
1993 [ /ANALYSIS=@var{var_list} ]
1995 [ /EXTRACTION=@{PC, PAF@}]
1997 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
1999 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [AIC] [SIG] [ALL] [DEFAULT] ]
2003 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
2005 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
2007 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
2010 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
2011 common factors in the data or for data reduction purposes.
2013 The @subcmd{VARIABLES} subcommand is required (unless the @subcmd{MATRIX IN}
2014 subcommand is used).
2015 It lists the variables which are to partake in the analysis. (The @subcmd{ANALYSIS}
2016 subcommand may optionally further limit the variables that
2017 participate; it is useful primarily in conjunction with @subcmd{MATRIX IN}.)
2019 If @subcmd{MATRIX IN} instead of @subcmd{VARIABLES} is specified, then the analysis
2020 is performed on a pre-prepared correlation or covariance matrix file instead of on
2021 individual data cases. Typically the matrix file will have been generated by
2022 @cmd{MATRIX DATA} (@pxref{MATRIX DATA}) or provided by a third party.
2023 If specified, @subcmd{MATRIX IN} must be followed by @samp{COV} or @samp{CORR},
2024 then by @samp{=} and @var{file_spec} all in parentheses.
2025 @var{file_spec} may either be an asterisk, which indicates the currently loaded
2026 dataset, or it may be a file name to be loaded. @xref{MATRIX DATA}, for the expected
2029 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors
2030 (components) are extracted from the data.
2031 If @subcmd{PC} is specified, then Principal Components Analysis is used.
2032 If @subcmd{PAF} is specified, then Principal Axis Factoring is
2033 used. By default Principal Components Analysis is used.
2035 The @subcmd{/ROTATION} subcommand is used to specify the method by which the
2036 extracted solution is rotated. Three orthogonal rotation methods are available:
2037 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
2038 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
2039 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
2040 The default value of @var{k} is 5.
2041 If you don't want any rotation to be performed, the word @subcmd{NOROTATE}
2042 prevents the command from performing any rotation on the data.
2044 The @subcmd{/METHOD} subcommand should be used to determine whether the
2045 covariance matrix or the correlation matrix of the data is
2046 to be analysed. By default, the correlation matrix is analysed.
2048 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
2051 @item @subcmd{UNIVARIATE}
2052 A table of mean values, standard deviations and total weights are printed.
2053 @item @subcmd{INITIAL}
2054 Initial communalities and eigenvalues are printed.
2055 @item @subcmd{EXTRACTION}
2056 Extracted communalities and eigenvalues are printed.
2057 @item @subcmd{ROTATION}
2058 Rotated communalities and eigenvalues are printed.
2059 @item @subcmd{CORRELATION}
2060 The correlation matrix is printed.
2061 @item @subcmd{COVARIANCE}
2062 The covariance matrix is printed.
2064 The determinant of the correlation or covariance matrix is printed.
2066 The anti-image covariance and anti-image correlation matrices are printed.
2068 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
2070 The significance of the elements of correlation matrix is printed.
2072 All of the above are printed.
2073 @item @subcmd{DEFAULT}
2074 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
2077 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues is
2078 printed. This can be useful for visualizing the factors and deciding
2079 which factors (components) should be retained.
2081 The @subcmd{/FORMAT} subcommand determined how data are to be
2082 displayed in loading matrices. If @subcmd{SORT} is specified, then
2083 the variables are sorted in descending order of significance. If
2084 @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute
2085 value is less than @var{n} are not printed. If the keyword
2086 @subcmd{DEFAULT} is specified, or if no @subcmd{/FORMAT} subcommand is
2087 specified, then no sorting is performed, and all coefficients are printed.
2089 You can use the @subcmd{/CRITERIA} subcommand to specify how the number of
2090 extracted factors (components) are chosen. If @subcmd{FACTORS(@var{n})} is
2091 specified, where @var{n} is an integer, then @var{n} factors are
2092 extracted. Otherwise, the @subcmd{MINEIGEN} setting is used.
2093 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues
2094 are greater than or equal to @var{l} are extracted. The default value
2095 of @var{l} is 1. The @subcmd{ECONVERGE} setting has effect only when
2096 using iterative algorithms for factor extraction (such as Principal Axis
2097 Factoring). @subcmd{ECONVERGE(@var{delta})} specifies that
2098 iteration should cease when the maximum absolute value of the
2099 communality estimate between one iteration and the previous is less
2100 than @var{delta}. The default value of @var{delta} is 0.001.
2102 The @subcmd{ITERATE(@var{m})} may appear any number of times and is
2103 used for two different purposes. It is used to set the maximum number
2104 of iterations (@var{m}) for convergence and also to set the maximum
2105 number of iterations for rotation.
2106 Whether it affects convergence or rotation depends upon which
2107 subcommand follows the @subcmd{ITERATE} subcommand.
2108 If @subcmd{EXTRACTION} follows, it affects convergence.
2109 If @subcmd{ROTATION} follows, it affects rotation.
2110 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a
2111 @subcmd{ITERATE} subcommand, then the entire subcommand is ignored.
2112 The default value of @var{m} is 25.
2114 The @cmd{MISSING} subcommand determines the handling of missing
2115 variables. If @subcmd{INCLUDE} is set, then user-missing values are
2116 included in the calculations, but system-missing values are not.
2117 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2118 values are excluded as well as system-missing values. This is the
2119 default. If @subcmd{LISTWISE} is set, then the entire case is excluded
2120 from analysis whenever any variable specified in the @cmd{VARIABLES}
2121 subcommand contains a missing value.
2123 If @subcmd{PAIRWISE} is set, then a case is considered missing only if
2124 either of the values for the particular coefficient are missing.
