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.
37 @node DESCRIPTIVES, FREQUENCIES, Statistics, Statistics
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)}
166 @node FREQUENCIES, EXAMINE, DESCRIPTIVES, Statistics
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}}
317 @node EXAMINE, GRAPH, FREQUENCIES, Statistics
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.
494 @node GRAPH, CORRELATIONS, EXAMINE, Statistics
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
521 @node SCATTERPLOT, HISTOGRAM, GRAPH, GRAPH
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.
540 @node HISTOGRAM, BAR CHART, SCATTERPLOT, GRAPH
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}.
556 @node BAR CHART, , HISTOGRAM, GRAPH
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.
610 @node CORRELATIONS, CROSSTABS, GRAPH, Statistics
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}.
673 @node CROSSTABS, CTABLES, CORRELATIONS, Statistics
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}}
900 @node CTABLES, FACTOR, CROSSTABS, Statistics
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 @t{/MRSETS COUNTDUPLICATES=}@{@t{YES} @math{|} @t{NO}@}
944 @t{/SMISSING} @{@t{VARIABLE} @math{|} @t{LISTWISE}@}
945 @t{/PCOMPUTE} @t{&}@i{category}@t{=EXPR(}@i{expression}@t{)}
946 @t{/PPROPERTIES} @t{&}@i{category}@dots{}
947 [@t{LABEL=}@i{string}]
948 [@t{FORMAT=}[@i{summary} @i{format}]@dots{}]
949 [@t{HIDESOURCECATS=}@{@t{NO} @math{|} @t{YES}@}
950 @t{/WEIGHT VARIABLE=}@i{variable}
951 @t{/HIDESMALLCOUNTS COUNT=@i{count}}
954 The following subcommands follow @code{TABLE} and apply only to the
955 previous @code{TABLE}. All of these subcommands are optional:
959 [@t{POSITION=}@{@t{COLUMN} @math{|} @t{ROW} @math{|} @t{LAYER}@}]
960 [@t{VISIBLE=}@{@t{YES} @math{|} @t{NO}@}]
961 @t{/CLABELS} @{@t{AUTO} @math{|} @{@t{ROWLABELS}@math{|}@t{COLLABELS}@}@t{=}@{@t{OPPOSITE}@math{|}@t{LAYER}@}@}
962 @t{/CRITERIA CILEVEL=}@i{percentage}
963 @t{/CATEGORIES} @t{VARIABLES=}@i{variables}
964 @{@t{[}@i{value}@t{,} @i{value}@dots{}@t{]}
965 @math{|} [@t{ORDER=}@{@t{A} @math{|} @t{D}@}]
966 [@t{KEY=}@{@t{VALUE} @math{|} @t{LABEL} @math{|} @i{summary}@t{(}@i{variable}@t{)}@}]
967 [@t{MISSING=}@{@t{EXCLUDE} @math{|} @t{INCLUDE}@}]@}
968 [@t{TOTAL=}@{@t{NO} @math{|} @t{YES}@} [@t{LABEL=}@i{string}] [@t{POSITION=}@{@t{AFTER} @math{|} @t{BEFORE}@}]]
969 [@t{EMPTY=}@{@t{INCLUDE} @math{|} @t{EXCLUDE}@}]
971 [@t{TITLE=}@i{string}@dots{}]
972 [@t{CAPTION=}@i{string}@dots{}]
973 [@t{CORNER=}@i{string}@dots{}]
974 @t{/SIGTEST TYPE=CHISQUARE}
975 [@t{ALPHA=}@i{siglevel}]
976 [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
977 [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
978 @t{/COMPARETEST TYPE=}@{@t{PROP} @math{|} @t{MEAN}@}
979 [@t{ALPHA=}@i{value}[@t{,} @i{value}]]
980 [@t{ADJUST=}@{@t{BONFERRONI} @math{|} @t{BH} @math{|} @t{NONE}@}]
981 [@t{INCLUDEMRSETS=}@{@t{YES} @math{|} @t{NO}@}]
982 [@t{MEANSVARIANCE=}@{@t{ALLCATS} @math{|} @t{TESTEDCATS}@}]
983 [@t{CATEGORIES=}@{@t{ALLVISIBLE} @math{|} @t{SUBTOTALS}@}]
984 [@t{MERGE=}@{@t{NO} @math{|} @t{YES}@}]
985 [@t{STYLE=}@{@t{APA} @math{|} @t{SIMPLE}@}]
986 [@t{SHOWSIG=}@{@t{NO} @math{|} @t{YES}@}]
989 The @code{CTABLES} (aka ``custom tables'') command produces
990 multi-dimensional tables from categorical and scale data. It offers
991 many options for data summarization and formatting.
993 This section's examples use data from the 2008 (USA) National Survey
994 of Drinking and Driving Attitudes and Behaviors, a public domain data
995 set from the (USA) National Highway Traffic Administration and
996 available at @url{https://data.transportation.gov}. @pspp{} includes
997 this data set, with a slightly modified dictionary, as
998 @file{examples/nhtsa.sav}.
1002 * CTABLES Data Summarization::
1005 @node CTABLES Basics, CTABLES Data Summarization, CTABLES, CTABLES
1008 The only required subcommand is @code{TABLE}, which specifies the
1009 variables to include along each axis:
1011 @t{/TABLE} @i{rows} [@t{BY} @i{columns} [@t{BY} @i{layers}]]
1014 In @code{TABLE}, each of @var{rows}, @var{columns}, and @var{layers}
1015 is either empty or an axis expression that specifies one or more
1016 variables. At least one must specify an axis expression.
1019 * CTABLES Categorical Variable Basics::
1020 * CTABLES Scalar Variable Basics::
1021 * CTABLES Overriding Measurement Level::
1022 * CTABLES Multiple Response Sets::
1025 @node CTABLES Categorical Variable Basics, CTABLES Scalar Variable Basics, CTABLES Basics, CTABLES Basics
1026 @subsubsection Categorical Variables
1028 An axis expression that names a categorical variable divides the data
1029 into cells according to the values of that variable. When all the
1030 variables named on @code{TABLE} are categorical, by default each cell
1031 displays the number of cases that it contains, so specifying a single
1032 variable yields a frequency table:
1035 CTABLES /TABLE=AgeGroup.
1037 @psppoutput {ctables1}
1040 Specifying a row and a column categorical variable yields a
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 If @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, CTABLES Overriding Measurement Level, CTABLES Categorical Variable Basics, CTABLES Basics
1080 @subsubsection Scalar Variables
1082 Categorical variables make @code{CTABLES} divide tables into cells.
1083 With scalar variables, @code{CTABLES} instead calculates a summary
1084 measure, by default the mean, of the values that fall into a cell.
1085 For example, if the only variable specified is a scalar variable, then
1086 the output is a single cell that holds the mean of all of the data:
1089 CTABLES /TABLE qnd1.
1091 @psppoutput {ctables6}
1093 A scalar variable may nest with categorical variables. The following
1094 example shows the mean age of survey respondents across gender and
1098 CTABLES /TABLE qns3a > qnd1 BY region.
1100 @psppoutput {ctables7}
1102 The order of nesting of scalar and categorical variables affects table
1103 labeling, but it does not affect the data displayed in the table. The
1104 following example shows how the output changes when the nesting order
1105 of the scalar and categorical variable are interchanged:
1108 CTABLES /TABLE qnd1 > qns3a BY region.
1110 @psppoutput {ctables8}
1112 Only a single scalar variable may appear in each section; that is, a
1113 scalar variable may not nest inside a scalar variable directly or
1114 indirectly. Scalar variables may only appear on one axis within
1117 @node CTABLES Overriding Measurement Level, CTABLES Multiple Response Sets, CTABLES Scalar Variable Basics, CTABLES Basics
1118 @subsubsection Overriding Measurement Level
1120 By default, @code{CTABLES} uses a variable's measurement level to
1121 decide whether to treat it as categorical or scalar. Variables
1122 assigned the nominal or ordinal measurement level are treated as
1123 categorical, and scalar variables are treated as scalar.
