1 @node Statistics, Utilities, Conditionals and Looping, Top
4 This chapter documents the statistical procedures that PSPP supports so
7 @c If you add any new commands, then don't forget to remove the entry in
8 @c not-implemented.texi
11 * DESCRIPTIVES:: Descriptive statistics.
12 * FREQUENCIES:: Frequency tables.
13 * EXAMINE:: Testing data for normality.
14 * CROSSTABS:: Crosstabulation tables.
15 * T-TEST:: Test hypotheses about means.
16 * ONEWAY:: One way analysis of variance.
17 * RANK:: Compute rank scores.
18 * REGRESSION:: Linear regression.
21 @node DESCRIPTIVES, FREQUENCIES, Statistics, Statistics
28 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
29 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
31 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
32 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
33 SESKEWNESS,SEKURTOSIS@}
34 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
35 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
39 The @cmd{DESCRIPTIVES} procedure reads the active file and outputs
41 statistics requested by the user. In addition, it can optionally
44 The VARIABLES subcommand, which is required, specifies the list of
45 variables to be analyzed. Keyword VARIABLES is optional.
47 All other subcommands are optional:
49 The MISSING subcommand determines the handling of missing variables. If
50 INCLUDE is set, then user-missing values are included in the
51 calculations. If NOINCLUDE is set, which is the default, user-missing
52 values are excluded. If VARIABLE is set, then missing values are
53 excluded on a variable by variable basis; if LISTWISE is set, then
54 the entire case is excluded whenever any value in that case has a
55 system-missing or, if INCLUDE is set, user-missing value.
57 The FORMAT subcommand affects the output format. Currently the
58 LABELS/NOLABELS and NOINDEX/INDEX settings are not used. When SERIAL is
59 set, both valid and missing number of cases are listed in the output;
60 when NOSERIAL is set, only valid cases are listed.
62 The SAVE subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
63 the specified variables. The Z scores are saved to new variables.
64 Variable names are generated by trying first the original variable name
65 with Z prepended and truncated to a maximum of 8 characters, then the
66 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
67 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
68 variable names can be specified explicitly on VARIABLES in the variable
69 list by enclosing them in parentheses after each variable.
71 The STATISTICS subcommand specifies the statistics to be displayed:
75 All of the statistics below.
79 Standard error of the mean.
85 Kurtosis and standard error of the kurtosis.
87 Skewness and standard error of the skewness.
97 Mean, standard deviation of the mean, minimum, maximum.
99 Standard error of the kurtosis.
101 Standard error of the skewness.
104 The SORT subcommand specifies how the statistics should be sorted. Most
105 of the possible values should be self-explanatory. NAME causes the
106 statistics to be sorted by name. By default, the statistics are listed
107 in the order that they are specified on the VARIABLES subcommand. The A
108 and D settings request an ascending or descending sort order,
111 @node FREQUENCIES, EXAMINE, DESCRIPTIVES, Statistics
118 /FORMAT=@{TABLE,NOTABLE,LIMIT(limit)@}
119 @{STANDARD,CONDENSE,ONEPAGE[(onepage_limit)]@}
121 @{AVALUE,DVALUE,AFREQ,DFREQ@}
124 /MISSING=@{EXCLUDE,INCLUDE@}
125 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
126 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
127 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
129 /PERCENTILES=percent@dots{}
131 (These options are not currently implemented.)
138 /VARIABLES=var_list (low,high)@dots{}
141 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
143 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
144 (including median and mode) and percentiles.
146 In the future, @cmd{FREQUENCIES} will also support graphical output in the
147 form of bar charts and histograms. In addition, it will be able to
148 support percentiles for grouped data.
150 The VARIABLES subcommand is the only required subcommand. Specify the
151 variables to be analyzed. In most cases, this is all that is required.
152 This is known as @dfn{general mode}.
154 Occasionally, one may want to invoke a special mode called @dfn{integer
155 mode}. Normally, in general mode, PSPP will automatically determine
156 what values occur in the data. In integer mode, the user specifies the
157 range of values that the data assumes. To invoke this mode, specify a
158 range of data values in parentheses, separated by a comma. Data values
159 inside the range are truncated to the nearest integer, then assigned to
160 that value. If values occur outside this range, they are discarded.
