Statistics by Groups (Breakdown) - Lists of Tables tab

Select the Lists of tables tab in the Statistics by Groups (Breakdown) dialog box to access options to specify up to six lists of grouping variables and a list of dependent variables. This tab also contains options to compute a large number of results spreadsheets for each table (all possible combinations of grouping variables) in batch; that is, without requiring any further user input.

Grouping variables

Click this button to display a standard variable selection dialog box in which you select at least one list of grouping variables; breakdown tables are computed for all possible combinations of grouping variables from the six lists. Note that Statistica automatically takes all valid integer codes in the respective grouping variables to construct the tables.

Dependent variables

Click this button to display a standard variable selection dialog box in which you can select the list of dependent variables for the breakdown tables.

Output tables

The settings in this group box determine the types of results spreadsheets to be computed for each table (combination of grouping variables), and the detail of results for each dependent variable. Note that statistics reported in the spreadsheets depend on the selection of Statistics.

Summary table of means

Select this check box to display a spreadsheet containing the summary table of means (along with any specified Statistics) computed for each combination of grouping variables when you click the Summary button in the Statistics by Groups (Breakdown) dialog box.

Detailed two-way tables

Select this check box to display spreadsheets with two-way tables when you click the Summary button in the Statistics by Groups (Breakdown) dialog box. If more than two lists of grouping variables are selected, tables are produced for the last two grouping variables in the current table, within the respective levels of preceding grouping variables.

Within-group correlations

Select this check box to compute spreadsheets of within-group correlation matrices of the dependent variables for each combination of grouping variables when you click the Summary button in the Statistics by Groups (Breakdown) dialog box. Note that this option is only applicable if you have selected more than one dependent variable.

Analysis of variance

Select this check box to display a spreadsheet containing the summary ANOVA tables for each selected dependent variable when you click the Summary button in the Statistics by Groups (Breakdown) dialog box.

Levene test

Select this check box to display a spreadsheet containing the Levene test for each selected dependent variable when you click the Summary button in the Statistics by Groups (Breakdown) dialog box. The significance tests reported by the Analysis of variance option (see above) are based on the assumption that the variances in the different groups are the same (homogeneous). A powerful statistical test of this assumption is Levene's test (however, see also the description of the Brown-Forsythe modification of this test below). For each dependent variable, an analysis of variance is performed on the absolute deviations of values from the respective group means. If the Levene test is statistically significant, the hypothesis of homogeneous variances should be rejected. Note that the F statistic (in ANOVA) provides a robust test for mean differences as long as 1) the N per group is greater than 10 (and, in particular, in the case of equal N), and 2) the means across groups are not correlated with the standard deviations across groups. Thus, a significant Levene test does not necessarily call into question the validity of the ANOVA results. Also, in the case of unbalanced designs (i.e., unequal N per group), the Levene test is itself not very robust, as has recently been pointed out in, for example, Glass and Hopkins (1996; see also the next paragraph).

Brown & Forsythe (HOV)

Select this check box to display a spreadsheet containing the Brown & Forsythe test for each selected dependent variable when you click the Summary button in the Statistics by Groups (Breakdown) dialog box. Recently, some authors (e.g., Glass and Hopkins, 1996) have called into question the power of the Levene test for unequal variances. Specifically, the absolute deviation (from the group means) scores can be expected to be highly skewed; thus, the normality assumption for the ANOVA of those absolute deviation scores is usually violated. This poses a particular problem when there is unequal N in the two (or more) groups that are to be compared. A more robust test that is very similar to the Levene test has been proposed by Brown and Forsythe (1974). Instead of performing the ANOVA on the deviations from the mean, we can perform the analysis on the deviations from the group medians. Olejnik and Algina (1987) have shown that this test gives quite accurate error rates even when the underlying distributions for the raw scores deviate significantly from the normal distribution. However, recently, Glass and Hopkins (1996, p. 436) have pointed out that both the Levene test as well as the Brown-Forsythe modification suffer from what those authors call a fatal flaw, namely, that both tests themselves rely on the homogeneity of variances assumption (of the absolute deviations from the means or medians); and hence, it is not clear how robust these tests are themselves in the presence of significant variance heterogeneity and unequal N.

Statistics

The selections in this group box determine the statistics that are reported in the Summary tables of means and the Detailed two-way tables that are displayed when you click the Summary button in the Statistics by Groups (Breakdown) dialog box. For a brief description of the available statistics, see Statistics in Breakdown Procedures.