I am comparing two discrete variables (where the values can be one and zero only) with a third one using chi square test and Cohen d for the effect size. In my comparison, I found that my Cohen d was greater than one, with a significant p-value. I searched the web and found a vague post that said that this indicate that the difference between the means in this case is larger than the standard deviation. But how can I report such result? Is it valid? Does that mean that the effect is very strong or something else. Perhaps, chi square is not the right test? Sample data is given below and the results .

Thanks very much for your help.

this is how my data looks like.

var1 var2 var3

0 1 1

1 0 1

etc.

sample size: 827

I am trying to see how var3 is correlated with var1 and var2. The results of chi square between var3, var2 and var1 are:

cat p dof x2 cohenD

var1 0 1 65.586 -2.307

var2 0 1 191.834 -1.548