162 The FORMAT subcommand controls the output format. It has several
167 TABLE, the default, causes a frequency table to be output for every
168 variable specified. NOTABLE prevents them from being output. LIMIT
169 with a numeric argument causes them to be output except when there are
170 more than the specified number of values in the table.
173 STANDARD frequency tables contain more complete information, but also to
174 take up more space on the printed page. CONDENSE frequency tables are
175 less informative but take up less space. ONEPAGE with a numeric
176 argument will output standard frequency tables if there are the
177 specified number of values or less, condensed tables otherwise. ONEPAGE
178 without an argument defaults to a threshold of 50 values.
181 LABELS causes value labels to be displayed in STANDARD frequency
182 tables. NOLABLES prevents this.
185 Normally frequency tables are sorted in ascending order by value. This
186 is AVALUE. DVALUE tables are sorted in descending order by value.
187 AFREQ and DFREQ tables are sorted in ascending and descending order,
188 respectively, by frequency count.
191 SINGLE spaced frequency tables are closely spaced. DOUBLE spaced
192 frequency tables have wider spacing.
195 OLDPAGE and NEWPAGE are not currently used.
198 The MISSING subcommand controls the handling of user-missing values.
199 When EXCLUDE, the default, is set, user-missing values are not included
200 in frequency tables or statistics. When INCLUDE is set, user-missing
201 are included. System-missing values are never included in statistics,
202 but are listed in frequency tables.
204 The available STATISTICS are the same as available in @cmd{DESCRIPTIVES}
205 (@pxref{DESCRIPTIVES}), with the addition of MEDIAN, the data's median
206 value, and MODE, the mode. (If there are multiple modes, the smallest
207 value is reported.) By default, the mean, standard deviation of the
208 mean, minimum, and maximum are reported for each variable.
210 PERCENTILES causes the specified percentiles to be reported.
211 The percentiles should be presented at a list of numbers between 0
213 The NTILES subcommand causes the percentiles to be reported at the
214 boundaries of the data set divided into the specified number of ranges.
215 For instance, @code{/NTILES=4} would cause quartiles to be reported.
218 @node EXAMINE, CROSSTABS, FREQUENCIES, Statistics
219 @comment node-name, next, previous, up
223 @cindex Normality, testing for
227 VARIABLES=var_list [BY factor_list ]
228 /STATISTICS=@{DESCRIPTIVES, EXTREME[(n)], ALL, NONE@}
229 /PLOT=@{STEMLEAF, BOXPLOT, NPPLOT, SPREADLEVEL(n), HISTOGRAM,
232 /COMPARE=@{GROUPS,VARIABLES@}
233 /ID=@{case_number, var_name@}
235 /PERCENTILE=[value_list]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
236 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
237 [@{NOREPORT,REPORT@}]
241 The @cmd{EXAMINE} command is used to test how closely a distribution is to a
242 normal distribution. It also shows you outliers and extreme values.
244 The VARIABLES subcommand specifies the dependent variables and the
245 independent variable to use as factors for the analysis. Variables
246 listed before the first BY keyword are the dependent variables.
247 The dependent variables may optionally be followed by a list of
248 factors which tell PSPP how to break down the analysis for each
249 dependent variable. The format for each factor is
255 The STATISTICS subcommand specifies the analysis to be done.
256 DESCRIPTIVES will produce a table showing some parametric and
257 non-parametrics statistics. EXTREME produces a table showing extreme
258 values of the dependent variable. A number in parentheses determines
259 how many upper and lower extremes to show. The default number is 5.
262 The PLOT subcommand specifies which plots are to be produced if any.
264 The COMPARE subcommand is only relevant if producing boxplots, and it is only
265 useful there is more than one dependent variable and at least one factor. If
266 /COMPARE=GROUPS is specified, then one plot per dependent variable is produced,
267 containing boxplots for all the factors.
268 If /COMPARE=VARIABLES is specified, then one plot per factor is produced, each
269 each containing one boxplot per dependent variable.
270 If the /COMPARE subcommand is ommitted, then PSPP uses the default value of
273 The CINTERVAL subcommand specifies the confidence interval to use in
274 calculation of the descriptives command. The default it 95%.