2125 The default is @subcmd{LISTWISE}.
2131 @cindex univariate analysis of variance
2132 @cindex fixed effects
2133 @cindex factorial anova
2134 @cindex analysis of variance
2139 GLM @var{dependent_vars} BY @var{fixed_factors}
2140 [/METHOD = SSTYPE(@var{type})]
2141 [/DESIGN = @var{interaction_0} [@var{interaction_1} [... @var{interaction_n}]]]
2142 [/INTERCEPT = @{INCLUDE|EXCLUDE@}]
2143 [/MISSING = @{INCLUDE|EXCLUDE@}]
2146 The @cmd{GLM} procedure can be used for fixed effects factorial Anova.
2148 The @var{dependent_vars} are the variables to be analysed.
2149 You may analyse several variables in the same command in which case they should all
2150 appear before the @code{BY} keyword.
2152 The @var{fixed_factors} list must be one or more categorical variables. Normally it
2153 does not make sense to enter a scalar variable in the @var{fixed_factors} and doing
2154 so may cause @pspp{} to do a lot of unnecessary processing.
2156 The @subcmd{METHOD} subcommand is used to change the method for producing the sums of
2157 squares. Available values of @var{type} are 1, 2 and 3. The default is type 3.
2159 You may specify a custom design using the @subcmd{DESIGN} subcommand.
2160 The design comprises a list of interactions where each interaction is a
2161 list of variables separated by a @samp{*}. For example the command
2163 GLM subject BY sex age_group race
2164 /DESIGN = age_group sex group age_group*sex age_group*race
2166 @noindent specifies the model @math{subject = age_group + sex + race + age_group*sex + age_group*race}.
2167 If no @subcmd{DESIGN} subcommand is specified, then the default is all possible combinations
2168 of the fixed factors. That is to say
2170 GLM subject BY sex age_group race
2173 @math{subject = age_group + sex + race + age_group*sex + age_group*race + sex*race + age_group*sex*race}.
2176 The @subcmd{MISSING} subcommand determines the handling of missing
2178 If @subcmd{INCLUDE} is set then, for the purposes of GLM analysis,
2179 only system-missing values are considered
2180 to be missing; user-missing values are not regarded as missing.
2181 If @subcmd{EXCLUDE} is set, which is the default, then user-missing
2182 values are considered to be missing as well as system-missing values.
2183 A case for which any dependent variable or any factor
2184 variable has a missing value is excluded from the analysis.
2186 @node LOGISTIC REGRESSION
2187 @section LOGISTIC REGRESSION
2189 @vindex LOGISTIC REGRESSION
2190 @cindex logistic regression
2191 @cindex bivariate logistic regression
2194 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
2196 [/CATEGORICAL = @var{categorical_predictors}]
2198 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
2200 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
2202 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
2203 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
2204 [CUT(@var{cut_point})]]
2206 [/MISSING = @{INCLUDE|EXCLUDE@}]
2209 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
2210 variable in terms of one or more predictor variables.
2212 The minimum command is
2214 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
2216 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
2217 are the predictor variables whose coefficients the procedure estimates.
2219 By default, a constant term is included in the model.
2220 Hence, the full model is
2223 = b_0 + b_1 {\bf x_1}
2229 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
2230 Simple variables as well as interactions between variables may be listed here.
2232 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
2233 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
2235 An iterative Newton-Raphson procedure is used to fit the model.
2236 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
2237 and other parameters.
2238 The value of @var{cut_point} is used in the classification table. It is the
2239 threshold above which predicted values are considered to be 1. Values
2240 of @var{cut_point} must lie in the range [0,1].
2241 During iterations, if any one of the stopping criteria are satisfied, the procedure is
2242 considered complete.
2243 The stopping criteria are:
2245 @item The number of iterations exceeds @var{max_iterations}.
2246 The default value of @var{max_iterations} is 20.
2247 @item The change in the all coefficient estimates are less than @var{min_delta}.
2248 The default value of @var{min_delta} is 0.001.
2249 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
2250 The default value of @var{min_delta} is zero.
2251 This means that this criterion is disabled.
2252 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
2253 In other words, the probabilities are close to zero or one.
2254 The default value of @var{min_epsilon} is 0.00000001.
2258 The @subcmd{PRINT} subcommand controls the display of optional statistics.
2259 Currently there is one such option, @subcmd{CI}, which indicates that the
2260 confidence interval of the odds ratio should be displayed as well as its value.
2261 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
2262 confidence level of the desired confidence interval.
2264 The @subcmd{MISSING} subcommand determines the handling of missing
2266 If @subcmd{INCLUDE} is set, then user-missing values are included in the
2267 calculations, but system-missing values are not.
2268 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2269 values are excluded as well as system-missing values.
2270 This is the default.
2281 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
2283 [ /@{@var{var_list}@}
2284 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
2286 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
2287 [VARIANCE] [KURT] [SEKURT]
2288 [SKEW] [SESKEW] [FIRST] [LAST]
2289 [HARMONIC] [GEOMETRIC]
2294 [/MISSING = [INCLUDE] [DEPENDENT]]
2297 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
2298 statistics, either for the dataset as a whole or for categories of data.
2300 The simplest form of the command is
2304 @noindent which calculates the mean, count and standard deviation for @var{v}.
2305 If you specify a grouping variable, for example
2307 MEANS @var{v} BY @var{g}.
2309 @noindent then the means, counts and standard deviations for @var{v} after having
2310 been grouped by @var{g} are calculated.
2311 Instead of the mean, count and standard deviation, you could specify the statistics
2312 in which you are interested:
2314 MEANS @var{x} @var{y} BY @var{g}
2315 /CELLS = HARMONIC SUM MIN.
