# How can Cohen's d < 1.96 ever be statistically significant?

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.

• Cohen's $d$ is determined using the standard deviation (typically of the available sample). Hypothesis testing is performed using the standard error $\frac{sd}{\sqrt{N}}$. The former assesses how big of a standardized difference you observed. The latter is used to determine the probability that you obtained a sample with the characteristics you did from a population of interest. – Matt Barstead Jan 22 '18 at 10:48