What is Cohen's d and why should you care?
Cohen's d is a statistical measure that gives you the effect size, highlighting the difference between two groups while considering the variability within each group.
Formula
$$d = \frac{M_{2} - M_{1}}{S_{p}}$$
Where:
- d is Cohen's d (effect size)
- M₁ is the mean of Group 1
- M₂ is the mean of Group 2
- Sₚ is the pooled standard deviation
The pooled standard deviation is calculated as:
$$S_{p} = \sqrt{\frac{S_{1}^{2} + S_{2}^{2}}{2}}$$
Where S₁ and S₂ are the standard deviations of Group 1 and Group 2.
Calculation Example
- Mean of Group 1 (M₁): 70
- Mean of Group 2 (M₂): 85
- Standard Deviation of Group 1 (S₁): 10
- Standard Deviation of Group 2 (S₂): 15
Step 1: Calculate the Pooled Standard Deviation
$$S_{p} = \sqrt{\frac{10^{2} + 15^{2}}{2}} = \sqrt{\frac{100 + 225}{2}} = \sqrt{162.5} \approx 12.75$$
Step 2: Calculate Cohen's d
$$d = \frac{85 - 70}{12.75} \approx 1.18$$
So, Cohen's d here is approximately 1.18, indicating a substantial effect size.
Interpreting Cohen's d
| Effect Size | Cohen's d Value |
|---|---|
| Small | 0.2 |
| Medium | 0.5 |
| Large | 0.8 |
A value of 1.18 indicates a large effect size, meaning the difference between the two groups is practically significant.