Chi square effect size - why to use the Crammer's V and not only Phi

obh

Active Member
Hi

The recommendation:

For the goodness of fit, or table 2*2: Phi=sqrt(χ2/n)

For association:
DF'=min(row-1,cols-1)
Crammer's V=sqrt(χ2/(n*DF')

But also the definition of small/,medium/large is divided by sqrt(DF')
For example DF'=1 it is (0.1-small, 0.3- medium, 0.5 - large)
For DF'=2 it is small: 0.1/sqrt(2)=0.07 medium: 0.3/sqrt(2)=0.21 ..

So the Crammer's V= is divided by sqrt(DF') and also the scale.
So what is the point of using the Crammer's V ?
Why not only the Phi ???

gianmarco

TS Contributor
Hello,
i do not totally understand your question, but I will try to answer.
Phi does not reach its upper ceiling (1) for tables larger than 2x2.
In this instance, better to use Cramer's V (which is also called Cramer's phi in some books).
Hope this helps
Best

obh

Active Member
Thank you, Gianmarco

Sorry if I wasn't clear.
I understand the advantage of using Cramer's V with possible values between 0 and 1.
I noticed the interpretation of the effect size is only by Phi.

For a 2*2 table:
when phi=0.3 the interpretation is a medium effect.
For 3*4 table:
when phi=0.3 the interpretation is a medium effect.
or in this case, V=0.3/sqrt(2)=0.21, and the interpretation is a medium effect.

So when using the Cramer's V we change the scale to be between 0 and 1, which is good, but we also change the interpretation scale...
which is in my opinion not so good ...
PS, I don't know the reason for changing the interpretation scales ...
I also know the power calculation is based on w which is actually phi, also in case of tables larger than 2*2, this also may hints that phi is the preferred measurement for effect size, what do you think?