(Simple) Analysis of Variance

By simple analysis of variance, I refer basically to unifactorial analysis of variance, that is, an ANOVA with a single factor.

oneway income status, t sch

computes the overall F-test for income (dependent variable) by status (group variable) plus the Bartlett test for equality of variances between groups. Option t or tabulate yields a summary table with mean, s.d. and n of cases for each group and the total sample. Option sch or scheffe computes the Scheffé test for post-hoc differences between groups.

The results for the Scheffé test may look like this:

                    Comparison of mean(attitude)
                              by class
                              (Scheffe)
row mean-
col mean       1. manual    2. clerk     3. service

2. clerk        -.014519
                   0.972

3. service      -.067295    -.052776
                   0.039       0.311

4. owners        .046974     .061492        .114268
                   0.437       0.308          0.000

This means, for instance, that the value of "attitude" is about .0145 lower in group 2 than in group 1, but the difference is not statististically significant. The value in group 3 is about .0673 lower than the value in group 1; this difference is statistically significant at the 5 per cent level. The value of group 3 is also about .0528 lower than the value of group 2, but this difference is not statistically significant. Obviously, group 4 has higher values than any other group; but only the difference with group 3 reaches statistical significance.

A few other post-hoc tests are available, such as the Bonferroni multiple-comparison test (option b).