I want to investigate if there are significant differences in the difference of two groups. I have two populations and both populations have a control group and a experiment group. To investigate if there are signifcant differences between the two populations in the difference between the control group and experiment group I used Cohen's d effect size.
The outcome of the Cohen's d effect size was that there are no significant differences between the populations, however in one population there is a significant difference between the control group and the experiment group while in the other there is no significant difference between the two groups. Should in that case the Cohen's d effect size outcome not be that there is a significant difference between the two populations?