A Measure of Association and Post Hoc Tests

If the null is not rejected in ANOVA, then the analysis stops because the conclusion is that the IVs and DV are not related. If the null is rejected, however, it is customary to explore the statistically significant results in more detail using measures of association (MAs) and post hoc tests. Measures of association permit an assessment of the strength of the relationship between the IV and the DV, and post hoc tests allow researchers to determine which groups are significantly different from which other ones. The MA that will be discussed here is fairly easy to calculate by hand, but the post hoc tests will be discussed and then demonstrated in the SPSS section, because they are computationally intensive.

Omega squared (ω2) is an MA for ANOVA that is expressed as the proportion of the total variability in the sample that is due to between-group differences. Omega squared can be left as a proportion or multiplied by

100 to form a percentage. Larger values of ω2 indicate stronger IV–DV relationships, whereas smaller values signal weaker associations. Omega squared is computed as

Omega squared: A measure of association used in ANOVA when the null has been rejected in order to assess the magnitude of the relationship between the independent and dependent variables. This measure shows the proportion of the total variability in the sample that is attributable to between-group differences.