2317 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
2320 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
2324 @cindex arithmetic mean
2325 The arithmetic mean.
2326 @item @subcmd{COUNT}
2327 The count of the values.
2328 @item @subcmd{STDDEV}
2329 The standard deviation.
2330 @item @subcmd{SEMEAN}
2331 The standard error of the mean.
2333 The sum of the values.
2338 @item @subcmd{RANGE}
2339 The difference between the maximum and minimum values.
2340 @item @subcmd{VARIANCE}
2342 @item @subcmd{FIRST}
2343 The first value in the category.
2345 The last value in the category.
2348 @item @subcmd{SESKEW}
2349 The standard error of the skewness.
2352 @item @subcmd{SEKURT}
2353 The standard error of the kurtosis.
2354 @item @subcmd{HARMONIC}
2355 @cindex harmonic mean
2357 @item @subcmd{GEOMETRIC}
2358 @cindex geometric mean
2362 In addition, three special keywords are recognized:
2364 @item @subcmd{DEFAULT}
2365 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
2367 All of the above statistics are calculated.
2369 No statistics are calculated (only a summary is shown).
2373 More than one @dfn{table} can be specified in a single command.
2374 Each table is separated by a @samp{/}. For
2378 @var{c} @var{d} @var{e} BY @var{x}
2379 /@var{a} @var{b} BY @var{x} @var{y}
2380 /@var{f} BY @var{y} BY @var{z}.
2382 has three tables (the @samp{TABLE =} is optional).
2383 The first table has three dependent variables @var{c}, @var{d} and @var{e}
2384 and a single categorical variable @var{x}.
2385 The second table has two dependent variables @var{a} and @var{b},
2386 and two categorical variables @var{x} and @var{y}.
2387 The third table has a single dependent variables @var{f}
2388 and a categorical variable formed by the combination of @var{y} and @var{z}.
2391 By default values are omitted from the analysis only if missing values
2392 (either system missing or user missing)
2393 for any of the variables directly involved in their calculation are
2395 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
2396 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
2398 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
2399 variables or in the categorical variables should be taken at their face
2400 value, and not excluded.
2402 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
2403 variables should be taken at their face value, however cases which
2404 have user missing values for the categorical variables should be omitted
2405 from the calculation.
2407 @subsection Example Means
2409 The dataset in @file{repairs.sav} contains the mean time between failures (@exvar{mtbf})
2410 for a sample of artifacts produced by different factories and trialed under
2411 different operating conditions.
2412 Since there are four combinations of categorical variables, by simply looking
2413 at the list of data, it would be hard to how the scores vary for each category.
2414 @ref{means:ex} shows one way of tabulating the @exvar{mtbf} in a way which is
2415 easier to understand.
2417 @float Example, means:ex
2418 @psppsyntax {means.sps}
2419 @caption {Running @cmd{MEANS} on the @exvar{mtbf} score with categories @exvar{factory} and @exvar{environment}}
2422 The results are shown in @ref{means:res}. The figures shown indicate the mean,
2423 standard deviation and number of samples in each category.
2424 These figures however do not indicate whether the results are statistically
2425 significant. For that, you would need to use the procedures @cmd{ONEWAY}, @cmd{GLM} or
2426 @cmd{T-TEST} depending on the hypothesis being tested.
2428 @float Result, means:res
2430 @caption {The @exvar{mtbf} categorised by @exvar{factory} and @exvar{environment}}
2433 Note that there is no limit to the number of variables for which you can calculate
2434 statistics, nor to the number of categorical variables per layer, nor the number
2436 However, running @cmd{MEANS} on a large numbers of variables, or with categorical variables
2437 containing a large number of distinct values may result in an extremely large output, which
2438 will not be easy to interpret.
2439 So you should consider carefully which variables to select for participation in the analysis.
2445 @cindex nonparametric tests
2450 nonparametric test subcommands
2455 [ /STATISTICS=@{DESCRIPTIVES@} ]
2457 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
2459 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
2462 @cmd{NPAR TESTS} performs nonparametric tests.
2463 Non parametric tests make very few assumptions about the distribution of the
2465 One or more tests may be specified by using the corresponding subcommand.
2466 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
2467 produces for each variable that is the subject of any test.
2469 Certain tests may take a long time to execute, if an exact figure is required.
2470 Therefore, by default asymptotic approximations are used unless the
2471 subcommand @subcmd{/METHOD=EXACT} is specified.
2472 Exact tests give more accurate results, but may take an unacceptably long
2473 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
2474 after which the test is abandoned, and a warning message printed.
2475 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
2476 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
2481 * BINOMIAL:: Binomial Test
2482 * CHISQUARE:: Chi-square Test
2483 * COCHRAN:: Cochran Q Test
2484 * FRIEDMAN:: Friedman Test
2485 * KENDALL:: Kendall's W Test
2486 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
2487 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
2488 * MANN-WHITNEY:: Mann Whitney U Test
2489 * MCNEMAR:: McNemar Test
2490 * MEDIAN:: Median Test
2492 * SIGN:: The Sign Test
2493 * WILCOXON:: Wilcoxon Signed Ranks Test
2498 @subsection Binomial test
2500 @cindex binomial test
2503 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
2506 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
2507 variable with that of a binomial distribution.
2508 The variable @var{p} specifies the test proportion of the binomial
2510 The default value of 0.5 is assumed if @var{p} is omitted.
2512 If a single value appears after the variable list, then that value is
2513 used as the threshold to partition the observed values. Values less
2514 than or equal to the threshold value form the first category. Values
2515 greater than the threshold form the second category.
2517 If two values appear after the variable list, then they are used
2518 as the values which a variable must take to be in the respective
2520 Cases for which a variable takes a value equal to neither of the specified
2521 values, take no part in the test for that variable.