1125 Use the @code{VARIABLE LEVEL} command to change a variable's
1126 measurement level. To treat a variable as categorical or scalar only
1127 for one use on @code{CTABLES}, add @samp{[C]} or @samp{[S]},
1128 respectively, after the variable name. The following example shows
1129 how to analyze the scalar variable @code{qn20} as categorical:
1132 CTABLES /TABLE qn20 [C] BY qns3a.
1134 @psppoutput {ctables9}
1136 @node CTABLES Multiple Response Sets, , CTABLES Overriding Measurement Level, CTABLES Basics
1137 @subsubheading Multiple Response Sets
1139 The @code{CTABLES} command does not yet support multiple response
1142 @node CTABLES Data Summarization, , CTABLES Basics, CTABLES
1143 @subsection Data Summarization
1145 The @code{CTABLES} command allows the user to control how the data are
1146 summarized with summary specifications, which are enclosed in square
1147 brackets following a variable name on the @code{TABLE} subcommand.
1148 When all the variables are categorical, summary specifications can be
1149 given for the innermost nested variables on any one axis. When a
1150 scalar variable is present, only the scalar variable may have summary
1151 specifications. The following example includes a summary
1152 specification for column and row percentages for categorical
1153 variables, and mean and median for a scalar variable:
1157 /TABLE=qnd1 [MEAN, MEDIAN] BY qns3a
1158 /TABLE=AgeGroup [COLPCT, ROWPCT] BY qns3a.
1160 @psppoutput {ctables10}
1162 A summary specification may override the default label and format by
1163 appending a string or format specification or both (in that order) to
1164 the summary function name. For example:
1167 CTABLES /TABLE=AgeGroup [COLPCT 'Gender %' PCT5.0,
1168 ROWPCT 'Age Group %' PCT5.0]
1171 @psppoutput {ctables11}
1173 Parentheses are a shorthand to apply summary specifications to
1174 multiple variables. For example, both of these commands:
1177 CTABLES /TABLE=AgeGroup[COLPCT] + qns1[COLPCT] BY qns3a.
1178 CTABLES /TABLE=(AgeGroup + qns1)[COLPCT] BY qns3a.
1182 produce the same output shown below:
1184 @psppoutput {ctables12}
1186 The following sections list the available summary functions.
1189 * CTABLES Summary Functions for Categorical and Scale Variables::
1192 @node CTABLES Summary Functions for Categorical and Scale Variables, , CTABLES Data Summarization, CTABLES Data Summarization
1193 @subsubsection Summary Functions for Categorical and Scale Variables
1195 This section lists the summary functions that can be applied to cells
1196 in @code{CTABLES}. Many of these functions have an @var{area} in
1197 their names. The supported areas are:
1201 Areas that correspond to parts of @dfn{subtables}, whose contents are
1202 the cells that pair an innermost row variable and an innermost column
1207 A row within a subtable.
1210 A column within a subtable.
1213 All the cells in a subtable
1217 Areas that correspond to parts of @dfn{sections}, where stacked
1218 variables divide each section from another:
1225 A layer within a section.
1228 A row in one layer within a section.
1231 A column in one layer within a section.
1235 The following table lists summary functions that may be applied to any
1236 variable regardless of whether it is categorical or scalar, along with
1237 their default labels:
1240 @item @code{COUNT} (``Count'')
1241 The sum of weights in a cell.
1243 @item @i{area}@code{PCT} or @i{area}@code{PCT.COUNT} (``@i{Area} %'')
1244 A percentage within the specified @var{area}.
1246 @item @i{area}@code{PCT.VALIDN} (``@i{Area} Valid N %'')
1247 A percentage of valid values within the specified @var{area}.
1249 @item @i{area}@code{PCT.TOTALN} (``@i{Area} Total N %'')
1250 A percentage of total values within the specified @var{area}.
1253 The following table lists summary functions that apply only to scale
1257 @item @code{MAXIMUM} (``Maximum'')
1260 @item @code{MEAN} (``Mean'')
1263 @item @code{MEDIAN} (``Median'')
1266 @item @code{MINIMUM} (``Minimum'')
1269 @item @code{MISSING} (``Missing'')
1270 Sum of weights of user- and system-missing values.
1272 @item @code{MODE} (``Mode'')
1273 The highest-frequency value. Ties are broken by taking the smallest mode.
1275 @item @i{area}@code{PCT.SUM} (``@i{Area} Sum %'')
1276 Percentage of the sum of the values across @var{area}.
1278 @item @code{PTILE} @i{n} (``Percentile @i{n}'')
1279 The @var{n}th percentile, where @math{0 @leq{} @var{n} @leq{} 100}.
1281 @item @code{RANGE} (``Range'')
1282 The maximum minus the minimum.
1284 @item @code{SEMEAN} (``Std Error of Mean'')
1285 The standard error of the mean.
1287 @item @code{STDDEV} (``Std Deviation'')
1288 The standard deviation.
1290 @item @code{SUM} (``Sum'')
1293 @item @code{TOTALN} (``Total N'')
1294 The sum of total count weights.
1296 @item @code{VALIDN} (``Valid N'')
1297 The sum of valid count weights.
1299 @item @code{VARIANCE} (``Variance'')
1303 If the @code{WEIGHT} subcommand specified an adjustment weight
1304 variable, then the following summary functions use its value instead
1305 of the dictionary weight variable. Otherwise, they are equivalent to
1306 the summary function without the @samp{E}-prefix:
1309 @item @code{ECOUNT} (``Adjusted Count'')
1310 @item @code{ETOTALN} (``Adjusted Total N'')
1311 @item @code{EVALIDN} (``Adjusted Valid N'')
1314 The following summary functions with a @samp{U}-prefix are equivalent
1315 to those without a prefix, except that they use unweighted counts:
1318 @item @code{UCOUNT} (``Unweighted Count'')
1319 @item @code{U}@i{area}@code{PCT} or @code{U}@i{area}@code{PCT.COUNT} (``Unweighted @i{Area} %'')
1320 @item @code{U}@i{area}@code{PCT.VALIDN} (``Unweighted @i{Area} Valid N %'')
1321 @item @code{U}@i{area}@code{PCT.TOTALN} (``Unweighted @i{Area} Total N %'')
1322 @item @code{UMEAN} (``Unweighted Mean'')
1323 @item @code{UMEDIAN} (``Unweighted Median'')
1324 @item @code{UMISSING} (``Unweighted Missing'')
1325 @item @code{UMODE} (``Unweight Mode'')
1326 @item @code{U}@i{area}@code{PCT.SUM} (``Unweighted @i{Area} Sum %'')
1327 @item @code{UPTILE} @i{n} (``Unweighted Percentile @i{n}'')
1328 @item @code{USEMEAN} (``Unweighted Std Error of Mean'')
1329 @item @code{USTDDEV} (``Unweighted Std Deviation'')
1330 @item @code{USUM} (``Unweighted Sum'')
1331 @item @code{UTOTALN} (``Unweighted Total N'')
1332 @item @code{UVALIDN} (``Unweighted Valid N'')
1333 @item @code{UVARIANCE} (``Unweighted Variance'')
1336 @node FACTOR, GLM, CTABLES, Statistics
1340 @cindex factor analysis
1341 @cindex principal components analysis
1342 @cindex principal axis factoring
1343 @cindex data reduction
1347 VARIABLES=@var{var_list},
1348 MATRIX IN (@{CORR,COV@}=@{*,@var{file_spec}@})
1351 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
1353 [ /ANALYSIS=@var{var_list} ]
1355 [ /EXTRACTION=@{PC, PAF@}]
1357 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}]
1359 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [AIC] [SIG] [ALL] [DEFAULT] ]
1363 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
1365 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
1367 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
1370 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
1371 common factors in the data or for data reduction purposes.
1373 The @subcmd{VARIABLES} subcommand is required (unless the @subcmd{MATRIX IN}
1374 subcommand is used).
