I need to calculate sample size based on this equation but I am give hedges g instead of cohen D: pwr.t.test(d = , sig.level= , power = , type = c("two.sample"))
• d=effect size
• sig.level=significant level
• power=power of test
• type=type of test
I do not know how to convert the Hedge's g effect size of g=1.116 to Cohen's d since the N they refer to in the paper seems to refer to studies rather than subjects
I wonder if Hedge's g was reported because of variance heterogeneity? If so, this chapter from the PASS documentation may be helpful:
- https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/PASS/Two-Sample_T-Tests_Allowing_Unequal_Variance.pdf
See also Russ Lenth's comments on basing sample size estimates on standardized effect size measures without considering the underlying means and SDs:
- https://homepage.stat.uiowa.edu/~rlenth/Power/2badHabits.pdf
HTH.
Hello Youssef Soliman
As far as I know, you can use the following formula
Cohen's d = Hedge's g * root (N/df).
Since you say your study is of type independent t-test, so
df=N-2
so
Cohen's d = Hedge's g * root (N/N-2).
Unfortunately, the answer #2 (@Abolfazl Ghoodjani) is wrong.
Normally you calculate Hedges' g from Cohen's d using the formula
g = c(m)*d (Formula 1)
with m = n1 + n2 − 2 (the degrees of freedom of the independent groups t-test) and n1 and n2 the group sizes.
The formula for the correction factor c is
c = gamma(m/2)/(sqrt(m/2)*gamma((m-1)/2)) (Formula 2)
which can be approximated by
c = 1 - 3/(4*m - 1) (Formula 3)
If you want to calculate Cohen's d from Hedges' g you reverse Formula 1:
d = g/c(m)
For example, a two independent groups t-test with n1 = 52 and n2 = 22 has 72 degrees of freedom (m). According to this,
c = 1 - 3(4*72 - 1) = .98954704.
If Hedges' g = -.1041649 then
Cohen's d = -.1041649/.98954704 = -.10526523
By the way: There is confusion in the literature about the meaning of Cohen's d and Hedges' g -- sometimes they are mixed up and this may be the case in your question, as well. Hence I am recommending to read the following paper that tries to unravel this confusion before you try to convert the one measure into the other:
Enzmann, D. (2015). Notes on Effect Size Measures for the Difference of Means From Two Independent Groups: The Case of Cohen's d and Hedges' g.
Technical Report Notes on Effect Size Measures for the Difference of Means Fr...
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