Statistics
**********

This chapter documents the statistical procedures that pspp supports so far.

DESCRIPTIVES
============

     DESCRIPTIVES
             /VARIABLES=VAR_LIST
             /MISSING={VARIABLE,LISTWISE} {INCLUDE,NOINCLUDE}
             /FORMAT={LABELS,NOLABELS} {NOINDEX,INDEX} {LINE,SERIAL}
             /SAVE
             /STATISTICS={ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
                          SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
                          SESKEWNESS,SEKURTOSIS}
             /SORT={NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
                    RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME}
                   {A,D}

The DESCRIPTIVES procedure reads the active dataset and outputs descriptive statistics requested by the user.  In addition, it can optionally compute Z-scores.

The VARIABLES subcommand, which is required, specifies the list of variables to be analyzed.  Keyword VARIABLES is optional.

All other subcommands are optional:

The MISSING subcommand determines the handling of missing variables.  If INCLUDE is set, then user-missing values are included in the calculations.  If NOINCLUDE is set, which is the default, user-missing values are excluded.  If VARIABLE is set, then missing values are excluded on a variable by variable basis; if LISTWISE is set, then the entire case is excluded whenever any value in that case has a system-missing or, if INCLUDE is set, user-missing value.

The FORMAT subcommand affects the output format.  Currently the LABELS/NOLABELS and NOINDEX/INDEX settings are not used. When SERIAL is set, both valid and missing number of cases are listed in the output; when NOSERIAL is set, only valid cases are listed.

The SAVE subcommand causes DESCRIPTIVES to calculate Z scores for all the specified variables.  The Z scores are saved to new variables. Variable names are generated by trying first the original variable name with Z prepended and truncated to a maximum of 8 characters, then the names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence.  In addition, Z score variable names can be specified explicitly on VARIABLES in the variable list by enclosing them in parentheses after each variable.

The STATISTICS subcommand specifies the statistics to be displayed:

ALL
     All of the statistics below.

MEAN
     Arithmetic mean.

SEMEAN
     Standard error of the mean.

STDDEV
     Standard deviation.

VARIANCE
     Variance.

KURTOSIS
     Kurtosis and standard error of the kurtosis.

SKEWNESS
     Skewness and standard error of the skewness.

RANGE
     Range.

MINIMUM
     Minimum value.

MAXIMUM
     Maximum value.

SUM
     Sum.

DEFAULT
     Mean, standard deviation of the mean, minimum, maximum.

SEKURTOSIS
     Standard error of the kurtosis.

SESKEWNESS
     Standard error of the skewness.

The SORT subcommand specifies how the statistics should be sorted.  Most of the possible values should be self-explanatory.  NAME causes the statistics to be sorted by name.  By default, the statistics are listed in the order that they are specified on the VARIABLES subcommand. The A and D settings request an ascending or descending sort order, respectively.

FREQUENCIES
===========

     FREQUENCIES
             /VARIABLES=VAR_LIST
             /FORMAT={TABLE,NOTABLE,LIMIT(LIMIT)}
                     {AVALUE,DVALUE,AFREQ,DFREQ}
             /MISSING={EXCLUDE,INCLUDE}
             /STATISTICS={DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
                          KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
                          SESKEWNESS,SEKURTOSIS,ALL,NONE}
             /NTILES=NTILES
             /PERCENTILES=percent...
             /HISTOGRAM=[MINIMUM(X_MIN)] [MAXIMUM(X_MAX)]
                        [{FREQ[(Y_MAX)],PERCENT[(Y_MAX)]}] [{NONORMAL,NORMAL}]
             /PIECHART=[MINIMUM(X_MIN)] [MAXIMUM(X_MAX)]
                       [{FREQ,PERCENT}] [{NOMISSING,MISSING}]

     (These options are not currently implemented.)
             /BARCHART=...
             /HBAR=...
             /GROUPED=...

The FREQUENCIES procedure outputs frequency tables for specified variables. FREQUENCIES can also calculate and display descriptive statistics (including median and mode) and percentiles, FREQUENCIES can also output histograms and pie charts.

The VARIABLES subcommand is the only required subcommand.  Specify the variables to be analyzed.

The FORMAT subcommand controls the output format.  It has several possible settings:

  subcmd TABLE, the default, causes a frequency table to be output for every variable specified.  NOTABLE prevents them from being output.  LIMIT with a numeric argument causes them to be output except when there are more than the specified number of values in the table.

  subcmd Normally frequency tables are sorted in ascending order by value.  This is AVALUE.  DVALUE tables are sorted in descending order by value. AFREQ and DFREQ tables are sorted in ascending and descending order, respectively, by frequency count.

The MISSING subcommand controls the handling of user-missing values. When EXCLUDE, the default, is set, user-missing values are not included in frequency tables or statistics.  When INCLUDE is set, user-missing are included.  System-missing values are never included in statistics, but are listed in frequency tables.

The available STATISTICS are the same as available in DESCRIPTIVES (see DESCRIPTIVES), with the addition of MEDIAN, the data's median value, and MODE, the mode.  (If there are multiple modes, the smallest value is reported.)  By default, the mean, standard deviation of the mean, minimum, and maximum are reported for each variable.

PERCENTILES causes the specified percentiles to be reported. The percentiles should  be presented at a list of numbers between 0 and 100 inclusive. The NTILES subcommand causes the percentiles to be reported at the boundaries of the data set divided into the specified number of ranges. For instance, /NTILES=4 would cause quartiles to be reported.

The HISTOGRAM subcommand causes the output to include a histogram for each specified numeric variable.  The X axis by default ranges from the minimum to the maximum value observed in the data, but the MINIMUM and MAXIMUM keywords can set an explicit range.  Specify NORMAL to superimpose a normal curve on the histogram.  Histograms are not created for string variables.

The PIECHART subcommand adds a pie chart for each variable to the data.  Each slice represents one value, with the size of the slice proportional to the value's frequency.  By default, all non-missing values are given slices.  The MINIMUM and MAXIMUM keywords can be used to limit the displayed slices to a given range of values.  The MISSING keyword adds slices for missing values.