1375 It lists the variables which are to partake in the analysis. (The @subcmd{ANALYSIS}
1376 subcommand may optionally further limit the variables that
1377 participate; it is useful primarily in conjunction with @subcmd{MATRIX IN}.)
1379 If @subcmd{MATRIX IN} instead of @subcmd{VARIABLES} is specified, then the analysis
1380 is performed on a pre-prepared correlation or covariance matrix file instead of on
1381 individual data cases. Typically the matrix file will have been generated by
1382 @cmd{MATRIX DATA} (@pxref{MATRIX DATA}) or provided by a third party.
1383 If specified, @subcmd{MATRIX IN} must be followed by @samp{COV} or @samp{CORR},
1384 then by @samp{=} and @var{file_spec} all in parentheses.
1385 @var{file_spec} may either be an asterisk, which indicates the currently loaded
1386 dataset, or it may be a file name to be loaded. @xref{MATRIX DATA}, for the expected
1389 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors
1390 (components) are extracted from the data.
1391 If @subcmd{PC} is specified, then Principal Components Analysis is used.
1392 If @subcmd{PAF} is specified, then Principal Axis Factoring is
1393 used. By default Principal Components Analysis is used.
1395 The @subcmd{/ROTATION} subcommand is used to specify the method by which the
1396 extracted solution is rotated. Three orthogonal rotation methods are available:
1397 @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
1398 There is one oblique rotation method, @i{viz}: @subcmd{PROMAX}.
1399 Optionally you may enter the power of the promax rotation @var{k}, which must be enclosed in parentheses.
1400 The default value of @var{k} is 5.
1401 If you don't want any rotation to be performed, the word @subcmd{NOROTATE}
1402 prevents the command from performing any rotation on the data.
1404 The @subcmd{/METHOD} subcommand should be used to determine whether the
1405 covariance matrix or the correlation matrix of the data is
1406 to be analysed. By default, the correlation matrix is analysed.
1408 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
1411 @item @subcmd{UNIVARIATE}
1412 A table of mean values, standard deviations and total weights are printed.
1413 @item @subcmd{INITIAL}
1414 Initial communalities and eigenvalues are printed.
1415 @item @subcmd{EXTRACTION}
1416 Extracted communalities and eigenvalues are printed.
1417 @item @subcmd{ROTATION}
1418 Rotated communalities and eigenvalues are printed.
1419 @item @subcmd{CORRELATION}
1420 The correlation matrix is printed.
1421 @item @subcmd{COVARIANCE}
1422 The covariance matrix is printed.
1424 The determinant of the correlation or covariance matrix is printed.
1426 The anti-image covariance and anti-image correlation matrices are printed.
1428 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
1430 The significance of the elements of correlation matrix is printed.
1432 All of the above are printed.
1433 @item @subcmd{DEFAULT}
1434 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
1437 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues is
1438 printed. This can be useful for visualizing the factors and deciding
1439 which factors (components) should be retained.
1441 The @subcmd{/FORMAT} subcommand determined how data are to be
1442 displayed in loading matrices. If @subcmd{SORT} is specified, then
1443 the variables are sorted in descending order of significance. If
1444 @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute
1445 value is less than @var{n} are not printed. If the keyword
1446 @subcmd{DEFAULT} is specified, or if no @subcmd{/FORMAT} subcommand is
1447 specified, then no sorting is performed, and all coefficients are printed.
1449 You can use the @subcmd{/CRITERIA} subcommand to specify how the number of
1450 extracted factors (components) are chosen. If @subcmd{FACTORS(@var{n})} is
1451 specified, where @var{n} is an integer, then @var{n} factors are
1452 extracted. Otherwise, the @subcmd{MINEIGEN} setting is used.
1453 @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues
1454 are greater than or equal to @var{l} are extracted. The default value
1455 of @var{l} is 1. The @subcmd{ECONVERGE} setting has effect only when
1456 using iterative algorithms for factor extraction (such as Principal Axis
1457 Factoring). @subcmd{ECONVERGE(@var{delta})} specifies that
1458 iteration should cease when the maximum absolute value of the
1459 communality estimate between one iteration and the previous is less
1460 than @var{delta}. The default value of @var{delta} is 0.001.
1462 The @subcmd{ITERATE(@var{m})} may appear any number of times and is
1463 used for two different purposes. It is used to set the maximum number
1464 of iterations (@var{m}) for convergence and also to set the maximum
1465 number of iterations for rotation.
1466 Whether it affects convergence or rotation depends upon which
1467 subcommand follows the @subcmd{ITERATE} subcommand.
1468 If @subcmd{EXTRACTION} follows, it affects convergence.
1469 If @subcmd{ROTATION} follows, it affects rotation.
1470 If neither @subcmd{ROTATION} nor @subcmd{EXTRACTION} follow a
1471 @subcmd{ITERATE} subcommand, then the entire subcommand is ignored.
1472 The default value of @var{m} is 25.
1474 The @cmd{MISSING} subcommand determines the handling of missing
1475 variables. If @subcmd{INCLUDE} is set, then user-missing values are
1476 included in the calculations, but system-missing values are not.
1477 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1478 values are excluded as well as system-missing values. This is the
1479 default. If @subcmd{LISTWISE} is set, then the entire case is excluded
1480 from analysis whenever any variable specified in the @cmd{VARIABLES}
1481 subcommand contains a missing value.
1483 If @subcmd{PAIRWISE} is set, then a case is considered missing only if
1484 either of the values for the particular coefficient are missing.
1485 The default is @subcmd{LISTWISE}.
1487 @node GLM, LOGISTIC REGRESSION, FACTOR, Statistics
1491 @cindex univariate analysis of variance
1492 @cindex fixed effects
1493 @cindex factorial anova
1494 @cindex analysis of variance
1499 GLM @var{dependent_vars} BY @var{fixed_factors}
1500 [/METHOD = SSTYPE(@var{type})]
1501 [/DESIGN = @var{interaction_0} [@var{interaction_1} [... @var{interaction_n}]]]
1502 [/INTERCEPT = @{INCLUDE|EXCLUDE@}]
1503 [/MISSING = @{INCLUDE|EXCLUDE@}]
1506 The @cmd{GLM} procedure can be used for fixed effects factorial Anova.
1508 The @var{dependent_vars} are the variables to be analysed.
1509 You may analyse several variables in the same command in which case they should all
1510 appear before the @code{BY} keyword.
1512 The @var{fixed_factors} list must be one or more categorical variables. Normally it
1513 does not make sense to enter a scalar variable in the @var{fixed_factors} and doing
1514 so may cause @pspp{} to do a lot of unnecessary processing.
1516 The @subcmd{METHOD} subcommand is used to change the method for producing the sums of
1517 squares. Available values of @var{type} are 1, 2 and 3. The default is type 3.
1519 You may specify a custom design using the @subcmd{DESIGN} subcommand.
1520 The design comprises a list of interactions where each interaction is a
1521 list of variables separated by a @samp{*}. For example the command
1523 GLM subject BY sex age_group race
1524 /DESIGN = age_group sex group age_group*sex age_group*race
1526 @noindent specifies the model @math{subject = age_group + sex + race + age_group*sex + age_group*race}.
1527 If no @subcmd{DESIGN} subcommand is specified, then the default is all possible combinations
1528 of the fixed factors. That is to say
1530 GLM subject BY sex age_group race
1533 @math{subject = age_group + sex + race + age_group*sex + age_group*race + sex*race + age_group*sex*race}.
1536 The @subcmd{MISSING} subcommand determines the handling of missing
1538 If @subcmd{INCLUDE} is set then, for the purposes of GLM analysis,
1539 only system-missing values are considered
1540 to be missing; user-missing values are not regarded as missing.
1541 If @subcmd{EXCLUDE} is set, which is the default, then user-missing
1542 values are considered to be missing as well as system-missing values.
1543 A case for which any dependent variable or any factor
1544 variable has a missing value is excluded from the analysis.