2523 If no values appear, then the variable must assume dichotomous
2525 If more than two distinct, non-missing values for a variable
2526 under test are encountered then an error occurs.
2528 If the test proportion is equal to 0.5, then a two tailed test is
2529 reported. For any other test proportion, a one tailed test is
2531 For one tailed tests, if the test proportion is less than
2532 or equal to the observed proportion, then the significance of
2533 observing the observed proportion or more is reported.
2534 If the test proportion is more than the observed proportion, then the
2535 significance of observing the observed proportion or less is reported.
2536 That is to say, the test is always performed in the observed
2539 @pspp{} uses a very precise approximation to the gamma function to
2540 compute the binomial significance. Thus, exact results are reported
2541 even for very large sample sizes.
2545 @subsection Chi-square Test
2547 @cindex chi-square test
2551 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
2555 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
2556 between the expected and observed frequencies of the categories of a variable.
2557 Optionally, a range of values may appear after the variable list.
2558 If a range is given, then non integer values are truncated, and values
2559 outside the specified range are excluded from the analysis.
2561 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
2563 There must be exactly one non-zero expected value, for each observed
2564 category, or the @subcmd{EQUAL} keyword must be specified.
2565 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
2566 consecutive expected categories all taking a frequency of @var{f}.
2567 The frequencies given are proportions, not absolute frequencies. The
2568 sum of the frequencies need not be 1.
2569 If no @subcmd{/EXPECTED} subcommand is given, then equal frequencies
2572 @subsubsection Chi-square Example
2574 A researcher wishes to investigate whether there are an equal number of
2575 persons of each sex in a population. The sample chosen for invesigation
2576 is that from the @file {physiology.sav} dataset. The null hypothesis for
2577 the test is that the population comprises an equal number of males and females.
2578 The analysis is performed as shown in @ref{chisquare:ex}.
2580 @float Example, chisquare:ex
2581 @psppsyntax {chisquare.sps}
2582 @caption {Performing a chi-square test to check for equal distribution of sexes}
2585 There is only one test variable, @i{viz:} @exvar{sex}. The other variables in the dataset
2588 @float Screenshot, chisquare:scr
2589 @psppimage {chisquare}
2590 @caption {Performing a chi-square test using the graphic user interface}
2593 In @ref{chisquare:res} the summary box shows that in the sample, there are more males
2594 than females. However the significance of chi-square result is greater than 0.05
2595 --- the most commonly accepted p-value --- and therefore
2596 there is not enough evidence to reject the null hypothesis and one must conclude
2597 that the evidence does not indicate that there is an imbalance of the sexes
2600 @float Result, chisquare:res
2601 @psppoutput {chisquare}
2602 @caption {The results of running a chi-square test on @exvar{sex}}
2607 @subsection Cochran Q Test
2609 @cindex Cochran Q test
2610 @cindex Q, Cochran Q
2613 [ /COCHRAN = @var{var_list} ]
2616 The Cochran Q test is used to test for differences between three or more groups.
2617 The data for @var{var_list} in all cases must assume exactly two
2618 distinct values (other than missing values).
2620 The value of Q is displayed along with its Asymptotic significance
2621 based on a chi-square distribution.
2624 @subsection Friedman Test
2626 @cindex Friedman test
2629 [ /FRIEDMAN = @var{var_list} ]
2632 The Friedman test is used to test for differences between repeated measures when
2633 there is no indication that the distributions are normally distributed.
2635 A list of variables which contain the measured data must be given. The procedure
2636 prints the sum of ranks for each variable, the test statistic and its significance.
2639 @subsection Kendall's W Test
2641 @cindex Kendall's W test
2642 @cindex coefficient of concordance
2645 [ /KENDALL = @var{var_list} ]
2648 The Kendall test investigates whether an arbitrary number of related samples come from the
2650 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
2651 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
2652 unity indicates complete agreement.
2655 @node KOLMOGOROV-SMIRNOV
2656 @subsection Kolmogorov-Smirnov Test
2657 @vindex KOLMOGOROV-SMIRNOV
2659 @cindex Kolmogorov-Smirnov test
2662 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
2665 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
2666 drawn from a particular distribution. Four distributions are supported, @i{viz:}
2667 Normal, Uniform, Poisson and Exponential.
2669 Ideally you should provide the parameters of the distribution against
2670 which you wish to test the data. For example, with the normal
2671 distribution the mean (@var{mu})and standard deviation (@var{sigma})
2672 should be given; with the uniform distribution, the minimum
2673 (@var{min})and maximum (@var{max}) value should be provided.
2674 However, if the parameters are omitted they are imputed from the
2675 data. Imputing the parameters reduces the power of the test so should
2676 be avoided if possible.
2678 In the following example, two variables @var{score} and @var{age} are
2679 tested to see if they follow a normal distribution with a mean of 3.5
2680 and a standard deviation of 2.0.
2683 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
2685 If the variables need to be tested against different distributions, then a separate
2686 subcommand must be used. For example the following syntax tests @var{score} against
2687 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
2688 is tested against a normal distribution of mean 40 and standard deviation 1.5.
2691 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
2692 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
2695 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
2697 @node KRUSKAL-WALLIS
2698 @subsection Kruskal-Wallis Test
2699 @vindex KRUSKAL-WALLIS
2701 @cindex Kruskal-Wallis test
2704 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
2707 The Kruskal-Wallis test is used to compare data from an
2708 arbitrary number of populations. It does not assume normality.
2709 The data to be compared are specified by @var{var_list}.
2710 The categorical variable determining the groups to which the
2711 data belongs is given by @var{var}. The limits @var{lower} and
2712 @var{upper} specify the valid range of @var{var}.
2713 If @var{upper} is smaller than @var{lower}, the PSPP will assume their values
2714 to be reversed. Any cases for which @var{var} falls outside
2715 [@var{lower}, @var{upper}] are ignored.
