I calculated a Cohen's d value of d= -2.1. I understand that there are small, medium, and large effect sizes. But in my case the d value is negative? Would it still be considered large since abs(-2.1)=2.1 is greater than 0.8? Or would it be small because it's negative and obviously less than 0.2? Thank you in advance. Best Regards
There is a growing opinion among statisticians that Cohen's $d$ has more problems than advantages. I recommend that you compute effect estimates in raw data or subject-matter units. Besides losing subject-matter interpretability, Cohen's $d$ invites one to make arbitrary categorizations as you did. See http://biostat.mc.vanderbilt.edu/ManuscriptChecklist for more discussion on the subject.
"Cohen's d is defined as the difference between two means divided by a standard deviation for the data" (from https://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d ) Obviously the sign is a matter of which way you take the difference. Thus, only abs(d) is relevant and the effect is considered "large" (whatever that means).