The FREQ and PERCENT options on HISTOGRAM and PIECHART are accepted but not currently honoured.

EXAMINE
=======

     EXAMINE
             VARIABLES= VAR1 [VAR2] ... [VARN]
                [BY FACTOR1 [BY SUBFACTOR1]
                  [ FACTOR2 [BY SUBFACTOR2]]
                  ...
                  [ FACTOR3 [BY SUBFACTOR3]]
                 ]
             /STATISTICS={DESCRIPTIVES, EXTREME[(N)], ALL, NONE}
             /PLOT={BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(T)], ALL, NONE}
             /CINTERVAL P
             /COMPARE={GROUPS,VARIABLES}
             /ID=IDENTITY_VARIABLE
             /{TOTAL,NOTOTAL}
             /PERCENTILE=[PERCENTILES]={HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL }
             /MISSING={LISTWISE, PAIRWISE} [{EXCLUDE, INCLUDE}]
     		[{NOREPORT,REPORT}]

The EXAMINE command is used to perform exploratory data analysis. In particular, it is useful for testing how closely a distribution follows a normal distribution, and for finding outliers and extreme values.

The VARIABLES subcommand is mandatory. It specifies the dependent variables and optionally variables to use as factors for the analysis. Variables listed before the first BY keyword (if any) are the dependent variables. The dependent variables may optionally be followed by a list of factors which tell pspp how to break down the analysis for each dependent variable.

Following the dependent variables, factors may be specified. The factors (if desired) should be preceeded by a single BY keyword. The format for each factor is

     FACTORVAR [BY SUBFACTORVAR].

Each unique combination of the values of  FACTORVAR and SUBFACTORVAR divide the dataset into cells. Statistics will be calculated for each cell and for the entire dataset (unless NOTOTAL is given).

The STATISTICS subcommand specifies which statistics to show. DESCRIPTIVES will produce a table showing some parametric and non-parametrics statistics. EXTREME produces a table showing the extremities of each cell. A number in parentheses, N determines how many upper and lower extremities to show. The default number is 5.

The subcommands TOTAL and NOTOTAL are mutually exclusive. If TOTAL appears, then statistics will be produced for the entire dataset as well as for each cell. If NOTOTAL appears, then statistics will be produced only for the cells (unless no factor variables have been given). These subcommands have no effect if there have  been no factor variables specified.

The PLOT subcommand specifies which plots are to be produced if any. Available plots are HISTOGRAM, NPPLOT,  BOXPLOT and SPREADLEVEL. The first three can be used to visualise how closely each cell conforms to a normal distribution, whilst the spread vs. level plot can be useful to visualise how the variance of differs between factors. Boxplots will also show you the outliers and extreme values.

The SPREADLEVEL plot displays the interquartile range versus the median.  It takes an optional parameter T, which specifies how the data should be transformed prior to plotting. The given value T is a power to which the data is raised.  For example, if T is given as 2, then the data will be squared. Zero, however is a special value.  If T is 0 or is omitted, then data will be transformed by taking its natural logarithm instead of raising to the power of T.

The COMPARE subcommand is only relevant if producing boxplots, and it is only useful there is more than one dependent variable and at least one factor. If /COMPARE=GROUPS is specified, then one plot per dependent variable is produced, each of which contain boxplots for all the cells. If /COMPARE=VARIABLES is specified, then one plot per cell is produced, each containing one boxplot per dependent variable. If the /COMPARE subcommand is omitted, then pspp behaves as if /COMPARE=GROUPS were given.

The ID subcommand is relevant only if /PLOT=BOXPLOT or /STATISTICS=EXTREME has been given. If given, it shoule provide the name of a variable which is to be used to labels extreme values and outliers. Numeric or string variables are permissible. If the ID subcommand is not given, then the casenumber will be used for labelling.

The CINTERVAL subcommand specifies the confidence interval to use in calculation of the descriptives command.  The default is 95%.

The PERCENTILES subcommand specifies which percentiles are to be calculated, and which algorithm to use for calculating them.  The default is to calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the HAVERAGE algorithm.

The TOTAL and NOTOTAL subcommands are mutually exclusive.  If NOTOTAL is given and factors have been specified in the VARIABLES subcommand, then then statistics for the unfactored dependent variables are produced in addition to the factored variables.  If there are no factors specified then TOTAL and NOTOTAL have no effect.

The following example will generate descriptive statistics and histograms for two variables SCORE1 and SCORE2. Two factors are given, viz: GENDER and GENDER BY CULTURE. Therefore, the descriptives and histograms will be generated for each distinct  value of GENDER and for each distinct combination of the values of GENDER and RACE. Since the NOTOTAL keyword is given, statistics and histograms for SCORE1 and SCORE2 covering the  whole dataset are not produced.

     EXAMINE SCORE1 SCORE2 BY
             GENDER
             GENDER BY CULTURE
             /STATISTICS = DESCRIPTIVES
             /PLOT = HISTOGRAM
             /NOTOTAL.

Here is a second example showing how the examine command can be used to find extremities.

     EXAMINE HEIGHT WEIGHT BY
             GENDER
             /STATISTICS = EXTREME (3)
             /PLOT = BOXPLOT
             /COMPARE = GROUPS
             /ID = NAME.

In this example, we look at the height and weight of a sample of individuals and how they differ between male and female. A table showing the 3 largest and the 3 smallest values of HEIGHT and WEIGHT for each gender, and for the whole dataset will be shown. Boxplots will also be produced. Because /COMPARE = GROUPS was given, boxplots for male and female will be shown in the same graphic, allowing us to easily see the difference between the genders. Since the variable NAME was specified on the ID subcommand, this will be used to label the extreme values.

Warning! If many dependent variables are specified, or if factor variables are specified for which there are many distinct values, then EXAMINE will produce a very large quantity of output.

