I am reviewing a study where I need to calculate an effect size of gender differences (Cohen's d). The study looks at the effect of effort on men and women, but do not report the standard deviations for me to calculate d, but do report an repeated measures ANOVA value interaction.

I was emailing the author and he was quite adamant that it is possible to calculate the effect size for gender differences. He said the F value is a result of MSeffect / MSerror.

As the means are reported in the paper, the author claims it should be possible to calculate the MSeffect by using the means. Once you have the MSeffect you can find the MSerror by using the reported F value. Once you have that you should be able to find the SDs for the means, and then Cohen's D can be calculated.

Problem is, I have no idea how to do this.

Here is the available data:

I have attached an image of the means.

Total N is 64, with 16 males and 16 females in both high and low effort conditions

Below is the reported interactions. Can this be done?

"The Ss in the high-incentive condition reported greater effort (F(1,60) = 18.0, p < 0.001) and showed lower Stroop interference (F(1,60) = 4.51, p < 0.05) than the Ss in the low-incentive condition."

The effect size in question that I need is the d for the difference between men and women in Stroop List time in the Low condition (see image).