1546 @node LOGISTIC REGRESSION, MEANS, GLM, Statistics
1547 @section LOGISTIC REGRESSION
1549 @vindex LOGISTIC REGRESSION
1550 @cindex logistic regression
1551 @cindex bivariate logistic regression
1554 LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
1556 [/CATEGORICAL = @var{categorical_predictors}]
1558 [@{/NOCONST | /ORIGIN | /NOORIGIN @}]
1560 [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
1562 [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
1563 [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
1564 [CUT(@var{cut_point})]]
1566 [/MISSING = @{INCLUDE|EXCLUDE@}]
1569 Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
1570 variable in terms of one or more predictor variables.
1572 The minimum command is
1574 LOGISTIC REGRESSION @var{y} WITH @var{x1} @var{x2} @dots{} @var{xn}.
1576 Here, @var{y} is the dependent variable, which must be dichotomous and @var{x1} @dots{} @var{xn}
1577 are the predictor variables whose coefficients the procedure estimates.
1579 By default, a constant term is included in the model.
1580 Hence, the full model is
1583 = b_0 + b_1 {\bf x_1}
1589 Predictor variables which are categorical in nature should be listed on the @subcmd{/CATEGORICAL} subcommand.
1590 Simple variables as well as interactions between variables may be listed here.
1592 If you want a model without the constant term @math{b_0}, use the keyword @subcmd{/ORIGIN}.
1593 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
1595 An iterative Newton-Raphson procedure is used to fit the model.
1596 The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
1597 and other parameters.
1598 The value of @var{cut_point} is used in the classification table. It is the
1599 threshold above which predicted values are considered to be 1. Values
1600 of @var{cut_point} must lie in the range [0,1].
1601 During iterations, if any one of the stopping criteria are satisfied, the procedure is
1602 considered complete.
1603 The stopping criteria are:
1605 @item The number of iterations exceeds @var{max_iterations}.
1606 The default value of @var{max_iterations} is 20.
1607 @item The change in the all coefficient estimates are less than @var{min_delta}.
1608 The default value of @var{min_delta} is 0.001.
1609 @item The magnitude of change in the likelihood estimate is less than @var{min_likelihood_delta}.
1610 The default value of @var{min_delta} is zero.
1611 This means that this criterion is disabled.
1612 @item The differential of the estimated probability for all cases is less than @var{min_epsilon}.
1613 In other words, the probabilities are close to zero or one.
1614 The default value of @var{min_epsilon} is 0.00000001.
1618 The @subcmd{PRINT} subcommand controls the display of optional statistics.
1619 Currently there is one such option, @subcmd{CI}, which indicates that the
1620 confidence interval of the odds ratio should be displayed as well as its value.
1621 @subcmd{CI} should be followed by an integer in parentheses, to indicate the
1622 confidence level of the desired confidence interval.
1624 The @subcmd{MISSING} subcommand determines the handling of missing
1626 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1627 calculations, but system-missing values are not.
1628 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1629 values are excluded as well as system-missing values.
1630 This is the default.
1632 @node MEANS, NPAR TESTS, LOGISTIC REGRESSION, Statistics
1641 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
1643 [ /@{@var{var_list}@}
1644 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
1646 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
1647 [VARIANCE] [KURT] [SEKURT]
1648 [SKEW] [SESKEW] [FIRST] [LAST]
1649 [HARMONIC] [GEOMETRIC]
1654 [/MISSING = [INCLUDE] [DEPENDENT]]
1657 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
1658 statistics, either for the dataset as a whole or for categories of data.
1660 The simplest form of the command is
1664 @noindent which calculates the mean, count and standard deviation for @var{v}.
1665 If you specify a grouping variable, for example
1667 MEANS @var{v} BY @var{g}.
1669 @noindent then the means, counts and standard deviations for @var{v} after having
1670 been grouped by @var{g} are calculated.
1671 Instead of the mean, count and standard deviation, you could specify the statistics
1672 in which you are interested:
1674 MEANS @var{x} @var{y} BY @var{g}
1675 /CELLS = HARMONIC SUM MIN.
1677 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
1680 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
1684 @cindex arithmetic mean
1685 The arithmetic mean.
1686 @item @subcmd{COUNT}
1687 The count of the values.
1688 @item @subcmd{STDDEV}
1689 The standard deviation.
1690 @item @subcmd{SEMEAN}
1691 The standard error of the mean.
1693 The sum of the values.
1698 @item @subcmd{RANGE}
1699 The difference between the maximum and minimum values.
1700 @item @subcmd{VARIANCE}
1702 @item @subcmd{FIRST}
1703 The first value in the category.
1705 The last value in the category.
1708 @item @subcmd{SESKEW}
1709 The standard error of the skewness.
1712 @item @subcmd{SEKURT}
1713 The standard error of the kurtosis.
1714 @item @subcmd{HARMONIC}
1715 @cindex harmonic mean
1717 @item @subcmd{GEOMETRIC}
1718 @cindex geometric mean
1722 In addition, three special keywords are recognized:
1724 @item @subcmd{DEFAULT}
1725 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
1727 All of the above statistics are calculated.
1729 No statistics are calculated (only a summary is shown).
1733 More than one @dfn{table} can be specified in a single command.
1734 Each table is separated by a @samp{/}. For
1738 @var{c} @var{d} @var{e} BY @var{x}
1739 /@var{a} @var{b} BY @var{x} @var{y}
1740 /@var{f} BY @var{y} BY @var{z}.
1742 has three tables (the @samp{TABLE =} is optional).
1743 The first table has three dependent variables @var{c}, @var{d} and @var{e}
1744 and a single categorical variable @var{x}.
1745 The second table has two dependent variables @var{a} and @var{b},
1746 and two categorical variables @var{x} and @var{y}.
1747 The third table has a single dependent variables @var{f}
1748 and a categorical variable formed by the combination of @var{y} and @var{z}.
1751 By default values are omitted from the analysis only if missing values
1752 (either system missing or user missing)
1753 for any of the variables directly involved in their calculation are
1755 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
1756 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
1758 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
1759 variables or in the categorical variables should be taken at their face
1760 value, and not excluded.
1762 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
1763 variables should be taken at their face value, however cases which
1764 have user missing values for the categorical variables should be omitted
1765 from the calculation.
1767 @subsection Example Means
1769 The dataset in @file{repairs.sav} contains the mean time between failures (@exvar{mtbf})
1770 for a sample of artifacts produced by different factories and trialed under
1771 different operating conditions.
1772 Since there are four combinations of categorical variables, by simply looking
1773 at the list of data, it would be hard to how the scores vary for each category.
1774 @ref{means:ex} shows one way of tabulating the @exvar{mtbf} in a way which is
1775 easier to understand.
1777 @float Example, means:ex
1778 @psppsyntax {means.sps}
1779 @caption {Running @cmd{MEANS} on the @exvar{mtbf} score with categories @exvar{factory} and @exvar{environment}}
1782 The results are shown in @ref{means:res}. The figures shown indicate the mean,
1783 standard deviation and number of samples in each category.
1784 These figures however do not indicate whether the results are statistically
1785 significant. For that, you would need to use the procedures @cmd{ONEWAY}, @cmd{GLM} or
1786 @cmd{T-TEST} depending on the hypothesis being tested.
1788 @float Result, means:res
1790 @caption {The @exvar{mtbf} categorised by @exvar{factory} and @exvar{environment}}
1793 Note that there is no limit to the number of variables for which you can calculate
1794 statistics, nor to the number of categorical variables per layer, nor the number
1796 However, running @cmd{MEANS} on a large numbers of variables, or with categorical variables
1797 containing a large number of distinct values may result in an extremely large output, which
1798 will not be easy to interpret.
1799 So you should consider carefully which variables to select for participation in the analysis.
1801 @node NPAR TESTS, T-TEST, MEANS, Statistics
1805 @cindex nonparametric tests
1810 nonparametric test subcommands
1815 [ /STATISTICS=@{DESCRIPTIVES@} ]
1817 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
1819 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
1822 @cmd{NPAR TESTS} performs nonparametric tests.
1823 Non parametric tests make very few assumptions about the distribution of the
1825 One or more tests may be specified by using the corresponding subcommand.
1826 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
1827 produces for each variable that is the subject of any test.
