The formula to calculate the Effect Size Index (Cohen's d) is:
\[ d = \frac{M_1 - M_2}{SD_{pooled}} \]
Where:
An Effect Size Index is a statistical tool used to measure the strength or magnitude of a relationship between variables in a study. It quantifies the size of the difference between groups, or the strength of the relationship between variables, providing a more meaningful measure than just a p-value from a hypothesis test. It allows researchers to understand not just if a treatment or condition has an effect, but the size of that effect, which can be crucial in fields like social sciences, education, and medicine.
Let's assume the following values:
Using the formula to calculate the Effect Size Index:
\[ SD_{pooled} = \sqrt{\frac{(10^2 + 12^2)}{2}} = \sqrt{\frac{(100 + 144)}{2}} = \sqrt{122} \approx 11.05 \]
\[ d = \frac{75 - 65}{11.05} \approx 0.90 \]
The Effect Size Index (Cohen's d) is approximately 0.90.
