In hypothesis testing, we often use p-values to determine if there is a statistically significant difference between two groups.
However, while a p-value can tell us whether or not there is a statistically significant difference between two groups, an effect size can tell us the size of this difference.
One of the most common ways to measure effect size is to use Hedges’ g, which is calculated as follows:
g = (x1 – x2) / √((n1-1)*s12 + (n2-1)*s22) / (n1+n2-2)
- x1, x2: The sample 1 mean and sample 2 mean, respectively
- n1, n2: The sample 1 size and sample 2 size, respectively
- s12, s22: The sample 1 variance and sample 2 variance, respectively
The following example shows how to calculate Hedges’ g for two samples.
Example: Calculating Hedge’s g
Suppose we have the following two samples:
- x1: 15.2
- s1: 4.4
- n1: 39
- x2: 14
- s2: 3.6
- n2: 34
Here is how to calculate Hedges’ g for these two samples:
- g = (x1 – x2) / √((n1-1)*s12 + (n2-1)*s22) / (n1+n2-2)
- g = (15.2 – 14) / √((39-1)*4.42 + (34-1)*3.62) / (39+34-2)
- g = 1.2 / 4.04788
- g = 0.29851
Hedges’ g turns out to be 0.29851.
Bonus: Use this online calculator to automatically calculate Hedges’ g for any two samples.
How to Interpret Hedges’ g
As a rule of thumb, here is how to interpret Hedge’s g:
- 0.2 = Small effect size
- 0.5 = Medium effect size
- 0.8 = Large effect size
In our example, an effect size of 0.29851 would likely be considered a small effect size. This means that even if the difference between the two group means is statistically significant, the actual difference between the group means is trivial.
Hedges’ g vs. Cohen’s d
Another common way to measure effect size is known as Cohen’s d, which uses the following formula:
d = (x1 – x2) / √(s12 + s22) / 2
The only difference between Cohen’s d and Hedges’ g is that Hedges’ g takes each sample size into consideration when calculating the overall effect size.
Thus, it’s recommended to use Hedge’s g to calculate effect size when the two sample sizes are not equal.
If the two sample sizes are equal then Hedges’ g and Cohen’s d will be the exact same value.