CORRELATIONS
============

     CORRELATIONS
          /VARIABLES = VAR_LIST [ WITH VAR_LIST ]
          [
           .
           .
           .
           /VARIABLES = VAR_LIST [ WITH VAR_LIST ]
           /VARIABLES = VAR_LIST [ WITH VAR_LIST ]
          ]

          [ /PRINT={TWOTAIL, ONETAIL} {SIG, NOSIG} ]
          [ /STATISTICS=DESCRIPTIVES XPROD ALL]
          [ /MISSING={PAIRWISE, LISTWISE} {INCLUDE, EXCLUDE} ]

The CORRELATIONS procedure produces tables of the Pearson correlation coefficient for a set of variables.  The significance of the coefficients are also given.

At least one VARIABLES subcommand is required. If the WITH keyword is used, then a non-square correlation table will be produced. The variables preceding WITH, will be used as the rows of the table, and the variables following will be the columns of the table. If no WITH subcommand is given, then a square, symmetrical table using all variables is produced.

The MISSING subcommand determines the handling of missing variables. If INCLUDE is set, then user-missing values are included in the calculations, but system-missing values are not. If EXCLUDE is set, which is the default, user-missing values are excluded as well as system-missing values.

If LISTWISE is set, then the entire case is excluded from analysis whenever any variable  specified in any /VARIABLES subcommand contains a missing value. If PAIRWISE is set, then a case is considered missing only if either of the values  for the particular coefficient are missing. The default is PAIRWISE.

The PRINT subcommand is used to control how the reported significance values are printed. If the TWOTAIL option is used, then a two-tailed test of significance is printed.  If the ONETAIL option is given, then a one-tailed test is used. The default is TWOTAIL.

If the NOSIG option is specified, then correlation coefficients with significance less than 0.05 are highlighted. If SIG is specified, then no highlighting is performed.  This is the default.

The STATISTICS subcommand requests additional statistics to be displayed.  The keyword DESCRIPTIVES requests that the mean, number of non-missing cases, and the non-biased estimator of the standard deviation are displayed. These statistics will be displayed in a separated table, for all the variables listed in any /VARIABLES subcommand. The XPROD keyword requests cross-product deviations and covariance estimators to be displayed for each pair of variables. The keyword ALL is the union of DESCRIPTIVES and XPROD.

CROSSTABS
=========

     CROSSTABS
             /TABLES=VAR_LIST BY VAR_LIST [BY VAR_LIST]...
             /MISSING={TABLE,INCLUDE,REPORT}
             /WRITE={NONE,CELLS,ALL}
             /FORMAT={TABLES,NOTABLES}
                     {PIVOT,NOPIVOT}
                     {AVALUE,DVALUE}
                     {NOINDEX,INDEX}
                     {BOX,NOBOX}
             /CELLS={COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
                     ASRESIDUAL,ALL,NONE}
             /STATISTICS={CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
                          KAPPA,ETA,CORR,ALL,NONE}

     (Integer mode.)
             /VARIABLES=VAR_LIST (LOW,HIGH)...

The CROSSTABS procedure displays crosstabulation tables requested by the user.  It can calculate several statistics for each cell in the crosstabulation tables.  In addition, a number of statistics can be calculated for each table itself.

The TABLES subcommand is used to specify the tables to be reported.  Any number of dimensions is permitted, and any number of variables per dimension is allowed.  The TABLES subcommand may be repeated as many times as needed.  This is the only required subcommand in general mode.

Occasionally, one may want to invoke a special mode called integer mode.  Normally, in general mode, pspp automatically determines what values occur in the data.  In integer mode, the user specifies the range of values that the data assumes.  To invoke this mode, specify the VARIABLES subcommand, giving a range of data values in parentheses for each variable to be used on the TABLES subcommand.  Data values inside the range are truncated to the nearest integer, then assigned to that value.  If values occur outside this range, they are discarded.  When it is present, the VARIABLES subcommand must precede the TABLES subcommand.

In general mode, numeric and string variables may be specified on TABLES.  In integer mode, only numeric variables are allowed.

The MISSING subcommand determines the handling of user-missing values. When set to TABLE, the default, missing values are dropped on a table by table basis.  When set to INCLUDE, user-missing values are included in tables and statistics.  When set to REPORT, which is allowed only in integer mode, user-missing values are included in tables but marked with an M (for ``missing'') and excluded from statistical calculations.

Currently the WRITE subcommand is ignored.

The FORMAT subcommand controls the characteristics of the crosstabulation tables to be displayed.  It has a number of possible settings:

  TABLES, the default, causes crosstabulation tables to be output. NOTABLES suppresses them.

  PIVOT, the default, causes each TABLES subcommand to be displayed in a pivot table format.  NOPIVOT causes the old-style crosstabulation format to be used.

  AVALUE, the default, causes values to be sorted in ascending order. DVALUE asserts a descending sort order.

  INDEX and NOINDEX are currently ignored.

  BOX and NOBOX is currently ignored.

The CELLS subcommand controls the contents of each cell in the displayed crosstabulation table.  The possible settings are:

COUNT
     Frequency count.

ROW
     Row percent.

COLUMN
     Column percent.

TOTAL
     Table percent.

EXPECTED
     Expected value.

RESIDUAL
     Residual.

SRESIDUAL
     Standardized residual.

ASRESIDUAL
     Adjusted standardized residual.

ALL
     All of the above.

NONE
     Suppress cells entirely.

/CELLS without any settings specified requests COUNT, ROW, COLUMN, and TOTAL. If CELLS is not specified at all then only COUNT will be selected.

The STATISTICS subcommand selects statistics for computation:

CHISQ

     Pearson chi-square, likelihood ratio, Fisher's exact test, continuity correction, linear-by-linear association.

PHI
     Phi.

CC
     Contingency coefficient.

LAMBDA
     Lambda.

UC
     Uncertainty coefficient.

BTAU
     Tau-b.

CTAU
     Tau-c.

RISK
     Risk estimate.

GAMMA
     Gamma.

D
     Somers' D.

KAPPA
     Cohen's Kappa.

ETA
     Eta.

CORR
     Spearman correlation, Pearson's r.

ALL
     All of the above.

NONE
     No statistics.

Selected statistics are only calculated when appropriate for the statistic.  Certain statistics require tables of a particular size, and some statistics are calculated only in integer mode.

