I am having trouble understanding the statistical significance of Cohen's d.
My reasoning goes like this: To conclude that experimental group differs from control group significantly (p < 0.05), the experimental group's mean must be 1.96z below or above the control group's mean. In this case the Cohen's d will also be about 2, right? If Cohen's d is lower than 2, also the z difference between groups will be lower than that, which means the means from two groups won't be statistically different from each other anymore.
Please correct my flawed understanding.