2717 The mean rank of each group as well as the chi-squared value and
2718 significance of the test are printed.
2719 The abbreviated subcommand @subcmd{K-W} may be used in place of
2720 @subcmd{KRUSKAL-WALLIS}.
2724 @subsection Mann-Whitney U Test
2725 @vindex MANN-WHITNEY
2727 @cindex Mann-Whitney U test
2728 @cindex U, Mann-Whitney U
2731 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
2734 The Mann-Whitney subcommand is used to test whether two groups of data
2735 come from different populations. The variables to be tested should be
2736 specified in @var{var_list} and the grouping variable, that determines
2737 to which group the test variables belong, in @var{var}.
2738 @var{Var} may be either a string or an alpha variable.
2739 @var{Group1} and @var{group2} specify the
2740 two values of @var{var} which determine the groups of the test data.
2741 Cases for which the @var{var} value is neither @var{group1} or
2742 @var{group2} are ignored.
2744 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the
2745 significance are printed.
2746 You may abbreviated the subcommand @subcmd{MANN-WHITNEY} to
2751 @subsection McNemar Test
2753 @cindex McNemar test
2756 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2759 Use McNemar's test to analyse the significance of the difference between
2760 pairs of correlated proportions.
2762 If the @code{WITH} keyword is omitted, then tests for all
2763 combinations of the listed variables are performed.
2764 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
2765 is also given, then the number of variables preceding @code{WITH}
2766 must be the same as the number following it.
2767 In this case, tests for each respective pair of variables are
2769 If the @code{WITH} keyword is given, but the
2770 @code{(PAIRED)} keyword is omitted, then tests for each combination
2771 of variable preceding @code{WITH} against variable following
2772 @code{WITH} are performed.
2774 The data in each variable must be dichotomous. If there are more
2775 than two distinct variables an error will occur and the test will
2779 @subsection Median Test
2784 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
2787 The median test is used to test whether independent samples come from
2788 populations with a common median.
2789 The median of the populations against which the samples are to be tested
2790 may be given in parentheses immediately after the
2791 @subcmd{/MEDIAN} subcommand. If it is not given, the median is imputed from the
2792 union of all the samples.
2794 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
2795 keyword @code{BY} must come next, and then the grouping variable. Two values
2796 in parentheses should follow. If the first value is greater than the second,
2797 then a 2 sample test is performed using these two values to determine the groups.
2798 If however, the first variable is less than the second, then a @i{k} sample test is
2799 conducted and the group values used are all values encountered which lie in the
2800 range [@var{value1},@var{value2}].
2804 @subsection Runs Test
2809 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
2812 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
2814 It works by examining the number of times a variable's value crosses a given threshold.
2815 The desired threshold must be specified within parentheses.
2816 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
2817 Following the threshold specification comes the list of variables whose values are to be
2820 The subcommand shows the number of runs, the asymptotic significance based on the
2824 @subsection Sign Test
2829 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2832 The @subcmd{/SIGN} subcommand tests for differences between medians of the
2834 The test does not make any assumptions about the
2835 distribution of the data.
2837 If the @code{WITH} keyword is omitted, then tests for all
2838 combinations of the listed variables are performed.
2839 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
2840 is also given, then the number of variables preceding @code{WITH}
2841 must be the same as the number following it.
2842 In this case, tests for each respective pair of variables are
2844 If the @code{WITH} keyword is given, but the
2845 @code{(PAIRED)} keyword is omitted, then tests for each combination
2846 of variable preceding @code{WITH} against variable following
2847 @code{WITH} are performed.
2850 @subsection Wilcoxon Matched Pairs Signed Ranks Test
2852 @cindex wilcoxon matched pairs signed ranks test
2855 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2858 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
2860 The test does not make any assumptions about the variances of the samples.
2861 It does however assume that the distribution is symmetrical.
2863 If the @subcmd{WITH} keyword is omitted, then tests for all
2864 combinations of the listed variables are performed.
2865 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
2866 is also given, then the number of variables preceding @subcmd{WITH}
2867 must be the same as the number following it.
2868 In this case, tests for each respective pair of variables are
2870 If the @subcmd{WITH} keyword is given, but the
2871 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
2872 of variable preceding @subcmd{WITH} against variable following
2873 @subcmd{WITH} are performed.
2882 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
2883 /CRITERIA=CI(@var{confidence})
2887 TESTVAL=@var{test_value}
2888 /VARIABLES=@var{var_list}
2891 (Independent Samples mode.)
2892 GROUPS=var(@var{value1} [, @var{value2}])
2893 /VARIABLES=@var{var_list}
2896 (Paired Samples mode.)
2897 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
2902 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
2904 It operates in one of three modes:
2906 @item One Sample mode.
2907 @item Independent Groups mode.
2912 Each of these modes are described in more detail below.
2913 There are two optional subcommands which are common to all modes.
2915 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
2916 in the tests. The default value is 0.95.
2919 The @cmd{MISSING} subcommand determines the handling of missing
2921 If @subcmd{INCLUDE} is set, then user-missing values are included in the
2922 calculations, but system-missing values are not.
2923 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2924 values are excluded as well as system-missing values.
2925 This is the default.
2927 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
2928 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
2929 @subcmd{/GROUPS} subcommands contains a missing value.
2930 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
2931 which they would be needed. This is the default.
2935 * One Sample Mode:: Testing against a hypothesized mean
2936 * Independent Samples Mode:: Testing two independent groups for equal mean
2937 * Paired Samples Mode:: Testing two interdependent groups for equal mean
2940 @node One Sample Mode
2941 @subsection One Sample Mode
2943 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
2944 This mode is used to test a population mean against a hypothesized
2946 The value given to the @subcmd{TESTVAL} subcommand is the value against
2947 which you wish to test.