/STATISTICS without any settings selects CHISQ.  If the STATISTICS subcommand is not given, no statistics are calculated.

Please note: Currently the implementation of CROSSTABS has the followings bugs:

  * Pearson's R (but not Spearman) is off a little.

  * T values for Spearman's R and Pearson's R are wrong.

  * Significance of symmetric and directional measures is not calculated.

  * Asymmetric ASEs and T values for lambda are wrong.

  * ASE of Goodman and Kruskal's tau is not calculated.

  * ASE of symmetric somers' d is wrong.

  * Approximate T of uncertainty coefficient is wrong.

Fixes for any of these deficiencies would be welcomed.

FACTOR
======

     FACTOR  VARIABLES=VAR_LIST

             [ /METHOD = {CORRELATION, COVARIANCE} ]

             [ /EXTRACTION={PC, PAF}]

             [ /ROTATION={VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE}]

             [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]

             [ /PLOT=[EIGEN] ]

             [ /FORMAT=[SORT] [BLANK(N)] [DEFAULT] ]

             [ /CRITERIA=[FACTORS(N)] [MINEIGEN(L)] [ITERATE(M)] [ECONVERGE (DELTA)] [DEFAULT] ]

             [ /MISSING=[{LISTWISE, PAIRWISE}] [{INCLUDE, EXCLUDE}] ]

The FACTOR command performs Factor Analysis or Principal Axis Factoring on a dataset.  It may be used to find common factors in the data or for data reduction purposes.

The VARIABLES subcommand is required.  It lists the variables which are to partake in the analysis.

The /EXTRACTION subcommand is used to specify the way in which factors (components) are extracted from the data. If PC is specified, then Principal Components Analysis is used. If PAF is specified, then Principal Axis Factoring is used. By default Principal Components Analysis will be used.

The /ROTATION subcommand is used to specify the method by which the extracted solution will be rotated. Three methods are available: VARIMAX (which is the default), EQUAMAX, and QUARTIMAX. If don't want any rotation to be performed, the word NOROTATE will prevent the command from performing any rotation on the data. Oblique rotations are not supported.

The /METHOD subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is to be analysed.  By default, the correlation matrix is analysed.

The /PRINT subcommand may be used to select which features of the analysis are reported:

  * UNIVARIATE A table of mean values, standard deviations and total weights are printed.

  * INITIAL Initial communalities and eigenvalues are printed.

  * EXTRACTION Extracted communalities and eigenvalues are printed.

  * ROTATION Rotated communalities and eigenvalues are printed.

  * CORRELATION The correlation matrix is printed.

  * COVARIANCE The covariance matrix is printed.

  * DET The determinant of the correlation or covariance matrix is printed.

  * KMO The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.

  * SIG The significance of the elements of correlation matrix is printed.

  * ALL All of the above are printed.

  * DEFAULT Identical to INITIAL and EXTRACTION.

If /PLOT=EIGEN is given, then a ``Scree'' plot of the eigenvalues will be printed.  This can be useful for visualizing which factors (components) should be retained.

The /FORMAT subcommand determined how data are to be displayed in loading matrices.  If SORT is specified, then the variables are sorted in descending order of significance.  If BLANK(N) is specified, then coefficients whose absolute value is less than N will not be printed.  If the keyword DEFAULT is given, or if no /FORMAT subcommand is given, then no sorting is performed, and all coefficients will be printed.

The /CRITERIA subcommand is used to specify how the number of extracted factors (components) are chosen. If FACTORS(N) is specified, where N is an integer, then N factors will be extracted.  Otherwise, the MINEIGEN setting will be used.  MINEIGEN(L) requests that all factors whose eigenvalues are greater than or equal to L are extracted. The default value of L is 1.    The ECONVERGE and ITERATE settings have effect only when iterative algorithms for factor extraction (such as Principal Axis Factoring) are used.   ECONVERGE(DELTA) specifies that iteration should cease when the maximum absolute value of the communality estimate between one iteration and the previous is less than DELTA. The default value of DELTA is 0.001. The ITERATE(M) setting sets the maximum number of iterations to M.  The default value of M is 25.

The MISSING subcommand determines the handling of missing variables. If INCLUDE is set, then user-missing values are included in the calculations, but system-missing values are not. If EXCLUDE is set, which is the default, user-missing values are excluded as well as system-missing values. This is the default. If LISTWISE is set, then the entire case is excluded from analysis whenever any variable  specified in the VARIABLES subcommand contains a missing value. If PAIRWISE is set, then a case is considered missing only if either of the values  for the particular coefficient are missing. The default is LISTWISE.

MEANS
=====

     MEANS [TABLES =]
           {VAR_LIST}
             [ BY {VAR_LIST} [BY {VAR_LIST} [BY {VAR_LIST} ... ]]]

           [ /{VAR_LIST}
              [ BY {VAR_LIST} [BY {VAR_LIST} [BY {VAR_LIST} ... ]]] ]

           [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
             [VARIANCE] [KURT] [SEKURT]
             [SKEW] [SESKEW] [FIRST] [LAST]
             [HARMONIC] [GEOMETRIC]
             [DEFAULT]
             [ALL]
             [NONE] ]

           [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]

You can use the MEANS command to calculate the arithmetic mean and similar statistics, either for the dataset as a whole or for categories of data.

The simplest form of the command is

     MEANS V.

which calculates the mean, count and standard deviation for V. If you specify a grouping variable, for example

     MEANS V BY G.

then the means, counts and standard deviations for V after having been grouped by G will be calculated. Instead of the mean, count and standard deviation, you could specify the statistics in which you are interested:

     MEANS X Y BY G
           /CELLS = HARMONIC SUM MIN.

This example calculates the harmonic mean, the sum and the minimum values of X and Y grouped by G.

The CELLS subcommand specifies which statistics to calculate.  The available statistics are:

  * MEAN The arithmetic mean.

  * COUNT The count of the values.

  * STDDEV The standard deviation.

  * SEMEAN The standard error of the mean.

  * SUM The sum of the values.

  * MIN The minimum value.

  * MAX The maximum value.

  * RANGE The difference between the maximum and minimum values.

