15.6 CROSSTABS

CROSSTABS
        /TABLES=var_list BY var_list [BY var_list]…
        /MISSING={TABLE,INCLUDE,REPORT}
        /FORMAT={TABLES,NOTABLES}
                {AVALUE,DVALUE}
        /CELLS={COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
                ASRESIDUAL,ALL,NONE}
        /COUNT={ASIS,CASE,CELL}
               {ROUND,TRUNCATE}
        /STATISTICS={CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
                     KAPPA,ETA,CORR,ALL,NONE}
        /BARCHART

(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 a footnote and excluded from statistical calculations.

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, which is equivalent to CELLS=NONE, suppresses them.
• AVALUE, the default, causes values to be sorted in ascending order. DVALUE asserts a descending sort order.

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 is selected.

By default, crosstabulation and statistics use raw case weights, without rounding. Use the /COUNT subcommand to perform rounding: CASE rounds the weights of individual weights as cases are read, CELL rounds the weights of cells within each crosstabulation table after it has been constructed, and ASIS explicitly specifies the default non-rounding behavior. When rounding is requested, ROUND, the default, rounds to the nearest integer and TRUNCATE rounds toward zero.

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.

The ‘/BARCHART’ subcommand produces a clustered bar chart for the first two variables on each table. If a table has more than two variables, the counts for the third and subsequent levels are aggregated and the chart is produced as if there were only two variables.

Please note: Currently the implementation of CROSSTABS has the following limitations:

• Significance of some directional measures is not calculated.
• Asymptotic standard error is not calculated for Goodman and Kruskal’s tau or symmetric Somers’ d.
• Approximate T is not calculated for symmetric uncertainty coefficient.

Fixes for any of these deficiencies would be welcomed.

• Crosstabs Example

15.6.1 Crosstabs Example

A researcher wishes to know if, in an industry, a person’s sex is related to the person’s occupation. To investigate this, she has determined that the personnel.sav is a representative, randomly selected sample of persons. The researcher’s null hypothesis is that a person’s sex has no relation to a person’s occupation. She uses a chi-squared test of independence to investigate the hypothesis.

get file="personnel.sav". crosstabs /tables= occupation by sex /cells = count expected /statistics=chisq.

Example 15.3: Running crosstabs on the sex and occupation variables

The syntax in Example 15.3 conducts a chi-squared test of independence. The line /tables = occupation by sex indicates that occupation and sex are the variables to be tabulated. To do this using the graphic user interface you must place these variable names respectively in the ‘Row’ and ‘Column’ fields as shown in Screenshot 15.3.

Screenshot 15.3: The Crosstabs dialog box with the sex and occupation variables selected

Similarly, the ‘Cells’ button shows a dialog box to select the count and expected options. All other cell options can be deselected for this test.

You would use the ‘Format’ and ‘Statistics’ buttons to select options for the FORMAT and STATISTICS subcommands. In this example, the ‘Statistics’ requires only the ‘Chisq’ option to be checked. All other options should be unchecked. No special settings are required from the ‘Format’ dialog.

As shown in Results 15.1 CROSSTABS generates a contingency table containing the observed count and the expected count of each sex and each occupation. The expected count is the count which would be observed if the null hypothesis were true.

The significance of the Pearson Chi-Square value is very much larger than the normally accepted value of 0.05 and so one cannot reject the null hypothesis. Thus the researcher must conclude that a person’s sex has no relation to the person’s occupation.

Summary Cases Valid Missing Total N Percent N Percent N Percent occupation × sex 54 96.4% 2 3.6% 56 100.0% occupation × sex sex Total Male Female occupation Artist Count 2 6 8 Expected 4.89 3.11 .15 Baker Count 1 1 2 Expected 1.22 .78 .04 Barrister Count 0 1 1 Expected .61 .39 .02 Carpenter Count 3 1 4 Expected 2.44 1.56 .07 Cleaner Count 4 0 4 Expected 2.44 1.56 .07 Cook Count 3 2 5 Expected 3.06 1.94 .09 Manager Count 4 4 8 Expected 4.89 3.11 .15 Mathematician Count 3 1 4 Expected 2.44 1.56 .07 Painter Count 1 1 2 Expected 1.22 .78 .04 Payload Specialist Count 1 0 1 Expected .61 .39 .02 Plumber Count 5 0 5 Expected 3.06 1.94 .09 Scientist Count 5 2 7 Expected 4.28 2.72 .13 Scrientist Count 0 1 1 Expected .61 .39 .02 Tailor Count 1 1 2 Expected 1.22 .78 .04 Total Count 33 21 54 Expected .61 .39 1.00 Chi-Square Tests Value df Asymptotic Sig. (2-tailed) Pearson Chi-Square 15.59 13 .272 Likelihood Ratio 19.66 13 .104 N of Valid Cases 54

Results 15.1: The results of a test of independence between sex and occupation