2948 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
2949 tell @pspp{} which variables you wish to test.
2951 @subsubsection Example - One Sample T-test
2953 A researcher wishes to know whether the weight of persons in a population
2954 is different from the national average.
2955 The samples are drawn from the population under investigation and recorded
2956 in the file @file{physiology.sav}.
2957 From the Department of Health, she
2958 knows that the national average weight of healthy adults is 76.8kg.
2959 Accordingly the @subcmd{TESTVAL} is set to 76.8.
2960 The null hypothesis therefore is that the mean average weight of the
2961 population from which the sample was drawn is 76.8kg.
2963 As previously noted (@pxref{Identifying incorrect data}), one
2964 sample in the dataset contains a weight value
2965 which is clearly incorrect. So this is excluded from the analysis
2966 using the @cmd{SELECT} command.
2968 @float Example, one-sample-t:ex
2969 @psppsyntax {one-sample-t.sps}
2970 @caption {Running a one sample T-Test after excluding all non-positive values}
2973 @float Screenshot, one-sample-t:scr
2974 @psppimage {one-sample-t}
2975 @caption {Using the One Sample T-Test dialog box to test @exvar{weight} for a mean of 76.8kg}
2979 @ref{one-sample-t:res} shows that the mean of our sample differs from the test value
2980 by -1.40kg. However the significance is very high (0.610). So one cannot
2981 reject the null hypothesis, and must conclude there is not enough evidence
2982 to suggest that the mean weight of the persons in our population is different
2985 @float Results, one-sample-t:res
2986 @psppoutput {one-sample-t}
2987 @caption {The results of a one sample T-test of @exvar{weight} using a test value of 76.8kg}
2990 @node Independent Samples Mode
2991 @subsection Independent Samples Mode
2993 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
2995 This mode is used to test whether two groups of values have the
2996 same population mean.
2997 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
2998 tell @pspp{} the dependent variables you wish to test.
3000 The variable given in the @subcmd{GROUPS} subcommand is the independent
3001 variable which determines to which group the samples belong.
3002 The values in parentheses are the specific values of the independent
3003 variable for each group.
3004 If the parentheses are omitted and no values are given, the default values
3005 of 1.0 and 2.0 are assumed.
3007 If the independent variable is numeric,
3008 it is acceptable to specify only one value inside the parentheses.
3009 If you do this, cases where the independent variable is
3010 greater than or equal to this value belong to the first group, and cases
3011 less than this value belong to the second group.
3012 When using this form of the @subcmd{GROUPS} subcommand, missing values in
3013 the independent variable are excluded on a listwise basis, regardless
3014 of whether @subcmd{/MISSING=LISTWISE} was specified.
3016 @subsubsection Example - Independent Samples T-test
3018 A researcher wishes to know whether within a population, adult males
3019 are taller than adult females.
3020 The samples are drawn from the population under investigation and recorded
3021 in the file @file{physiology.sav}.
3023 As previously noted (@pxref{Identifying incorrect data}), one
3024 sample in the dataset contains a height value
3025 which is clearly incorrect. So this is excluded from the analysis
3026 using the @cmd{SELECT} command.
3029 @float Example, indepdendent-samples-t:ex
3030 @psppsyntax {independent-samples-t.sps}
3031 @caption {Running a independent samples T-Test after excluding all observations less than 200kg}
3035 The null hypothesis is that both males and females are on average
3038 @float Screenshot, independent-samples-t:scr
3039 @psppimage {independent-samples-t}
3040 @caption {Using the Independent Sample T-test dialog, to test for differences of @exvar{height} between values of @exvar{sex}}
3044 In this case, the grouping variable is @exvar{sex}, so this is entered
3045 as the variable for the @subcmd{GROUP} subcommand. The group values are 0 (male) and
3048 If you are running the proceedure using syntax, then you need to enter
3049 the values corresponding to each group within parentheses.
3050 If you are using the graphic user interface, then you have to open
3051 the ``Define Groups'' dialog box and enter the values corresponding
3052 to each group as shown in @ref{define-groups-t:scr}. If, as in this case, the dataset has defined value
3053 labels for the group variable, then you can enter them by label
3056 @float Screenshot, define-groups-t:scr
3057 @psppimage {define-groups-t}
3058 @caption {Setting the values of the grouping variable for an Independent Samples T-test}
3061 From @ref{independent-samples-t:res}, one can clearly see that the @emph{sample} mean height
3062 is greater for males than for females. However in order to see if this
3063 is a significant result, one must consult the T-Test table.
3065 The T-Test table contains two rows; one for use if the variance of the samples
3066 in each group may be safely assumed to be equal, and the second row
3067 if the variances in each group may not be safely assumed to be equal.
3069 In this case however, both rows show a 2-tailed significance less than 0.001 and
3070 one must therefore reject the null hypothesis and conclude that within
3071 the population the mean height of males and of females are unequal.
3073 @float Result, independent-samples-t:res
3074 @psppoutput {independent-samples-t}
3075 @caption {The results of an independent samples T-test of @exvar{height} by @exvar{sex}}
3078 @node Paired Samples Mode
3079 @subsection Paired Samples Mode
3081 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
3082 Use this mode when repeated measures have been taken from the same
3084 If the @subcmd{WITH} keyword is omitted, then tables for all
3085 combinations of variables given in the @cmd{PAIRS} subcommand are
3087 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
3088 is also given, then the number of variables preceding @subcmd{WITH}
3089 must be the same as the number following it.
3090 In this case, tables for each respective pair of variables are
3092 In the event that the @subcmd{WITH} keyword is given, but the
3093 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
3094 of variable preceding @subcmd{WITH} against variable following
3095 @subcmd{WITH} are generated.
