# Why do I get completely different Effect Sizes using same data but different methods?

When I calculate Effect Sizes (Cohen's d) on the same study using different methods I get completely different effect sizes.

For example: (t=4.81, P<0.001, d=0.41)

I also calculated d=0.41 using reported means and standard deviations, i.e.:

But, using just the t value and sample size of 16, I get 1.76:

0.41 and 1.76 are vastly different. Are these both Cohen's d, and if so, aren't they supposed to be equivalent?

• I think $d=\frac{\bar{x_1}-\bar{x_2}}{s}$ is the formula for Cohen's d. Where is the second fromula from? Do you have a reference? Jul 8 '15 at 2:19
• From here (formula 2). I also get effect sizes of a similar magnitude when calculating from t using online calculators such as this one Jul 8 '15 at 2:32

I did some simulations, it seems the results of two formulas are the same. Just list my R code and resutls below.

set.seed(123)
x<-rnorm(100,mean=5, sd=2)
y<-rnorm(100,mean=10, sd=3)
u1<-mean(x)
sd1<-sd(x)
u2<-mean(y)
sd2<-sd(y)
t.test(y,x)
s_pool<-sqrt((99*sd1^2+99*sd2^2)/200)

d1<-(u2-u1)/s_pool

d2<-13.1186*sqrt((200/10000)*(200/198))


$d_1$=1.864599

$d_2$=1.864597

I got almost the same results.

The t is 13.1186 here.

• So it does work! In my case it seems the problem is that the studies are reporting pre and post measures, so the t-test is paired. Jul 8 '15 at 5:51
• Then it is not two indepdent samples anymore. Jul 8 '15 at 5:55
• That's the answer then. I am mistakenly trying to deduct effect size using an independent t-test in a study that used a dependent t-test. Jul 8 '15 at 8:46