  * VARIANCE The variance.

  * FIRST The first value in the category.

  * LAST The last value in the category.

  * SKEW The skewness.

  * SESKEW The standard error of the skewness.

  * KURT The kurtosis

  * SEKURT The standard error of the kurtosis.

  * HARMONIC The harmonic mean.

  * GEOMETRIC The geometric mean.

In addition, three special keywords are recognized:

  * DEFAULT This is the same as MEAN COUNT STDDEV.

  * ALL All of the above statistics will be calculated.

  * NONE No statistics will be calculated (only a summary will be shown).

More than one table can be specified in a single command. Each table is separated by a /. For example

     MEANS TABLES =
           C D E BY X
           /A B BY X Y
           /F BY Y BY Z.

has three tables (the TABLE = is optional). The first table has three dependent variables C, D and E and a single categorical variable X. The second table has two dependent variables A and B, and two categorical variables X and Y. The third table has a single dependent variables F and a categorical variable formed by the combination of Y and Z.

By default values are omitted from the analysis only if missing values (either system missing or user missing) for any of the variables directly involved in their calculation are encountered. This behaviour can be modified with the  /MISSING subcommand. Three options are possible: TABLE, INCLUDE and DEPENDENT.

/MISSING = TABLE causes cases to be dropped if any variable is missing in the table specification currently being processed, regardless of whether it is needed to calculate the statistic.

/MISSING = INCLUDE says that user missing values, either in the dependent variables or in the categorical variables should be taken at their face value, and not excluded.

/MISSING = DEPENDENT says that user missing values, in the dependent variables should be taken at their face value, however cases which have user missing values for the categorical variables should be omitted from the calculation.

NPAR TESTS
==========

     NPAR TESTS

          nonparametric test subcommands
          .
          .
          .

          [ /STATISTICS={DESCRIPTIVES} ]

          [ /MISSING={ANALYSIS, LISTWISE} {INCLUDE, EXCLUDE} ]

          [ /METHOD=EXACT [ TIMER [(N)] ] ]

NPAR TESTS performs nonparametric tests. Non parametric tests make very few assumptions about the distribution of the data. One or more tests may be specified by using the corresponding subcommand. If the /STATISTICS subcommand is also specified, then summary statistics are produces for each variable that is the subject of any test.

Certain tests may take a long time to execute, if an exact figure is required. Therefore, by default asymptotic approximations are used unless the subcommand /METHOD=EXACT is specified. Exact tests give more accurate results, but may take an unacceptably long time to perform.  If the TIMER keyword is used, it sets a maximum time, after which the test will be abandoned, and a warning message printed. The time, in minutes, should be specified in parentheses after the TIMER keyword. If the TIMER keyword is given without this figure, then a default value of 5 minutes is used.

Binomial test
-------------

          [ /BINOMIAL[(P)]=VAR_LIST[(VALUE1[, VALUE2)] ] ]

The /BINOMIAL subcommand compares the observed distribution of a dichotomous variable with that of a binomial distribution. The variable P specifies the test proportion of the binomial distribution. The default value of 0.5 is assumed if P is omitted.

If a single value appears after the variable list, then that value is used as the threshold to partition the observed values. Values less than or equal to the threshold value form the first category.  Values greater than the threshold form the second category.

If two values appear after the variable list, then they will be used as the values which a variable must take to be in the respective category. Cases for which a variable takes a value equal to neither of the specified values, take no part in the test for that variable.

If no values appear, then the variable must assume dichotomous values. If more than two distinct, non-missing values for a variable under test are encountered then an error occurs.

If the test proportion is equal to 0.5, then a two tailed test is reported.   For any other test proportion, a one tailed test is reported. For one tailed tests, if the test proportion is less than or equal to the observed proportion, then the significance of observing the observed proportion or more is reported. If the test proportion is more than the observed proportion, then the significance of observing the observed proportion or less is reported. That is to say, the test is always performed in the observed direction.

pspp uses a very precise approximation to the gamma function to compute the binomial significance.  Thus, exact results are reported even for very large sample sizes.

Chisquare Test
--------------

          [ /CHISQUARE=VAR_LIST[(LO,HI)] [/EXPECTED={EQUAL|F1, F2 ... FN}] ]

The /CHISQUARE subcommand produces a chi-square statistic for the differences between the expected and observed frequencies of the categories of a variable. Optionally, a range of values may appear after the variable list. If a range is given, then non integer values are truncated, and values outside the  specified range are excluded from the analysis.

The /EXPECTED subcommand specifies the expected values of each category. There must be exactly one non-zero expected value, for each observed category, or the EQUAL keywork must be specified. You may use the notation N*F to specify N consecutive expected categories all taking a frequency of F. The frequencies given are proportions, not absolute frequencies.  The sum of the frequencies need not be 1. If no /EXPECTED subcommand is given, then then equal frequencies are expected.

Cochran Q Test
--------------

          [ /COCHRAN = VAR_LIST ]

The Cochran Q test is used to test for differences between three or more groups. The data for VAR_LIST in all cases must assume exactly two distinct values (other than missing values).

The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.

Friedman Test
-------------

          [ /FRIEDMAN = VAR_LIST ]

The Friedman test is used to test for differences between repeated measures when there is no indication that the distributions are normally distributed.

A list of variables which contain the measured data must be given.  The procedure prints the sum of ranks for each variable, the test statistic and its significance.

Kendall's W Test
----------------

          [ /KENDALL = VAR_LIST ]

The Kendall test investigates whether an arbitrary number of related samples come from the same population. It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed. It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of unity indicates complete agreement.

Kolmogorov-Smirnov Test
-----------------------

          [ /KOLMOGOROV-SMIRNOV ({NORMAL [MU, SIGMA], UNIFORM [MIN, MAX], POISSON [LAMBDA], EXPONENTIAL [SCALE] }) = VAR_LIST ]

The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is drawn from a particular distribution.  Four distributions are supported, viz: Normal, Uniform, Poisson and Exponential.

