Effect Size Index Calculator

Formula

The formula to calculate the Effect Size Index (Cohen's d) is:

\[ d = \frac{M_1 - M_2}{SD_{pooled}} \]

Where:

\( d \) is the Effect Size Index (Cohen's d)
\( M_1 \) is the Mean of Group 1
\( M_2 \) is the Mean of Group 2
\( SD_{pooled} \) is the Pooled Standard Deviation

What is an Effect Size Index?

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.

Example Calculation

Let's assume the following values:

Mean of Group 1 (M₁) = 75
Mean of Group 2 (M₂) = 65
Standard Deviation of Group 1 (SD₁) = 10
Standard Deviation of Group 2 (SD₂) = 12

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.