3102 @cindex analysis of variance
3107 [/VARIABLES = ] @var{var_list} BY @var{var}
3108 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
3109 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
3110 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
3111 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
3114 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
3115 variables factored by a single independent variable.
3116 It is used to compare the means of a population
3117 divided into more than two groups.
3119 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
3121 The list of variables must be followed by the @subcmd{BY} keyword and
3122 the name of the independent (or factor) variable.
3124 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
3125 ancillary information. The options accepted are:
3128 Displays descriptive statistics about the groups factored by the independent
3131 Displays the Levene test of Homogeneity of Variance for the
3132 variables and their groups.
3135 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
3136 differences between the groups.
3137 The subcommand must be followed by a list of numerals which are the
3138 coefficients of the groups to be tested.
3139 The number of coefficients must correspond to the number of distinct
3140 groups (or values of the independent variable).
3141 If the total sum of the coefficients are not zero, then @pspp{} will
3142 display a warning, but will proceed with the analysis.
3143 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
3144 to specify different contrast tests.
3145 The @subcmd{MISSING} subcommand defines how missing values are handled.
3146 If @subcmd{LISTWISE} is specified then cases which have missing values for
3147 the independent variable or any dependent variable are ignored.
3148 If @subcmd{ANALYSIS} is specified, then cases are ignored if the independent
3149 variable is missing or if the dependent variable currently being
3150 analysed is missing. The default is @subcmd{ANALYSIS}.
3151 A setting of @subcmd{EXCLUDE} means that variables whose values are
3152 user-missing are to be excluded from the analysis. A setting of
3153 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
3155 Using the @code{POSTHOC} subcommand you can perform multiple
3156 pairwise comparisons on the data. The following comparison methods
3160 Least Significant Difference.
3161 @item @subcmd{TUKEY}
3162 Tukey Honestly Significant Difference.
3163 @item @subcmd{BONFERRONI}
3165 @item @subcmd{SCHEFFE}
3167 @item @subcmd{SIDAK}
3170 The Games-Howell test.
3174 Use the optional syntax @code{ALPHA(@var{value})} to indicate that
3175 @cmd{ONEWAY} should perform the posthoc tests at a confidence level of
3176 @var{value}. If @code{ALPHA(@var{value})} is not specified, then the
3177 confidence level used is 0.05.
3180 @section QUICK CLUSTER
3181 @vindex QUICK CLUSTER
3183 @cindex K-means clustering
3187 QUICK CLUSTER @var{var_list}
3188 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
3189 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
3190 [/PRINT=@{INITIAL@} @{CLUSTER@}]
3191 [/SAVE[=[CLUSTER[(@var{membership_var})]] [DISTANCE[(@var{distance_var})]]]
3194 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
3195 dataset. This is useful when you wish to allocate cases into clusters
3196 of similar values and you already know the number of clusters.
3198 The minimum specification is @samp{QUICK CLUSTER} followed by the names
3199 of the variables which contain the cluster data. Normally you will also
3200 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
3201 number of clusters. If this is not specified, then @var{k} defaults to 2.
3203 If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
3204 the initial clusters is used. This will provide for faster execution but
3205 less well separated initial clusters and hence possibly an inferior final
3209 @cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
3210 The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
3211 During classification, @pspp{} will continue iterating until until @var{max_iter}
3212 iterations have been done or the convergence criterion (see below) is fulfilled.
3213 The default value of @var{max_iter} is 2.
3215 If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
3216 no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
3219 The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
3220 to set the convergence criterion. The value of convergence criterion is @var{epsilon}
3221 times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
3222 the mean cluster distance between one iteration and the next
3223 is less than the convergence criterion. The default value of @var{epsilon} is zero.
3225 The @subcmd{MISSING} subcommand determines the handling of missing variables.
3226 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
3227 value and not as missing values.
3228 If @subcmd{EXCLUDE} is set, which is the default, user-missing
3229 values are excluded as well as system-missing values.
3231 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
3232 whenever any of the clustering variables contains a missing value.
3233 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
3234 clustering variables contain missing values. Otherwise it is clustered
3235 on the basis of the non-missing values.
3236 The default is @subcmd{LISTWISE}.
3238 The @subcmd{PRINT} subcommand requests additional output to be printed.
3239 If @subcmd{INITIAL} is set, then the initial cluster memberships will
3241 If @subcmd{CLUSTER} is set, the cluster memberships of the individual
3242 cases are displayed (potentially generating lengthy output).
3244 You can specify the subcommand @subcmd{SAVE} to ask that each case's cluster membership
3245 and the euclidean distance between the case and its cluster center be saved to
3246 a new variable in the active dataset. To save the cluster membership use the
3247 @subcmd{CLUSTER} keyword and to save the distance use the @subcmd{DISTANCE} keyword.
3248 Each keyword may optionally be followed by a variable name in parentheses to specify
3249 the new variable which is to contain the saved parameter. If no variable name is specified,
3250 then PSPP will create one.
3258 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
3259 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
3260 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
3262 /MISSING=@{EXCLUDE,INCLUDE@}
3264 /RANK [INTO @var{var_list}]
3265 /NTILES(k) [INTO @var{var_list}]
3266 /NORMAL [INTO @var{var_list}]
3267 /PERCENT [INTO @var{var_list}]
3268 /RFRACTION [INTO @var{var_list}]
3269 /PROPORTION [INTO @var{var_list}]
3270 /N [INTO @var{var_list}]
3271 /SAVAGE [INTO @var{var_list}]
3274 The @cmd{RANK} command ranks variables and stores the results into new
3277 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
3278 more variables whose values are to be ranked.
3279 After each variable, @samp{A} or @samp{D} may appear, indicating that
3280 the variable is to be ranked in ascending or descending order.
