How can I intepret the effect sizes of Cramer's V when DF is high (like > 20)?

Dear All,
I am doing Pearson Chi Square analyses in SPSS. Besides looking at the Chi Square Sig. value I also want to look at Cramer's V to analyze the effect sizes. My dataset has 12 million observations na I found a value of 0.12 for the Cramer's V. Standards for interpreting Cramer’s seem to be:
DF=1 (0.10 = small effect) (0.30 = medium effect) (0.50=large effect)
DF=2 (0.07 = small effect) (0.21= medium effect) (0.35 = large effect)
DF=3 (0.06 = small effect) (0.17 = medium effect) (0.29 = large effect)
But, how can I interpret the effect sizes if DF exceeds 3? My cross tabulations often have a DF of 22 or higher.
Thank you!


TS Contributor
I had the same issue some months ago. I searched on the web, in relevant literature, and elsewhere, but I couldn't find a clear answer.
A viable option that I found to tackle that "issue" was to convert V into Cohen's w, which is a measure of effect size for categorical association. You will find the details (with the references I managed to put together) at page 319 (very first section of paragraph 6.1) of this article of mine:

The "regular" Cohen's thresholds for small, medium, and large effect (0.10, 0.30, 0.50) apply to w.

Hope this helps,