When we need to make a comparative analysis between two sets of data, we often resort to the effect size formula. This mathematical tool is highly efficient in making critical decisions and predicting future possibilities based on the comparison of the data sets. The process involves calculating the mean of both sets of data, subtracting them, and then determining the standard deviation for each set. Lastly, we compute the squares.
\[\LARGE d \; = \; \frac{M_{1}-M_{2}}{\sqrt{\frac{S_{1}^{2}+S_{2}^{2}}{2}}}\]
We can derive the effect size coefficient from the value “d” using the formula below:
\[\LARGE r \; = \; \frac{d}{\sqrt{d^{2}+4}}\]
Where,
d = Cohen’s index
M
1
= Mean of the first data set
M
2
= Mean of the second data set
S
1
= Standard deviation of the first data set
S
2
= Standard deviation of the second data set
r = Effect-size coefficient.