Ideally you should provide the parameters of the distribution against which you wish to test the data. For example, with the normal distribution  the mean (MU)and standard deviation (SIGMA) should be given; with the uniform distribution, the minimum (MIN)and maximum (MAX) value should be provided. However, if the parameters are omitted they will be imputed from the data. Imputing the parameters reduces the power of the test so should be avoided if possible.

In the following example, two variables SCORE and AGE are tested to see if they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.

       NPAR TESTS
             /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = SCORE AGE.

If the variables need to be tested against different distributions, then a separate subcommand must be used.  For example the following syntax tests SCORE against a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst AGE is tested against a normal distribution of mean 40 and standard deviation 1.5.

       NPAR TESTS
             /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = SCORE
             /KOLMOGOROV-SMIRNOV (normal 40 1.5) =  AGE.

The abbreviated subcommand  K-S may be used in place of KOLMOGOROV-SMIRNOV.

Kruskal-Wallis Test
-------------------

          [ /KRUSKAL-WALLIS = VAR_LIST BY var (LOWER, UPPER) ]

The Kruskal-Wallis test is used to compare data from an arbitrary number of populations.  It does not assume normality. The data to be compared are specified by VAR_LIST. The categorical variable determining the groups to which the data belongs is given by VAR. The limits LOWER and UPPER specify the valid range of VAR. Any cases for which VAR falls outside [LOWER, UPPER] will be ignored.

The mean rank of each group as well as the chi-squared value and significance of the test will be printed. The abbreviated subcommand  K-W may be used in place of KRUSKAL-WALLIS.

Mann-Whitney U Test
-------------------

          [ /MANN-WHITNEY = VAR_LIST BY var (GROUP1, GROUP2) ]

The Mann-Whitney subcommand is used to test whether two groups of data come from different populations. The variables to be tested should be specified in VAR_LIST and the grouping variable, that determines to which group the test variables belong, in VAR. VAR may be either a string or an alpha variable. GROUP1 and GROUP2 specify the two values of VAR which determine the groups of the test data. Cases for which the VAR value is neither GROUP1 or GROUP2 will be ignored.

The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed. The abbreviated subcommand  M-W may be used in place of MANN-WHITNEY.

McNemar Test
------------

          [ /MCNEMAR VAR_LIST [ WITH VAR_LIST [ (PAIRED) ]]]

Use McNemar's test to analyse the significance of the difference between pairs of correlated proportions.

If the WITH keyword is omitted, then tests for all combinations of the listed variables are performed. If the WITH keyword is given, and the (PAIRED) keyword is also given, then the number of variables preceding WITH must be the same as the number following it. In this case, tests for each respective pair of variables are performed. If the WITH keyword is given, but the (PAIRED) keyword is omitted, then tests for each combination of variable preceding WITH against variable following WITH are performed.

The data in each variable must be dichotomous.  If there are more than two distinct variables an error will occur and the test will not be run.

Median Test
-----------

          [ /MEDIAN [(VALUE)] = VAR_LIST BY VARIABLE (VALUE1, VALUE2) ]

The median test is used to test whether independent samples come from populations with a common median. The median of the populations against which the samples are to be tested may be given in parentheses immediately after the /MEDIAN subcommand.  If it is not given, the median will be imputed from the union of all the samples.

The variables of the samples to be tested should immediately follow the = sign. The keyword BY must come next, and then the grouping variable.  Two values in parentheses should follow.  If the first value is greater than the second, then a 2 sample test is performed using these two values to determine the groups. If however, the first variable is less than the second, then a k sample test is conducted and the group values used are all values encountered which lie in the range [VALUE1,VALUE2].

Runs Test
---------

          [ /RUNS ({MEAN, MEDIAN, MODE, VALUE})  = VAR_LIST ]

The /RUNS subcommand tests whether a data sequence is randomly ordered.

It works by examining the number of times a variable's value crosses a given threshold. The desired threshold must be specified within parentheses. It may either be specified as a number or as one of MEAN, MEDIAN or MODE. Following the threshold specification comes the list of variables whose values are to be tested.

The subcommand shows the number of runs, the asymptotic significance based on the length of the data.

Sign Test
---------

          [ /SIGN VAR_LIST [ WITH VAR_LIST [ (PAIRED) ]]]

The /SIGN subcommand tests for differences between medians of the variables listed. The test does not make any assumptions about the distribution of the data.

If the WITH keyword is omitted, then tests for all combinations of the listed variables are performed. If the WITH keyword is given, and the (PAIRED) keyword is also given, then the number of variables preceding WITH must be the same as the number following it. In this case, tests for each respective pair of variables are performed. If the WITH keyword is given, but the (PAIRED) keyword is omitted, then tests for each combination of variable preceding WITH against variable following WITH are performed.

Wilcoxon Matched Pairs Signed Ranks Test
----------------------------------------

          [ /WILCOXON VAR_LIST [ WITH VAR_LIST [ (PAIRED) ]]]

The /WILCOXON subcommand tests for differences between medians of the variables listed. The test does not make any assumptions about the variances of the samples. It does however assume that the distribution is symetrical.

If the WITH keyword is omitted, then tests for all combinations of the listed variables are performed. If the WITH keyword is given, and the (PAIRED) keyword is also given, then the number of variables preceding WITH must be the same as the number following it. In this case, tests for each respective pair of variables are performed. If the WITH keyword is given, but the (PAIRED) keyword is omitted, then tests for each combination of variable preceding WITH against variable following WITH are performed.

T-TEST
======

     T-TEST
             /MISSING={ANALYSIS,LISTWISE} {EXCLUDE,INCLUDE}
             /CRITERIA=CIN(CONFIDENCE)

     (One Sample mode.)
             TESTVAL=TEST_VALUE
             /VARIABLES=VAR_LIST

     (Independent Samples mode.)
             GROUPS=var(VALUE1 [, VALUE2])
             /VARIABLES=VAR_LIST

     (Paired Samples mode.)
             PAIRS=VAR_LIST [WITH VAR_LIST [(PAIRED)] ]

The T-TEST procedure outputs tables used in testing hypotheses about means. It operates in one of three modes:

  * One Sample mode.

  * Independent Groups mode.

  * Paired mode.

