The formula given in your link is for what I know as Cramer's Index. It standardizes results from 0 to 1 - no matter what df.

I am not very happy with the use of "effect", since what is being measured is contingency ("correlation").

As far as interpretation of results is concerned, Cohen's guidelines are commonly used. In other words, interpretation is not similarly to Pearson's r, where 0.50 would be considered a medium correlation at best.

Consider a 2x2 table as follows:

1 5

3 7

This gives me a Chi°2 of 0.8 and Phi (same as Cramer's V with df=1) of 0.223

Now let's expand the above table 4x, contigency should remain the same:

1 5 1 5

3 7 3 7

1 5 1 5

3 7 3 7

Chi^2 should now be 0.8 * 4 = 3.2

Cramer's V df = 3, therefore 0.129

Referring to Cohen's guidelines, both tables give us a contingency short of medium.

I am using the term Cramer's V (in my understanding it is Cramer's Index).

Caution: quick and dirty manual calculation. Would anyone care to check?