1829 Certain tests may take a long time to execute, if an exact figure is required.
1830 Therefore, by default asymptotic approximations are used unless the
1831 subcommand @subcmd{/METHOD=EXACT} is specified.
1832 Exact tests give more accurate results, but may take an unacceptably long
1833 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
1834 after which the test is abandoned, and a warning message printed.
1835 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
1836 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
1841 * BINOMIAL:: Binomial Test
1842 * CHISQUARE:: Chi-square Test
1843 * COCHRAN:: Cochran Q Test
1844 * FRIEDMAN:: Friedman Test
1845 * KENDALL:: Kendall's W Test
1846 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
1847 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
1848 * MANN-WHITNEY:: Mann Whitney U Test
1849 * MCNEMAR:: McNemar Test
1850 * MEDIAN:: Median Test
1852 * SIGN:: The Sign Test
1853 * WILCOXON:: Wilcoxon Signed Ranks Test
1857 @node BINOMIAL, CHISQUARE, NPAR TESTS, NPAR TESTS
1858 @subsection Binomial test
1860 @cindex binomial test
1863 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
1866 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
1867 variable with that of a binomial distribution.
1868 The variable @var{p} specifies the test proportion of the binomial
1870 The default value of 0.5 is assumed if @var{p} is omitted.
1872 If a single value appears after the variable list, then that value is
1873 used as the threshold to partition the observed values. Values less
1874 than or equal to the threshold value form the first category. Values
1875 greater than the threshold form the second category.
1877 If two values appear after the variable list, then they are used
1878 as the values which a variable must take to be in the respective
1880 Cases for which a variable takes a value equal to neither of the specified
1881 values, take no part in the test for that variable.
1883 If no values appear, then the variable must assume dichotomous
1885 If more than two distinct, non-missing values for a variable
1886 under test are encountered then an error occurs.
1888 If the test proportion is equal to 0.5, then a two tailed test is
1889 reported. For any other test proportion, a one tailed test is
1891 For one tailed tests, if the test proportion is less than
1892 or equal to the observed proportion, then the significance of
1893 observing the observed proportion or more is reported.
1894 If the test proportion is more than the observed proportion, then the
1895 significance of observing the observed proportion or less is reported.
1896 That is to say, the test is always performed in the observed
1899 @pspp{} uses a very precise approximation to the gamma function to
1900 compute the binomial significance. Thus, exact results are reported
1901 even for very large sample sizes.
1904 @node CHISQUARE, COCHRAN, BINOMIAL, NPAR TESTS
1905 @subsection Chi-square Test
1907 @cindex chi-square test
1911 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
1915 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
1916 between the expected and observed frequencies of the categories of a variable.
1917 Optionally, a range of values may appear after the variable list.
1918 If a range is given, then non integer values are truncated, and values
1919 outside the specified range are excluded from the analysis.
1921 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
1923 There must be exactly one non-zero expected value, for each observed
1924 category, or the @subcmd{EQUAL} keyword must be specified.
1925 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
1926 consecutive expected categories all taking a frequency of @var{f}.
1927 The frequencies given are proportions, not absolute frequencies. The
1928 sum of the frequencies need not be 1.
1929 If no @subcmd{/EXPECTED} subcommand is given, then equal frequencies
1932 @subsubsection Chi-square Example
1934 A researcher wishes to investigate whether there are an equal number of
1935 persons of each sex in a population. The sample chosen for invesigation
1936 is that from the @file {physiology.sav} dataset. The null hypothesis for
1937 the test is that the population comprises an equal number of males and females.
1938 The analysis is performed as shown in @ref{chisquare:ex}.
1940 @float Example, chisquare:ex
1941 @psppsyntax {chisquare.sps}
1942 @caption {Performing a chi-square test to check for equal distribution of sexes}
1945 There is only one test variable, @i{viz:} @exvar{sex}. The other variables in the dataset
1948 @float Screenshot, chisquare:scr
1949 @psppimage {chisquare}
1950 @caption {Performing a chi-square test using the graphic user interface}
1953 In @ref{chisquare:res} the summary box shows that in the sample, there are more males
1954 than females. However the significance of chi-square result is greater than 0.05
1955 --- the most commonly accepted p-value --- and therefore
1956 there is not enough evidence to reject the null hypothesis and one must conclude
1957 that the evidence does not indicate that there is an imbalance of the sexes
1960 @float Result, chisquare:res
1961 @psppoutput {chisquare}
1962 @caption {The results of running a chi-square test on @exvar{sex}}
1966 @node COCHRAN, FRIEDMAN, CHISQUARE, NPAR TESTS
1967 @subsection Cochran Q Test
1969 @cindex Cochran Q test
1970 @cindex Q, Cochran Q
1973 [ /COCHRAN = @var{var_list} ]
1976 The Cochran Q test is used to test for differences between three or more groups.
1977 The data for @var{var_list} in all cases must assume exactly two
1978 distinct values (other than missing values).
1980 The value of Q is displayed along with its Asymptotic significance
1981 based on a chi-square distribution.
1983 @node FRIEDMAN, KENDALL, COCHRAN, NPAR TESTS
1984 @subsection Friedman Test
1986 @cindex Friedman test
1989 [ /FRIEDMAN = @var{var_list} ]
1992 The Friedman test is used to test for differences between repeated measures when
1993 there is no indication that the distributions are normally distributed.
1995 A list of variables which contain the measured data must be given. The procedure
1996 prints the sum of ranks for each variable, the test statistic and its significance.
1998 @node KENDALL, KOLMOGOROV-SMIRNOV, FRIEDMAN, NPAR TESTS
1999 @subsection Kendall's W Test
2001 @cindex Kendall's W test
2002 @cindex coefficient of concordance
2005 [ /KENDALL = @var{var_list} ]
2008 The Kendall test investigates whether an arbitrary number of related samples come from the
2010 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
2011 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
2012 unity indicates complete agreement.
2015 @node KOLMOGOROV-SMIRNOV, KRUSKAL-WALLIS, KENDALL, NPAR TESTS
2016 @subsection Kolmogorov-Smirnov Test
2017 @vindex KOLMOGOROV-SMIRNOV
2019 @cindex Kolmogorov-Smirnov test
2022 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
2025 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
2026 drawn from a particular distribution. Four distributions are supported, @i{viz:}
2027 Normal, Uniform, Poisson and Exponential.
2029 Ideally you should provide the parameters of the distribution against
2030 which you wish to test the data. For example, with the normal
2031 distribution the mean (@var{mu})and standard deviation (@var{sigma})
2032 should be given; with the uniform distribution, the minimum
2033 (@var{min})and maximum (@var{max}) value should be provided.
2034 However, if the parameters are omitted they are imputed from the
2035 data. Imputing the parameters reduces the power of the test so should
2036 be avoided if possible.
2038 In the following example, two variables @var{score} and @var{age} are
2039 tested to see if they follow a normal distribution with a mean of 3.5
2040 and a standard deviation of 2.0.
2043 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
2045 If the variables need to be tested against different distributions, then a separate
2046 subcommand must be used. For example the following syntax tests @var{score} against
2047 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
2048 is tested against a normal distribution of mean 40 and standard deviation 1.5.
2051 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
2052 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
2055 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
2057 @node KRUSKAL-WALLIS, MANN-WHITNEY, KOLMOGOROV-SMIRNOV, NPAR TESTS
2058 @subsection Kruskal-Wallis Test
2059 @vindex KRUSKAL-WALLIS
2061 @cindex Kruskal-Wallis test
2064 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
2067 The Kruskal-Wallis test is used to compare data from an
2068 arbitrary number of populations. It does not assume normality.
2069 The data to be compared are specified by @var{var_list}.
2070 The categorical variable determining the groups to which the
2071 data belongs is given by @var{var}. The limits @var{lower} and
2072 @var{upper} specify the valid range of @var{var}.
2073 If @var{upper} is smaller than @var{lower}, the PSPP will assume their values
2074 to be reversed. Any cases for which @var{var} falls outside
2075 [@var{lower}, @var{upper}] are ignored.
