Effect Size in SPSS – One Sample t Test; Cohen's d

This video examines how to calculate and interpret an effect size for the one sample t test in SPSS. Effect sizes indicate the standard deviation difference between the two groups. Cohen's effect sizes:
Small = .20
Medium = .50
Large = .80

d = (sample mean - population mean)/standard deviation

Video Transcript: Jacob Cohen presented some effect sizes for a number of different tests. And for the t-test he gave what's now known as Cohen's d. Cohen's d for the one-sample t is equal to the mean difference divided by the standard deviation. And we can see the mean difference is right here in our output, 6.33, and the standard deviation is 8.11. So what we want to do is take 6.33 and divide that by 8.11, and we get a Cohen's d of .78. Now Cohen provided guidelines for d, where small was equal to .20, medium was .50, and large was .80. And these are just approximations, which Cohen emphasized in his book on effect sizes that he wrote, where he really strongly emphasized that these should not be taken as laws, but really just rules of thumb. But let's go ahead and apply these guidelines to our data, our results, and see what we get. So recall that we got an effect size of .78, right, our d was equal to .78. So that's almost large, but it's not quite. If we strictly apply these guidelines we could say that was a medium effect size; it's almost large, .78. Now, how would want interpret this? What this indicates, first of all, is that our study, our treatment, when we gave the students the new math program, it was it was a medium effect, it had a medium or moderate effect, that program, so it wasn't small, but it was medium in nature, moderate. Frankly, it almost was large. So really here we have a pretty good sized effect. Medium and large effects would be very good to see in most, in many studies at least, in the behavioral sciences. Now in different disciplines, a large effect, a medium effect, what's large, what's medium, can vary. But, overall, we like to see medium and large effects. So how would you interpret a d of .78? Well the way this could be interpreted is it's really just like a z-score. We could say students who took the new math program, our sample of 15, they scored .78, there's our d, .78 standard deviations higher on the math exam. That's what d means, it indicates the amount of standard deviation of a difference that we saw. In this case, since we were comparing our sample mean, based on the 15 people, to the untreated population mean of 80, this d indicates how much of a difference we saw between those two groups, our sample and the untreated population. So, once again, students who took the new math program scored .78 standard deviations higher on the math exam than the untreated population of mu = 80. Once again, that's a pretty good-sized effect. Most researchers who saw that kind of an effect in a study, in designing a math program to try and help people do better on a math test, would be quite happy with an effect size of .78. This concludes the presentation on Cohen's d for the one-sample t-test. Thanks for watching.

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