Basic Concepts
Cohen’s h can be used as a measure of the size of the effect between two proportions (i.e. p1 – p2). See Two-sample Proportion Test for background information.
2 arcsin √p1 – 2 arcsin √p2
We calculate Cohen’s h in Excel using the formula
=2*(ASIN(SQRT(p1))-ASIN(SQRT(p2))).
When no other information is available, the guidelines for the size of this effect are
h = .2: small effect, h = .5: medium effect, h = .8: large effect
Worksheet Function
Starting with Rel 9.8, the Real Statistics Resource Pack provides the following function
COHENH(p1, p2) = Cohen’s h effect size for the proportions p1 and p2.
Cohen’s h is defined as
=2*(ASIN(SQRT(p1))-ASIN(SQRT(p2)))
For Example 1 of Two-sample Proportion Test, we obtain the effect size
COHENH(.5,.6) = 2*(ASIN(SQRT(.5))-ASIN(SQRT(.6))) = -.20136
This is a small effect.
Reference
Wikipedia (2020) Cohen’s h
https://en.wikipedia.org/wiki/Cohen%27s_h
You could drop my question; I realized I had a table to percentages, not proportions, and that is why the SQRT(p1) were above 1.
The ASIN function requires a number between -1 and 1. Do you know how to calculate this if the square root of the proportion is more than 1 (i.e., the SQRT(p1) or SQRT(p2) part of the equation)?