2077 The mean rank of each group as well as the chi-squared value and
2078 significance of the test are printed.
2079 The abbreviated subcommand @subcmd{K-W} may be used in place of
2080 @subcmd{KRUSKAL-WALLIS}.
2083 @node MANN-WHITNEY, MCNEMAR, KRUSKAL-WALLIS, NPAR TESTS
2084 @subsection Mann-Whitney U Test
2085 @vindex MANN-WHITNEY
2087 @cindex Mann-Whitney U test
2088 @cindex U, Mann-Whitney U
2091 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
2094 The Mann-Whitney subcommand is used to test whether two groups of data
2095 come from different populations. The variables to be tested should be
2096 specified in @var{var_list} and the grouping variable, that determines
2097 to which group the test variables belong, in @var{var}.
2098 @var{Var} may be either a string or an alpha variable.
2099 @var{Group1} and @var{group2} specify the
2100 two values of @var{var} which determine the groups of the test data.
2101 Cases for which the @var{var} value is neither @var{group1} or
2102 @var{group2} are ignored.
2104 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the
2105 significance are printed.
2106 You may abbreviated the subcommand @subcmd{MANN-WHITNEY} to
2110 @node MCNEMAR, MEDIAN, MANN-WHITNEY, NPAR TESTS
2111 @subsection McNemar Test
2113 @cindex McNemar test
2116 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2119 Use McNemar's test to analyse the significance of the difference between
2120 pairs of correlated proportions.
2122 If the @code{WITH} keyword is omitted, then tests for all
2123 combinations of the listed variables are performed.
2124 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
2125 is also given, then the number of variables preceding @code{WITH}
2126 must be the same as the number following it.
2127 In this case, tests for each respective pair of variables are
2129 If the @code{WITH} keyword is given, but the
2130 @code{(PAIRED)} keyword is omitted, then tests for each combination
2131 of variable preceding @code{WITH} against variable following
2132 @code{WITH} are performed.
2134 The data in each variable must be dichotomous. If there are more
2135 than two distinct variables an error will occur and the test will
2138 @node MEDIAN, RUNS, MCNEMAR, NPAR TESTS
2139 @subsection Median Test
2144 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
2147 The median test is used to test whether independent samples come from
2148 populations with a common median.
2149 The median of the populations against which the samples are to be tested
2150 may be given in parentheses immediately after the
2151 @subcmd{/MEDIAN} subcommand. If it is not given, the median is imputed from the
2152 union of all the samples.
2154 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
2155 keyword @code{BY} must come next, and then the grouping variable. Two values
2156 in parentheses should follow. If the first value is greater than the second,
2157 then a 2 sample test is performed using these two values to determine the groups.
2158 If however, the first variable is less than the second, then a @i{k} sample test is
2159 conducted and the group values used are all values encountered which lie in the
2160 range [@var{value1},@var{value2}].
2163 @node RUNS, SIGN, MEDIAN, NPAR TESTS
2164 @subsection Runs Test
2169 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
2172 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
2174 It works by examining the number of times a variable's value crosses a given threshold.
2175 The desired threshold must be specified within parentheses.
2176 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
2177 Following the threshold specification comes the list of variables whose values are to be
2180 The subcommand shows the number of runs, the asymptotic significance based on the
2183 @node SIGN, WILCOXON, RUNS, NPAR TESTS
2184 @subsection Sign Test
2189 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2192 The @subcmd{/SIGN} subcommand tests for differences between medians of the
2194 The test does not make any assumptions about the
2195 distribution of the data.
2197 If the @code{WITH} keyword is omitted, then tests for all
2198 combinations of the listed variables are performed.
2199 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
2200 is also given, then the number of variables preceding @code{WITH}
2201 must be the same as the number following it.
2202 In this case, tests for each respective pair of variables are
2204 If the @code{WITH} keyword is given, but the
2205 @code{(PAIRED)} keyword is omitted, then tests for each combination
2206 of variable preceding @code{WITH} against variable following
2207 @code{WITH} are performed.
2209 @node WILCOXON, , SIGN, NPAR TESTS
2210 @subsection Wilcoxon Matched Pairs Signed Ranks Test
2212 @cindex wilcoxon matched pairs signed ranks test
2215 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
2218 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
2220 The test does not make any assumptions about the variances of the samples.
2221 It does however assume that the distribution is symmetrical.
2223 If the @subcmd{WITH} keyword is omitted, then tests for all
2224 combinations of the listed variables are performed.
2225 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
2226 is also given, then the number of variables preceding @subcmd{WITH}
2227 must be the same as the number following it.
2228 In this case, tests for each respective pair of variables are
2230 If the @subcmd{WITH} keyword is given, but the
2231 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
2232 of variable preceding @subcmd{WITH} against variable following
2233 @subcmd{WITH} are performed.
2235 @node T-TEST, ONEWAY, NPAR TESTS, Statistics
2242 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
2243 /CRITERIA=CI(@var{confidence})
2247 TESTVAL=@var{test_value}
2248 /VARIABLES=@var{var_list}
2251 (Independent Samples mode.)
2252 GROUPS=var(@var{value1} [, @var{value2}])
2253 /VARIABLES=@var{var_list}
2256 (Paired Samples mode.)
2257 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
2262 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
2264 It operates in one of three modes:
2266 @item One Sample mode.
2267 @item Independent Groups mode.
2272 Each of these modes are described in more detail below.
2273 There are two optional subcommands which are common to all modes.
2275 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
2276 in the tests. The default value is 0.95.
2279 The @cmd{MISSING} subcommand determines the handling of missing
2281 If @subcmd{INCLUDE} is set, then user-missing values are included in the
2282 calculations, but system-missing values are not.
2283 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2284 values are excluded as well as system-missing values.
2285 This is the default.
2287 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
2288 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
2289 @subcmd{/GROUPS} subcommands contains a missing value.
2290 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
2291 which they would be needed. This is the default.
2295 * One Sample Mode:: Testing against a hypothesized mean
2296 * Independent Samples Mode:: Testing two independent groups for equal mean
2297 * Paired Samples Mode:: Testing two interdependent groups for equal mean
2300 @node One Sample Mode, Independent Samples Mode, T-TEST, T-TEST
2301 @subsection One Sample Mode
2303 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
2304 This mode is used to test a population mean against a hypothesized
2306 The value given to the @subcmd{TESTVAL} subcommand is the value against
2307 which you wish to test.
2308 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
2309 tell @pspp{} which variables you wish to test.
2311 @subsubsection Example - One Sample T-test
2313 A researcher wishes to know whether the weight of persons in a population
2314 is different from the national average.
2315 The samples are drawn from the population under investigation and recorded
2316 in the file @file{physiology.sav}.
2317 From the Department of Health, she
2318 knows that the national average weight of healthy adults is 76.8kg.
2319 Accordingly the @subcmd{TESTVAL} is set to 76.8.
2320 The null hypothesis therefore is that the mean average weight of the
2321 population from which the sample was drawn is 76.8kg.
2323 As previously noted (@pxref{Identifying incorrect data}), one
2324 sample in the dataset contains a weight value
2325 which is clearly incorrect. So this is excluded from the analysis
2326 using the @cmd{SELECT} command.
2328 @float Example, one-sample-t:ex
2329 @psppsyntax {one-sample-t.sps}
2330 @caption {Running a one sample T-Test after excluding all non-positive values}
2333 @float Screenshot, one-sample-t:scr
2334 @psppimage {one-sample-t}
2335 @caption {Using the One Sample T-Test dialog box to test @exvar{weight} for a mean of 76.8kg}
2339 @ref{one-sample-t:res} shows that the mean of our sample differs from the test value
2340 by -1.40kg. However the significance is very high (0.610). So one cannot
2341 reject the null hypothesis, and must conclude there is not enough evidence
2342 to suggest that the mean weight of the persons in our population is different
2345 @float Results, one-sample-t:res
2346 @psppoutput {one-sample-t}
2347 @caption {The results of a one sample T-test of @exvar{weight} using a test value of 76.8kg}
2350 @node Independent Samples Mode, Paired Samples Mode, One Sample Mode, T-TEST
2351 @subsection Independent Samples Mode
2353 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
2355 This mode is used to test whether two groups of values have the
2356 same population mean.
