Pooled Effect Size Calculator

Formula

To calculate the Pooled Effect Size:

\[ d_p = \frac{d_1 \cdot (n_1 - 1) + d_2 \cdot (n_2 - 1)}{n_1 + n_2 - 2} \]

Where:

\(d_p\) is the Pooled Effect Size
\(d_1\) is the Effect Size of the First Group
\(n_1\) is the Sample Size of the First Group
\(d_2\) is the Effect Size of the Second Group
\(n_2\) is the Sample Size of the Second Group

What is a Pooled Effect Size?

A pooled effect size is a statistical measure that combines the effect sizes from different studies to provide a single estimate of the effect. It is commonly used in meta-analysis and systematic reviews to synthesize research findings across multiple studies. The pooled effect size gives a weighted average of the effect sizes, taking into account the sample size of each study, which provides a more precise estimate of the overall effect.

Example Calculation 1

Let's assume the following values:

Effect Size of First Group (\(d_1\)) = 0.5
Sample Size of First Group (\(n_1\)) = 30
Effect Size of Second Group (\(d_2\)) = 0.7
Sample Size of Second Group (\(n_2\)) = 40

Using the formula:

\[ d_p = \frac{0.5 \cdot (30 - 1) + 0.7 \cdot (40 - 1)}{30 + 40 - 2} = \frac{0.5 \cdot 29 + 0.7 \cdot 39}{68} = \frac{14.5 + 27.3}{68} = 0.612 \]

The Pooled Effect Size is approximately 0.612.

Example Calculation 2

Let's assume the following values:

Effect Size of First Group (\(d_1\)) = 0.3
Sample Size of First Group (\(n_1\)) = 25
Effect Size of Second Group (\(d_2\)) = 0.6
Sample Size of Second Group (\(n_2\)) = 35

Using the formula:

\[ d_p = \frac{0.3 \cdot (25 - 1) + 0.6 \cdot (35 - 1)}{25 + 35 - 2} = \frac{0.3 \cdot 24 + 0.6 \cdot 34}{58} = \frac{7.2 + 20.4}{58} = 0.474 \]

The Pooled Effect Size is approximately 0.474.