276 The PERCENTILES subcommand specifies which percentiles are to be calculated,
277 and which algorithm to use for calculating them. The default is to
278 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
281 The TOTAL and NOTOTAL subcommands are mutually exclusive. If NOTOTAL
282 is given and factors have been specified in the VARIABLES subcommand,
283 then then statistics for the unfactored dependent variables are
284 produced in addition to the factored variables. If there are no
285 factors specified then TOTAL and NOTOTAL have no effect.
288 If many dependent variable are given, or factors are given for which
289 there are many distinct values, then @cmd{EXAMINE} will produce a very
290 large quantity of output.
293 @node CROSSTABS, T-TEST, EXAMINE, Statistics
299 /TABLES=var_list BY var_list [BY var_list]@dots{}
300 /MISSING=@{TABLE,INCLUDE,REPORT@}
301 /WRITE=@{NONE,CELLS,ALL@}
302 /FORMAT=@{TABLES,NOTABLES@}
303 @{LABELS,NOLABELS,NOVALLABS@}
308 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
309 ASRESIDUAL,ALL,NONE@}
310 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
311 KAPPA,ETA,CORR,ALL,NONE@}
314 /VARIABLES=var_list (low,high)@dots{}
317 The @cmd{CROSSTABS} procedure displays crosstabulation
318 tables requested by the user. It can calculate several statistics for
319 each cell in the crosstabulation tables. In addition, a number of
320 statistics can be calculated for each table itself.
322 The TABLES subcommand is used to specify the tables to be reported. Any
323 number of dimensions is permitted, and any number of variables per
324 dimension is allowed. The TABLES subcommand may be repeated as many
325 times as needed. This is the only required subcommand in @dfn{general
328 Occasionally, one may want to invoke a special mode called @dfn{integer
329 mode}. Normally, in general mode, PSPP automatically determines
330 what values occur in the data. In integer mode, the user specifies the
331 range of values that the data assumes. To invoke this mode, specify the
332 VARIABLES subcommand, giving a range of data values in parentheses for
333 each variable to be used on the TABLES subcommand. Data values inside
334 the range are truncated to the nearest integer, then assigned to that
335 value. If values occur outside this range, they are discarded. When it
336 is present, the VARIABLES subcommand must precede the TABLES
339 In general mode, numeric and string variables may be specified on
340 TABLES. Although long string variables are allowed, only their
341 initial short-string parts are used. In integer mode, only numeric
342 variables are allowed.
344 The MISSING subcommand determines the handling of user-missing values.
345 When set to TABLE, the default, missing values are dropped on a table by
346 table basis. When set to INCLUDE, user-missing values are included in
347 tables and statistics. When set to REPORT, which is allowed only in
348 integer mode, user-missing values are included in tables but marked with
349 an @samp{M} (for ``missing'') and excluded from statistical
352 Currently the WRITE subcommand is ignored.
354 The FORMAT subcommand controls the characteristics of the
355 crosstabulation tables to be displayed. It has a number of possible
360 TABLES, the default, causes crosstabulation tables to be output.
361 NOTABLES suppresses them.
364 LABELS, the default, allows variable labels and value labels to appear
365 in the output. NOLABELS suppresses them. NOVALLABS displays variable
366 labels but suppresses value labels.
369 PIVOT, the default, causes each TABLES subcommand to be displayed in a
370 pivot table format. NOPIVOT causes the old-style crosstabulation format
374 AVALUE, the default, causes values to be sorted in ascending order.
375 DVALUE asserts a descending sort order.
378 INDEX/NOINDEX is currently ignored.
381 BOX/NOBOX is currently ignored.
384 The CELLS subcommand controls the contents of each cell in the displayed
385 crosstabulation table. The possible settings are:
401 Standardized residual.
403 Adjusted standardized residual.
407 Suppress cells entirely.
410 @samp{/CELLS} without any settings specified requests COUNT, ROW,
411 COLUMN, and TOTAL. If CELLS is not specified at all then only COUNT
414 The STATISTICS subcommand selects statistics for computation:
418 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
419 correction, linear-by-linear association.