2357 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
2358 tell @pspp{} the dependent variables you wish to test.
2360 The variable given in the @subcmd{GROUPS} subcommand is the independent
2361 variable which determines to which group the samples belong.
2362 The values in parentheses are the specific values of the independent
2363 variable for each group.
2364 If the parentheses are omitted and no values are given, the default values
2365 of 1.0 and 2.0 are assumed.
2367 If the independent variable is numeric,
2368 it is acceptable to specify only one value inside the parentheses.
2369 If you do this, cases where the independent variable is
2370 greater than or equal to this value belong to the first group, and cases
2371 less than this value belong to the second group.
2372 When using this form of the @subcmd{GROUPS} subcommand, missing values in
2373 the independent variable are excluded on a listwise basis, regardless
2374 of whether @subcmd{/MISSING=LISTWISE} was specified.
2376 @subsubsection Example - Independent Samples T-test
2378 A researcher wishes to know whether within a population, adult males
2379 are taller than adult females.
2380 The samples are drawn from the population under investigation and recorded
2381 in the file @file{physiology.sav}.
2383 As previously noted (@pxref{Identifying incorrect data}), one
2384 sample in the dataset contains a height value
2385 which is clearly incorrect. So this is excluded from the analysis
2386 using the @cmd{SELECT} command.
2389 @float Example, indepdendent-samples-t:ex
2390 @psppsyntax {independent-samples-t.sps}
2391 @caption {Running a independent samples T-Test after excluding all observations less than 200kg}
2395 The null hypothesis is that both males and females are on average
2398 @float Screenshot, independent-samples-t:scr
2399 @psppimage {independent-samples-t}
2400 @caption {Using the Independent Sample T-test dialog, to test for differences of @exvar{height} between values of @exvar{sex}}
2404 In this case, the grouping variable is @exvar{sex}, so this is entered
2405 as the variable for the @subcmd{GROUP} subcommand. The group values are 0 (male) and
2408 If you are running the proceedure using syntax, then you need to enter
2409 the values corresponding to each group within parentheses.
2410 If you are using the graphic user interface, then you have to open
2411 the ``Define Groups'' dialog box and enter the values corresponding
2412 to each group as shown in @ref{define-groups-t:scr}. If, as in this case, the dataset has defined value
2413 labels for the group variable, then you can enter them by label
2416 @float Screenshot, define-groups-t:scr
2417 @psppimage {define-groups-t}
2418 @caption {Setting the values of the grouping variable for an Independent Samples T-test}
2421 From @ref{independent-samples-t:res}, one can clearly see that the @emph{sample} mean height
2422 is greater for males than for females. However in order to see if this
2423 is a significant result, one must consult the T-Test table.
2425 The T-Test table contains two rows; one for use if the variance of the samples
2426 in each group may be safely assumed to be equal, and the second row
2427 if the variances in each group may not be safely assumed to be equal.
2429 In this case however, both rows show a 2-tailed significance less than 0.001 and
2430 one must therefore reject the null hypothesis and conclude that within
2431 the population the mean height of males and of females are unequal.
2433 @float Result, independent-samples-t:res
2434 @psppoutput {independent-samples-t}
2435 @caption {The results of an independent samples T-test of @exvar{height} by @exvar{sex}}
2438 @node Paired Samples Mode, , Independent Samples Mode, T-TEST
2439 @subsection Paired Samples Mode
2441 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
2442 Use this mode when repeated measures have been taken from the same
2444 If the @subcmd{WITH} keyword is omitted, then tables for all
2445 combinations of variables given in the @cmd{PAIRS} subcommand are
2447 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
2448 is also given, then the number of variables preceding @subcmd{WITH}
2449 must be the same as the number following it.
2450 In this case, tables for each respective pair of variables are
2452 In the event that the @subcmd{WITH} keyword is given, but the
2453 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
2454 of variable preceding @subcmd{WITH} against variable following
2455 @subcmd{WITH} are generated.
2458 @node ONEWAY, QUICK CLUSTER, T-TEST, Statistics
2462 @cindex analysis of variance
2467 [/VARIABLES = ] @var{var_list} BY @var{var}
2468 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
2469 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
2470 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
2471 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
2474 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
2475 variables factored by a single independent variable.
2476 It is used to compare the means of a population
2477 divided into more than two groups.
2479 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
2481 The list of variables must be followed by the @subcmd{BY} keyword and
2482 the name of the independent (or factor) variable.
2484 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
2485 ancillary information. The options accepted are:
2488 Displays descriptive statistics about the groups factored by the independent
2491 Displays the Levene test of Homogeneity of Variance for the
2492 variables and their groups.
2495 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
2496 differences between the groups.
2497 The subcommand must be followed by a list of numerals which are the
2498 coefficients of the groups to be tested.
2499 The number of coefficients must correspond to the number of distinct
2500 groups (or values of the independent variable).
2501 If the total sum of the coefficients are not zero, then @pspp{} will
2502 display a warning, but will proceed with the analysis.
2503 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
2504 to specify different contrast tests.
2505 The @subcmd{MISSING} subcommand defines how missing values are handled.
2506 If @subcmd{LISTWISE} is specified then cases which have missing values for
2507 the independent variable or any dependent variable are ignored.
2508 If @subcmd{ANALYSIS} is specified, then cases are ignored if the independent
2509 variable is missing or if the dependent variable currently being
2510 analysed is missing. The default is @subcmd{ANALYSIS}.
2511 A setting of @subcmd{EXCLUDE} means that variables whose values are
2512 user-missing are to be excluded from the analysis. A setting of
2513 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
2515 Using the @code{POSTHOC} subcommand you can perform multiple
2516 pairwise comparisons on the data. The following comparison methods
2520 Least Significant Difference.
2521 @item @subcmd{TUKEY}
2522 Tukey Honestly Significant Difference.
2523 @item @subcmd{BONFERRONI}
2525 @item @subcmd{SCHEFFE}
2527 @item @subcmd{SIDAK}
2530 The Games-Howell test.
2534 Use the optional syntax @code{ALPHA(@var{value})} to indicate that
2535 @cmd{ONEWAY} should perform the posthoc tests at a confidence level of
2536 @var{value}. If @code{ALPHA(@var{value})} is not specified, then the
2537 confidence level used is 0.05.
2539 @node QUICK CLUSTER, RANK, ONEWAY, Statistics
2540 @section QUICK CLUSTER
2541 @vindex QUICK CLUSTER
2543 @cindex K-means clustering
2547 QUICK CLUSTER @var{var_list}
2548 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]]
2549 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
2550 [/PRINT=@{INITIAL@} @{CLUSTER@}]
2551 [/SAVE[=[CLUSTER[(@var{membership_var})]] [DISTANCE[(@var{distance_var})]]]
2554 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
2555 dataset. This is useful when you wish to allocate cases into clusters
2556 of similar values and you already know the number of clusters.
2558 The minimum specification is @samp{QUICK CLUSTER} followed by the names
2559 of the variables which contain the cluster data. Normally you will also
2560 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
2561 number of clusters. If this is not specified, then @var{k} defaults to 2.
2563 If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select
2564 the initial clusters is used. This will provide for faster execution but
2565 less well separated initial clusters and hence possibly an inferior final
2569 @cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers.
2570 The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations.
2571 During classification, @pspp{} will continue iterating until until @var{max_iter}
2572 iterations have been done or the convergence criterion (see below) is fulfilled.
2573 The default value of @var{max_iter} is 2.
2575 If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers,
2576 no further update to the cluster centers is done. In this case, @var{max_iter}, if specified.
2579 The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used
2580 to set the convergence criterion. The value of convergence criterion is @var{epsilon}
2581 times the minimum distance between the @emph{initial} cluster centers. Iteration stops when
2582 the mean cluster distance between one iteration and the next
2583 is less than the convergence criterion. The default value of @var{epsilon} is zero.
