Can someone calculate Cohen's d for me from these data?

F(4, 42) = 39.37, p = 0.001, eta squared = 0.48

There were 3 groups measured on 3 times (pre-treatment, post-treatment, follow-up; I don't think SD is pooled for any of the SDs). There were three groups, with the third group being the control group:

          Pre-treatment  Post-treatment       Follow-up
Group 1    37.10 (4.04)    16.10 (2.51)    17.88 (2.66)
Group 2    34.40 (5.50)    18.30 (4.62)    18.25 (4.83)
Group 3    34.30 (6.54)    25.55 (3.55)    28.14 (2.41)

1 Answer 1


You cannot calculate a $d$ effect size for more than two groups. For this, you would need to use Cohen's $f$. To calculate this, you will need to specify what type of variance proportion you want to use (e.g., $\eta^2$ or partial-$\eta^2$. Once you have made this decision, you can extract the necessary info from the ANOVA summary table. Then you can use the formula $$f^2 = \frac{\eta^2}{1-\eta^2}$$

  • $\begingroup$ I have The n^2 in which is 0.48. And I just need the effect size of how group 1 and 2 do compared to group 3. I don’t have a computer program to do the math. So I could use some help hehe. I think The variance proportion I need to use is n^2. $\endgroup$ Commented Apr 4, 2018 at 14:47
  • $\begingroup$ Or maybe I need the effect size of group 1 versus group 3 and then the effect size og group 2 versus 3. Then I could compare the two effect sizes, right? $\endgroup$ Commented Apr 4, 2018 at 14:49
  • $\begingroup$ If you are just comparing two of the groups, use the MS-error from the final ANOVA summary table, the square root of this can be used as the pooled-standard deviation. Then, divide the difference between the two groups of focus by this value, and you can report these pair-wise comparison $d$ values. $\endgroup$
    – Gregg H
    Commented Apr 4, 2018 at 15:48
  • $\begingroup$ Is it possible to compare all there groups? And how? $\endgroup$ Commented Apr 6, 2018 at 7:53
  • $\begingroup$ Yes, the Cohen's $f$ compares all three groups at once. $\endgroup$
    – Gregg H
    Commented Apr 6, 2018 at 12:25

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