3281 Ascending is the default.
3282 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
3283 which are to serve as group variables.
3284 In this case, the cases are gathered into groups, and ranks calculated
3287 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
3288 default is to take the mean value of all the tied cases.
3290 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
3291 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
3292 functions are requested.
3294 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
3295 variables created should appear in the output.
3297 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
3298 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
3299 If none are given, then the default is RANK.
3300 The @subcmd{NTILES} subcommand must take an integer specifying the number of
3301 partitions into which values should be ranked.
3302 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
3303 variables which are the variables to be created and receive the rank
3304 scores. There may be as many variables specified as there are
3305 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
3306 then the variable names are automatically created.
3308 The @subcmd{MISSING} subcommand determines how user missing values are to be
3309 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
3310 user-missing are to be excluded from the rank scores. A setting of
3311 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
3313 @include regression.texi
3317 @section RELIABILITY
3322 /VARIABLES=@var{var_list}
3323 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
3324 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
3325 /SUMMARY=@{TOTAL,ALL@}
3326 /MISSING=@{EXCLUDE,INCLUDE@}
3329 @cindex Cronbach's Alpha
3330 The @cmd{RELIABILITY} command performs reliability analysis on the data.
3332 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
3333 upon which analysis is to be performed.
3335 The @subcmd{SCALE} subcommand determines the variables for which
3336 reliability is to be calculated. If @subcmd{SCALE} is omitted, then analysis for
3337 all variables named in the @subcmd{VARIABLES} subcommand are used.
3338 Optionally, the @var{name} parameter may be specified to set a string name
3341 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
3342 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
3343 then the variables are divided into 2 subsets. An optional parameter
3344 @var{n} may be given, to specify how many variables to be in the first subset.
3345 If @var{n} is omitted, then it defaults to one half of the variables in the
3346 scale, or one half minus one if there are an odd number of variables.
3347 The default model is @subcmd{ALPHA}.
3349 By default, any cases with user missing, or system missing values for
3350 any variables given in the @subcmd{VARIABLES} subcommand are omitted
3351 from the analysis. The @subcmd{MISSING} subcommand determines whether
3352 user missing values are included or excluded in the analysis.
3354 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
3355 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
3356 analysis tested against the totals.
3358 @subsection Example - Reliability
3360 Before analysing the results of a survey -- particularly for a multiple choice survey --
3361 it is desireable to know whether the respondents have considered their answers
3362 or simply provided random answers.
3364 In the following example the survey results from the file @file{hotel.sav} are used.
3365 All five survey questions are included in the reliability analysis.
3366 However, before running the analysis, the data must be preprocessed.
3367 An examination of the survey questions reveals that two questions, @i{viz:} v3 and v5
3368 are negatively worded, whereas the others are positively worded.
3369 All questions must be based upon the same scale for the analysis to be meaningful.
3370 One could use the @cmd{RECODE} command (@pxref{RECODE}), however a simpler way is
3371 to use @cmd{COMPUTE} (@pxref{COMPUTE}) and this is what is done in @ref{reliability:ex}.
3373 @float Example, reliability:ex
3374 @psppsyntax {reliability.sps}
3375 @caption {Investigating the reliability of survey responses}
3378 In this case, all variables in the data set are used. So we can use the special
3379 keyword @samp{ALL} (@pxref{BNF}).
3381 @float Screenshot, reliability:src
3382 @psppimage {reliability}
3383 @caption {Reliability dialog box with all variables selected}
3386 @ref{reliability:res} shows that Cronbach's Alpha is 0.11 which is a value normally considered too
3387 low to indicate consistency within the data. This is possibly due to the small number of
3388 survey questions. The survey should be redesigned before serious use of the results are
3391 @float Result, reliability:res
3392 @psppoutput {reliability}
3393 @caption {The results of the reliability command on @file{hotel.sav}}
3401 @cindex Receiver Operating Characteristic
3402 @cindex Area under curve
3405 ROC @var{var_list} BY @var{state_var} (@var{state_value})
3406 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
3407 /PRINT = [ SE ] [ COORDINATES ]
3408 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
3409 [ TESTPOS (@{LARGE,SMALL@}) ]
3410 [ CI (@var{confidence}) ]
3411 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
3412 /MISSING=@{EXCLUDE,INCLUDE@}
3416 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
3417 of a dataset, and to estimate the area under the curve.
3418 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
3420 The mandatory @var{var_list} is the list of predictor variables.
3421 The variable @var{state_var} is the variable whose values represent the actual states,
3422 and @var{state_value} is the value of this variable which represents the positive state.
3424 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
3425 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
3426 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
3427 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
3428 By default, the curve is drawn with no reference line.
3430 The optional subcommand @subcmd{PRINT} determines which additional
3431 tables should be printed. Two additional tables are available. The
3432 @subcmd{SE} keyword says that standard error of the area under the
3433 curve should be printed as well as the area itself. In addition, a
3434 p-value for the null hypothesis that the area under the curve equals
3435 0.5 is printed. The @subcmd{COORDINATES} keyword says that a
3436 table of coordinates of the @subcmd{ROC} curve should be printed.
3438 The @subcmd{CRITERIA} subcommand has four optional parameters:
3440 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
3441 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
3442 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
3444 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
3445 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
3447 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
3449 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
3450 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
3451 exponential distribution estimate.
3452 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
3453 equal to the number of negative actual states.
3454 The default is @subcmd{FREE}.
3456 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
3459 The @subcmd{MISSING} subcommand determines whether user missing values are to
3460 be included or excluded in the analysis. The default behaviour is to
3462 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
3463 or if the variable @var{state_var} is missing, then the entire case is
3466 @c LocalWords: subcmd subcommand