2585 The @subcmd{MISSING} subcommand determines the handling of missing variables.
2586 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
2587 value and not as missing values.
2588 If @subcmd{EXCLUDE} is set, which is the default, user-missing
2589 values are excluded as well as system-missing values.
2591 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
2592 whenever any of the clustering variables contains a missing value.
2593 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
2594 clustering variables contain missing values. Otherwise it is clustered
2595 on the basis of the non-missing values.
2596 The default is @subcmd{LISTWISE}.
2598 The @subcmd{PRINT} subcommand requests additional output to be printed.
2599 If @subcmd{INITIAL} is set, then the initial cluster memberships will
2601 If @subcmd{CLUSTER} is set, the cluster memberships of the individual
2602 cases are displayed (potentially generating lengthy output).
2604 You can specify the subcommand @subcmd{SAVE} to ask that each case's cluster membership
2605 and the euclidean distance between the case and its cluster center be saved to
2606 a new variable in the active dataset. To save the cluster membership use the
2607 @subcmd{CLUSTER} keyword and to save the distance use the @subcmd{DISTANCE} keyword.
2608 Each keyword may optionally be followed by a variable name in parentheses to specify
2609 the new variable which is to contain the saved parameter. If no variable name is specified,
2610 then PSPP will create one.
2612 @node RANK, RELIABILITY, QUICK CLUSTER, Statistics
2618 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
2619 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
2620 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
2622 /MISSING=@{EXCLUDE,INCLUDE@}
2624 /RANK [INTO @var{var_list}]
2625 /NTILES(k) [INTO @var{var_list}]
2626 /NORMAL [INTO @var{var_list}]
2627 /PERCENT [INTO @var{var_list}]
2628 /RFRACTION [INTO @var{var_list}]
2629 /PROPORTION [INTO @var{var_list}]
2630 /N [INTO @var{var_list}]
2631 /SAVAGE [INTO @var{var_list}]
2634 The @cmd{RANK} command ranks variables and stores the results into new
2637 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
2638 more variables whose values are to be ranked.
2639 After each variable, @samp{A} or @samp{D} may appear, indicating that
2640 the variable is to be ranked in ascending or descending order.
2641 Ascending is the default.
2642 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
2643 which are to serve as group variables.
2644 In this case, the cases are gathered into groups, and ranks calculated
2647 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
2648 default is to take the mean value of all the tied cases.
2650 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
2651 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
2652 functions are requested.
2654 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
2655 variables created should appear in the output.
2657 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
2658 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
2659 If none are given, then the default is RANK.
2660 The @subcmd{NTILES} subcommand must take an integer specifying the number of
2661 partitions into which values should be ranked.
2662 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
2663 variables which are the variables to be created and receive the rank
2664 scores. There may be as many variables specified as there are
2665 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
2666 then the variable names are automatically created.
2668 The @subcmd{MISSING} subcommand determines how user missing values are to be
2669 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
2670 user-missing are to be excluded from the rank scores. A setting of
2671 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
2673 @include regression.texi
2676 @node RELIABILITY, ROC, RANK, Statistics
2677 @section RELIABILITY
2682 /VARIABLES=@var{var_list}
2683 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
2684 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
2685 /SUMMARY=@{TOTAL,ALL@}
2686 /MISSING=@{EXCLUDE,INCLUDE@}
2689 @cindex Cronbach's Alpha
2690 The @cmd{RELIABILITY} command performs reliability analysis on the data.
2692 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
2693 upon which analysis is to be performed.
2695 The @subcmd{SCALE} subcommand determines the variables for which
2696 reliability is to be calculated. If @subcmd{SCALE} is omitted, then analysis for
2697 all variables named in the @subcmd{VARIABLES} subcommand are used.
2698 Optionally, the @var{name} parameter may be specified to set a string name
2701 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
2702 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
2703 then the variables are divided into 2 subsets. An optional parameter
2704 @var{n} may be given, to specify how many variables to be in the first subset.
2705 If @var{n} is omitted, then it defaults to one half of the variables in the
2706 scale, or one half minus one if there are an odd number of variables.
2707 The default model is @subcmd{ALPHA}.
2709 By default, any cases with user missing, or system missing values for
2710 any variables given in the @subcmd{VARIABLES} subcommand are omitted
2711 from the analysis. The @subcmd{MISSING} subcommand determines whether
2712 user missing values are included or excluded in the analysis.
2714 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
2715 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
2716 analysis tested against the totals.
2718 @subsection Example - Reliability
2720 Before analysing the results of a survey -- particularly for a multiple choice survey --
2721 it is desireable to know whether the respondents have considered their answers
2722 or simply provided random answers.
2724 In the following example the survey results from the file @file{hotel.sav} are used.
2725 All five survey questions are included in the reliability analysis.
2726 However, before running the analysis, the data must be preprocessed.
2727 An examination of the survey questions reveals that two questions, @i{viz:} v3 and v5
2728 are negatively worded, whereas the others are positively worded.
2729 All questions must be based upon the same scale for the analysis to be meaningful.
2730 One could use the @cmd{RECODE} command (@pxref{RECODE}), however a simpler way is
2731 to use @cmd{COMPUTE} (@pxref{COMPUTE}) and this is what is done in @ref{reliability:ex}.
2733 @float Example, reliability:ex
2734 @psppsyntax {reliability.sps}
2735 @caption {Investigating the reliability of survey responses}
2738 In this case, all variables in the data set are used. So we can use the special
2739 keyword @samp{ALL} (@pxref{BNF}).
2741 @float Screenshot, reliability:src
2742 @psppimage {reliability}
2743 @caption {Reliability dialog box with all variables selected}
2746 @ref{reliability:res} shows that Cronbach's Alpha is 0.11 which is a value normally considered too
2747 low to indicate consistency within the data. This is possibly due to the small number of
2748 survey questions. The survey should be redesigned before serious use of the results are
2751 @float Result, reliability:res
2752 @psppoutput {reliability}
2753 @caption {The results of the reliability command on @file{hotel.sav}}
2757 @node ROC, , RELIABILITY, Statistics
2761 @cindex Receiver Operating Characteristic
2762 @cindex Area under curve
2765 ROC @var{var_list} BY @var{state_var} (@var{state_value})
2766 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
2767 /PRINT = [ SE ] [ COORDINATES ]
2768 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
2769 [ TESTPOS (@{LARGE,SMALL@}) ]
2770 [ CI (@var{confidence}) ]
2771 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
2772 /MISSING=@{EXCLUDE,INCLUDE@}
2776 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
2777 of a dataset, and to estimate the area under the curve.
2778 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
2780 The mandatory @var{var_list} is the list of predictor variables.
2781 The variable @var{state_var} is the variable whose values represent the actual states,
2782 and @var{state_value} is the value of this variable which represents the positive state.
2784 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
2785 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
2786 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
2787 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
2788 By default, the curve is drawn with no reference line.
2790 The optional subcommand @subcmd{PRINT} determines which additional
2791 tables should be printed. Two additional tables are available. The
2792 @subcmd{SE} keyword says that standard error of the area under the
2793 curve should be printed as well as the area itself. In addition, a
2794 p-value for the null hypothesis that the area under the curve equals
2795 0.5 is printed. The @subcmd{COORDINATES} keyword says that a
2796 table of coordinates of the @subcmd{ROC} curve should be printed.
2798 The @subcmd{CRITERIA} subcommand has four optional parameters:
2800 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
2801 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
2802 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
2804 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
2805 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
2807 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
2809 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
2810 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
2811 exponential distribution estimate.
2812 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
2813 equal to the number of negative actual states.
2814 The default is @subcmd{FREE}.
2816 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
2819 The @subcmd{MISSING} subcommand determines whether user missing values are to
2820 be included or excluded in the analysis. The default behaviour is to
2822 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
2823 or if the variable @var{state_var} is missing, then the entire case is
2826 @c LocalWords: subcmd subcommand