Here's the context: From Libon et al. (2007): SOC/EXEC > AD made more errors on the Trails B (z= 2.13, p 0.016). Patients with SOC/EXEC also exhibited a trend toward more errors on the Trail Making Test—Part B compared to patients with SemD (z = 1.5, p 0.066).

I want to find convert the standard normal deviate z = 2.13 to an effect size (Cohen's d)

The standard normal deviate z = 2.13 is equivalent to .9834 or negative value (z = -2.13) = 1.0 - .9834 = .0166, meaning that 1.66% of the standard normal distribution is below this value, and 98.34 % is above.

So Dev, I used Rosenthal's formula that you cited: r = Z/squareroot N

i.e., Z divided by the square root of N (Rosenthal, 1991)

Square root of n (54) = 7.348

r = 2.13/7.348 = .2899

Then I used EFG to convert r to d = .60582

Additionally, I interpolated the t-statistic associated with p = .9834, but I think I used the wrong df (I used n-1 instead of n-2), and came up with ? (lost the piece of paper, which is why I didn't post this sooner!). Anyway, with this method, I came up with d=.66831 (interpolation by hand, but with df = 53)

I did this because I could not find an interpolation procedure in Clin Tools or when I looked quickly on the web. Of course, later I found many, and I was curious if I did the interpolations correctly since its been like 15 years.

So using the t-distribution calculator here:

http://www.stat.tamu.edu/~west/applets/tdemo.htmlwith p = .9834 and df=52, t = 2.188 for df=52 and would be 2.187 for df=53.

Converted value of t=2.188 = Cohen’s d of .664 (with unequal sample sizes, 38 and 16)

So, any way you slice it, they are both medium effect sizes.

Please feel free to let me know if I did anything wrong here!

Thanks again for your help!

Ya-Ya