# Meta - Analysis - Effect size calculation

I am trying to include a study into my meta-analysis, that reports results of an ANOVA: F(1,76) = 11.23, p = 0.001, n²=0,13 My question is how to calculate Hedge g from this data? I work with R, using the esc-package to calculate effect sizes. If I use this package I get an extremely high Hedge g (2.54), which is outstanding compared to the other included studies. If I try to calculate effect size form n² (transform n² to d and than to Hedge g) the effect size is much smaller (0.782). Which of this two ways is the correct one?

Assuming that F-test comes from a one-way ANOVA (testing the mean difference between two conditions), then the F-value is just the square of the t-statistic for an independent samples t-test. So, we know $$t = \sqrt{11.23}$$. And we can concert the t-statistic into a standardized mean difference (Cohen's d) with $$d = t \times \sqrt{1/n_1 + 1/n_2.}$$ The groups sizes are not given, but we know that the denominator degrees of freedom are 76 and then the total sample size must have been 78. So, assuming that $$n_1 = n_2 = 78/2 = 39$$, we get $$d = \sqrt{11.23} \times \sqrt{2/39} = 0.76$$. The bias correction factor that turns this d value into Hedges' g is so close to 1 here that this is also the Hedges' g value. So, the value you computed (0.78) is very close and the difference could just be due to rounding. At any rate, 2.54 is totally off.