Each of these modes are described in more detail below. There are two optional subcommands which are common to all modes.

The /CRITERIA subcommand tells pspp the confidence interval used in the tests.  The default value is 0.95.

The MISSING subcommand determines the handling of missing variables. If INCLUDE is set, then user-missing values are included in the calculations, but system-missing values are not. If EXCLUDE is set, which is the default, user-missing values are excluded as well as system-missing values. This is the default.

If LISTWISE is set, then the entire case is excluded from analysis whenever any variable  specified in the /VARIABLES, /PAIRS or /GROUPS subcommands contains a missing value. If ANALYSIS is set, then missing values are excluded only in the analysis for which they would be needed. This is the default.

One Sample Mode
---------------

The TESTVAL subcommand invokes the One Sample mode. This mode is used to test a population mean against a hypothesized mean. The value given to the TESTVAL subcommand is the value against which you wish to test. In this mode, you must also use the /VARIABLES subcommand to tell pspp which variables you wish to test.

Independent Samples Mode
------------------------

The GROUPS subcommand invokes Independent Samples mode or `Groups' mode. This mode is used to test whether two groups of values have the same population mean. In this mode, you must also use the /VARIABLES subcommand to tell pspp the dependent variables you wish to test.

The variable given in the GROUPS subcommand is the independent variable which determines to which group the samples belong. The values in parentheses are the specific values of the independent variable for each group. If the parentheses are omitted and no values are given, the default values of 1.0 and 2.0 are assumed.

If the independent variable is numeric, it is acceptable to specify only one value inside the parentheses. If you do this, cases where the independent variable is greater than or equal to this value belong to the first group, and cases less than this value belong to the second group. When using this form of the GROUPS subcommand, missing values in the independent variable are excluded on a listwise basis, regardless of whether /MISSING=LISTWISE was specified.

Paired Samples Mode
-------------------

The PAIRS subcommand introduces Paired Samples mode. Use this mode when repeated measures have been taken from the same samples. If the WITH keyword is omitted, then tables for all combinations of variables given in the PAIRS subcommand are generated. If the WITH keyword is given, and the (PAIRED) keyword is also given, then the number of variables preceding WITH must be the same as the number following it. In this case, tables for each respective pair of variables are generated. In the event that the WITH keyword is given, but the (PAIRED) keyword is omitted, then tables for each combination of variable preceding WITH against variable following WITH are generated.

ONEWAY
======

     ONEWAY
             [/VARIABLES = ] VAR_LIST BY VAR
             /MISSING={ANALYSIS,LISTWISE} {EXCLUDE,INCLUDE}
             /CONTRAST= VALUE1 [, VALUE2] ... [,VALUEN]
             /STATISTICS={DESCRIPTIVES,HOMOGENEITY}
             /POSTHOC={BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([VALUE])}

The ONEWAY procedure performs a one-way analysis of variance of variables factored by a single independent variable. It is used to compare the means of a population divided into more than two groups.

The dependent variables to be analysed should be given in the VARIABLES subcommand. The list of variables must be followed by the BY keyword and the name of the independent (or factor) variable.

You can use the STATISTICS subcommand to tell pspp to display ancilliary information.  The options accepted are:

  * DESCRIPTIVES Displays descriptive statistics about the groups factored by the independent variable.

  * HOMOGENEITY Displays the Levene test of Homogeneity of Variance for the variables and their groups.

The CONTRAST subcommand is used when you anticipate certain differences between the groups. The subcommand must be followed by a list of numerals which are the coefficients of the groups to be tested. The number of coefficients must correspond to the number of distinct groups (or values of the independent variable). If the total sum of the coefficients are not zero, then pspp will display a warning, but will proceed with the analysis. The CONTRAST subcommand may be given up to 10 times in order to specify different contrast tests. The MISSING subcommand defines how missing values are handled. If LISTWISE is specified then cases which have missing values for the independent variable or any dependent variable will be ignored. If ANALYSIS is specified, then cases will be ignored if the independent variable is missing or if the dependent variable currently being analysed is missing.  The default is ANALYSIS. A setting of EXCLUDE means that variables whose values are user-missing are to be excluded from the analysis. A setting of INCLUDE means they are to be included.  The default is EXCLUDE.

Using the POSTHOC subcommand you can perform multiple pairwise comparisons on the data. The following comparison methods are available:

  * LSD Least Significant Difference.

  * TUKEY Tukey Honestly Significant Difference.

  * BONFERRONI Bonferroni test.

  * SCHEFFE Scheffé's test.

  * SIDAK Sidak test.

  * GH The Games-Howell test.

The optional syntax ALPHA(VALUE) is used to indicate that VALUE should be used as the confidence level for which the posthoc tests will be performed. The default is 0.05.

QUICK CLUSTER
=============

     QUICK CLUSTER VAR_LIST
           [/CRITERIA=CLUSTERS(K) [MXITER(MAX_ITER)]]
           [/MISSING={EXCLUDE,INCLUDE} {LISTWISE, PAIRWISE}]

The QUICK CLUSTER command performs k-means clustering on the dataset.  This is useful when you wish to allocate cases into clusters of similar values and you already know the number of clusters.

The minimum specification is QUICK CLUSTER followed by the names of the variables which contain the cluster data.  Normally you will also want to specify /CRITERIA=CLUSTERS(K) where K is the number of clusters.  If this is not given, then K defaults to 2.

The command uses an iterative algorithm to determine the clusters for each case.  It will continue iterating until convergence, or until MAX_ITER iterations have been done.  The default value of MAX_ITER is 2.

The MISSING subcommand determines the handling of missing variables. If INCLUDE is set, then user-missing values are considered at their face value and not as missing values. If EXCLUDE is set, which is the default, user-missing values are excluded as well as system-missing values.

If LISTWISE is set, then the entire case is excluded from the analysis whenever any of the clustering variables contains a missing value. If PAIRWISE is set, then a case is considered missing only if all the clustering variables contain missing values.  Otherwise it is clustered on the basis of the non-missing values. The default is LISTWISE.

