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Nominal vs. Nominal

Part 3c: Effect size

We saw earlier that there is a significant association between the gender and marital status. However it was not the case that all men for example were married, and all women were divorced. To indicate the strength of the association Cramér's V (Cramér, 1946) is often used.

As for the interpretation for Cramér's V various rules of thumb exist but one of them is from Cohen (1988) who let's the interpretation depend on the degrees of freedom, shown in Table 1.

In our example the degrees of freedom is 4 and Cramér's V is .0094. This would make it negligible. We could add this to our report:

Gender and marital status showed to have a significant but negligible association, χ²(4, N = 1941) = 16.99, p < .001, V = .09. A pairwise z-test post hoc analysis with Bonferroni correction revealed that only for widowed there was a significant difference between the male and female percentage, p < .05.

Now we can complete the report on our analysis on the next page.

Two nominal variables

Introduction

Impression

Visualisation

Test for association

Post-hoc test

Effect size <=

Reporting

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