423 Contingency coefficient.
427 Uncertainty coefficient.
443 Spearman correlation, Pearson's r.
450 Selected statistics are only calculated when appropriate for the
451 statistic. Certain statistics require tables of a particular size, and
452 some statistics are calculated only in integer mode.
454 @samp{/STATISTICS} without any settings selects CHISQ. If the
455 STATISTICS subcommand is not given, no statistics are calculated.
457 @strong{Please note:} Currently the implementation of CROSSTABS has the
462 Pearson's R (but not Spearman) is off a little.
464 T values for Spearman's R and Pearson's R are wrong.
466 Significance of symmetric and directional measures is not calculated.
468 Asymmetric ASEs and T values for lambda are wrong.
470 ASE of Goodman and Kruskal's tau is not calculated.
472 ASE of symmetric somers' d is wrong.
474 Approximate T of uncertainty coefficient is wrong.
477 Fixes for any of these deficiencies would be welcomed.
479 @node T-TEST, ONEWAY, CROSSTABS, Statistics
480 @comment node-name, next, previous, up
486 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
487 /CRITERIA=CIN(confidence)
495 (Independent Samples mode.)
496 GROUPS=var(value1 [, value2])
500 (Paired Samples mode.)
501 PAIRS=var_list [WITH var_list [(PAIRED)] ]
506 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
508 It operates in one of three modes:
510 @item One Sample mode.
511 @item Independent Groups mode.
516 Each of these modes are described in more detail below.
517 There are two optional subcommands which are common to all modes.
519 The @cmd{/CRITERIA} subcommand tells PSPP the confidence interval used
520 in the tests. The default value is 0.95.
523 The @cmd{MISSING} subcommand determines the handling of missing
525 If INCLUDE is set, then user-missing values are included in the
526 calculations, but system-missing values are not.
527 If EXCLUDE is set, which is the default, user-missing
528 values are excluded as well as system-missing values.
531 If LISTWISE is set, then the entire case is excluded from analysis
532 whenever any variable specified in the @cmd{/VARIABLES}, @cmd{/PAIRS} or
533 @cmd{/GROUPS} subcommands contains a missing value.
534 If ANALYSIS is set, then missing values are excluded only in the analysis for
535 which they would be needed. This is the default.
539 * One Sample Mode:: Testing against a hypothesised mean
540 * Independent Samples Mode:: Testing two independent groups for equal mean
541 * Paired Samples Mode:: Testing two interdependent groups for equal mean
544 @node One Sample Mode, Independent Samples Mode, T-TEST, T-TEST
545 @subsection One Sample Mode
547 The @cmd{TESTVAL} subcommand invokes the One Sample mode.
548 This mode is used to test a population mean against a hypothesised
550 The value given to the @cmd{TESTVAL} subcommand is the value against
551 which you wish to test.
552 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
553 tell PSPP which variables you wish to test.
555 @node Independent Samples Mode, Paired Samples Mode, One Sample Mode, T-TEST
556 @comment node-name, next, previous, up
557 @subsection Independent Samples Mode
559 The @cmd{GROUPS} subcommand invokes Independent Samples mode or
561 This mode is used to test whether two groups of values have the
562 same population mean.
563 In this mode, you must also use the @cmd{/VARIABLES} subcommand to
564 tell PSPP the dependent variables you wish to test.
566 The variable given in the @cmd{GROUPS} subcommand is the independent
567 variable which determines to which group the samples belong.
568 The values in parentheses are the specific values of the independent
569 variable for each group.
570 If the parentheses are omitted and no values are given, the default values
571 of 1.0 and 2.0 are assumed.
573 If the independent variable is numeric,
574 it is acceptable to specify only one value inside the parentheses.
575 If you do this, cases where the independent variable is
576 less than or equal to this value belong to the first group, and cases
577 greater than this value belong to the second group.
578 When using this form of the @cmd{GROUPS} subcommand, missing values in
579 the independent variable are excluded on a listwise basis, regardless
580 of whether @cmd{/MISSING=LISTWISE} was specified.