RANK
====

     RANK
             [VARIABLES=] VAR_LIST [{A,D}] [BY VAR_LIST]
             /TIES={MEAN,LOW,HIGH,CONDENSE}
             /FRACTION={BLOM,TUKEY,VW,RANKIT}
             /PRINT[={YES,NO}
             /MISSING={EXCLUDE,INCLUDE}

             /RANK [INTO VAR_LIST]
             /NTILES(k) [INTO VAR_LIST]
             /NORMAL [INTO VAR_LIST]
             /PERCENT [INTO VAR_LIST]
             /RFRACTION [INTO VAR_LIST]
             /PROPORTION [INTO VAR_LIST]
             /N [INTO VAR_LIST]
             /SAVAGE [INTO VAR_LIST]

The RANK command ranks variables and stores the results into new variables.

The VARIABLES subcommand, which is mandatory, specifies one or more variables whose values are to be ranked. After each variable, A or D may appear, indicating that the variable is to be ranked in ascending or descending order. Ascending is the default. If a BY keyword appears, it should be followed by a list of variables which are to serve as group variables. In this case, the cases are gathered into groups, and ranks calculated for each group.

The TIES subcommand specifies how tied values are to be treated.  The default is to take the mean value of all the tied cases.

The FRACTION subcommand specifies how proportional ranks are to be calculated.  This only has any effect if NORMAL or PROPORTIONAL rank functions are requested.

The PRINT subcommand may be used to specify that a summary of the rank variables created should appear in the output.

The function subcommands are RANK, NTILES, NORMAL, PERCENT, RFRACTION, PROPORTION and SAVAGE.  Any number of function subcommands may appear. If none are given, then the default is RANK. The NTILES subcommand must take an integer specifying the number of partitions into which values should be ranked. Each subcommand may be followed by the INTO keyword and a list of variables which are the variables to be created and receive the rank scores.  There may be as many variables specified as there are variables named on the VARIABLES subcommand.  If fewer are specified, then the variable names are automatically created.

The MISSING subcommand determines how user missing values are to be treated. A setting of EXCLUDE means that variables whose values are user-missing are to be excluded from the rank scores. A setting of INCLUDE means they are to be included.  The default is EXCLUDE.

     [file regression.texi not included]

RELIABILITY
===========

     RELIABILITY
             /VARIABLES=VAR_LIST
             /SCALE (NAME) = {VAR_LIST, ALL}
             /MODEL={ALPHA, SPLIT[(N)]}
             /SUMMARY={TOTAL,ALL}
             /MISSING={EXCLUDE,INCLUDE}

The RELIABILTY command performs reliability analysis on the data.

The VARIABLES subcommand is required. It determines the set of variables upon which analysis is to be performed.

The SCALE subcommand determines which variables reliability is to be calculated for.  If it is omitted, then analysis for all variables named in the VARIABLES subcommand will be used. Optionally, the NAME parameter may be specified to set a string name for the scale.

The MODEL subcommand determines the type of analysis. If ALPHA is specified, then Cronbach's Alpha is calculated for the scale.  If the model is SPLIT, then the variables  are divided into 2 subsets.  An optional parameter N may be given, to specify how many variables to be in the first subset. If N is omitted, then it defaults to one half of the variables in the scale, or one half minus one if there are an odd number of variables. The default model is ALPHA.

By default, any cases with user missing, or system missing values for any variables given in the VARIABLES subcommand will be omitted from analysis. The MISSING subcommand determines whether user missing values are to be included or excluded in the analysis.

The SUMMARY subcommand determines the type of summary analysis to be performed. Currently there is only one type: SUMMARY=TOTAL, which displays per-item analysis tested against the totals.

ROC
===

     ROC     VAR_LIST BY STATE_VAR (STATE_VALUE)
             /PLOT = { CURVE [(REFERENCE)], NONE }
             /PRINT = [ SE ] [ COORDINATES ]
             /CRITERIA = [ CUTOFF({INCLUDE,EXCLUDE}) ]
               [ TESTPOS ({LARGE,SMALL}) ]
               [ CI (CONFIDENCE) ]
               [ DISTRIBUTION ({FREE, NEGEXPO }) ]
             /MISSING={EXCLUDE,INCLUDE}

The ROC command is used to plot the receiver operating characteristic curve of a dataset, and to estimate the area under the curve. This is useful for analysing the efficacy of a variable as a predictor of a state of nature.

The mandatory VAR_LIST is the list of predictor variables. The variable STATE_VAR is the variable whose values represent the actual states, and STATE_VALUE is the value of this variable which represents the positive state.

The optional subcommand PLOT is used to determine if and how the ROC curve is drawn. The keyword CURVE means that the ROC curve should be drawn, and the optional keyword REFERENCE, which should be enclosed in parentheses, says that the diagonal reference line should be drawn. If the keyword NONE is given, then no ROC curve is drawn. By default, the curve is drawn with no reference line.

The optional subcommand PRINT determines which additional tables should be printed. Two additional tables are available. The SE keyword says that standard error of the area under the curve should be printed as well as the area itself. In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be printed. The COORDINATES keyword says that a table of coordinates of the ROC curve should be printed.

The CRITERIA subcommand has four optional parameters:

  * The TESTPOS parameter may be LARGE or SMALL. LARGE is the default, and says that larger values in the predictor variables are to be considered positive.  SMALL indicates that smaller values should be considered positive.

  * The CI parameter specifies the confidence interval that should be printed. It has no effect if the SE keyword in the PRINT subcommand has not been given.

  * The DISTRIBUTION parameter determines the method to be used when estimating the area under the curve. There are two possibilities, viz: FREE and NEGEXPO. The FREE method uses a non-parametric estimate, and the NEGEXPO method a bi-negative exponential distribution estimate. The NEGEXPO method should only be used when the number of positive actual states is equal to the number of negative actual states. The default is FREE.

  * The CUTOFF parameter is for compatibility and is ignored.

The MISSING subcommand determines whether user missing values are to be included or excluded in the analysis.  The default behaviour is to exclude them. Cases are excluded on a listwise basis; if any of the variables in VAR_LIST or if the variable STATE_VAR is missing, then the entire case will be excluded.