# 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?

## 1 Answer

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.

Note that you don't know the correct sign of the d (g) value, so this must be inferred from other information provided in the article.

• Thank you very much for this information! – Martha Oct 25 '19 at 8:37
• Is there a certain procedure to highlight your answer? – Martha Oct 30 '19 at 15:04
• – Wolfgang Oct 30 '19 at 18:43