583 @node Paired Samples Mode, , Independent Samples Mode, T-TEST
584 @comment node-name, next, previous, up
585 @subsection Paired Samples Mode
587 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
588 Use this mode when repeated measures have been taken from the same
590 If the the @code{WITH} keyword is omitted, then tables for all
591 combinations of variables given in the @cmd{PAIRS} subcommand are
593 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
594 is also given, then the number of variables preceding @code{WITH}
595 must be the same as the number following it.
596 In this case, tables for each respective pair of variables are
598 In the event that the @code{WITH} keyword is given, but the
599 @code{(PAIRED)} keyword is omitted, then tables for each combination
600 of variable preceding @code{WITH} against variable following
601 @code{WITH} are generated.
604 @node ONEWAY, RANK, T-TEST, Statistics
605 @comment node-name, next, previous, up
609 @cindex analysis of variance
614 [/VARIABLES = ] var_list BY var
615 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
616 /CONTRASTS= value1 [, value2] ... [,valueN]
617 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
621 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
622 variables factored by a single independent variable.
623 It is used to compare the means of a population
624 divided into more than two groups.
626 The variables to be analysed should be given in the @code{VARIABLES}
628 The list of variables must be followed by the @code{BY} keyword and
629 the name of the independent (or factor) variable.
631 You can use the @code{STATISTICS} subcommand to tell PSPP to display
632 ancilliary information. The options accepted are:
635 Displays descriptive statistics about the groups factored by the independent
638 Displays the Levene test of Homogeneity of Variance for the
639 variables and their groups.
642 The @code{CONTRASTS} subcommand is used when you anticipate certain
643 differences between the groups.
644 The subcommand must be followed by a list of numerals which are the
645 coefficients of the groups to be tested.
646 The number of coefficients must correspond to the number of distinct
647 groups (or values of the independent variable).
648 If the total sum of the coefficients are not zero, then PSPP will
649 display a warning, but will proceed with the analysis.
650 The @code{CONTRASTS} subcommand may be given up to 10 times in order
651 to specify different contrast tests.
654 @node RANK, REGRESSION, ONEWAY, Statistics
655 @comment node-name, next, previous, up
663 [VARIABLES=] var_list [@{A,D@}] [BY var_list]
664 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
665 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
667 /MISSING=@{EXCLUDE,INCLUDE@}
669 /RANK [INTO var_list]
670 /NTILES(k) [INTO var_list]
671 /NORMAL [INTO var_list]
672 /PERCENT [INTO var_list]
673 /RFRACTION [INTO var_list]
674 /PROPORTION [INTO var_list]
676 /SAVAGE [INTO var_list]
679 The @cmd{RANK} command ranks variables and stores the results into new
682 The VARIABLES subcommand, which is mandatory, specifies one or
683 more variables whose values are to be ranked.
684 After each variable, @samp{A} or @samp{D} may appear, indicating that
685 the variable is to be ranked in ascending or descending order.
686 Ascending is the default.
687 If a BY keyword appears, it should be followed by a list of variables
688 which are to serve as group variables.
689 In this case, the cases are gathered into groups, and ranks calculated
692 The TIES subcommand specifies how tied values are to be treated. The
693 default is to take the mean value of all the tied cases.
695 The FRACTION subcommand specifies how proportional ranks are to be
696 calculated. This only has any effect if NORMAL or PROPORTIONAL rank
697 functions are requested.
699 The PRINT subcommand may be used to specify that a summary of the rank
700 variables created should appear in the output.
702 The function subcommands are RANK, NTILES, NORMAL, PERCENT, RFRACTION,
703 PROPORTION and SAVAGE. Any number of function subcommands may appear.
704 If none are given, then the default is RANK.
705 The NTILES subcommand must take an integer specifying the number of
706 partitions into which values should be ranked.
707 Each subcommand may be followed by the INTO keyword and a list of
708 variables which are the variables to be created and receive the rank
709 scores. There may be as many variables specified as there are
710 variables named on the VARIABLES subcommand. If fewer are specified,
711 then the variable names are automatically created.
713 The MISSING subcommand determines how user missing values are to be
714 treated. A setting of EXCLUDE means that variables whose values are
715 user-missing are to be excluded from the rank scores. A setting of
716 INCLUDE means they are to be included. The default is EXCLUDE.
718 @include regression.texi