Cohen's D Calculator
Calculate effect size to measure the magnitude of difference between two groups
Quick Examples:
1 Group 1
Optional (default: 30)
2 Group 2
Optional (default: 30)
Formula:
d = (M₁ - M₂) / spooled where spooled = √((s₁² + s₂²) / 2)
Cohen's d Effect Size
(Negative value indicates Group 2 > Group 1)
Effect Size Magnitude
Cohen's d
Standard effect size
Hedges' g
Bias-corrected
Pooled SD
spooled
Effect Size Interpretation (Cohen, 1988)
| Category | |d| Range | Interpretation |
|---|---|---|
| Negligible | < 0.2 | Very small or no practical effect |
| Small | 0.2 – 0.5 | Noticeable but small difference |
| Medium | 0.5 – 0.8 | Moderate, practically significant |
| Large | 0.8 – 1.2 | Substantial, clearly meaningful |
| Very Large | > 1.2 | Exceptionally large difference |
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About Cohen's D Calculator
What is Cohen's D?
Cohen's d is a standardized measure of effect size that quantifies the difference between two group means in terms of standard deviation units. Introduced by Jacob Cohen in 1988, it is one of the most widely used effect size measures in statistical analysis and research.
Cohen's d Formula:
d = (M₁ - M₂) / s_pooled
Where:
- M₁ = Mean of group 1
- M₂ = Mean of group 2
- s_pooled = Pooled standard deviation
Pooled Standard Deviation:
s_pooled = √((s₁² + s₂²) / 2)
Interpreting Cohen's D
Jacob Cohen proposed the following guidelines for interpreting effect sizes:
| Effect Size | d Value | Interpretation |
|---|---|---|
| Negligible | < 0.2 | Very small or no practical effect |
| Small | 0.2 | Noticeable but small difference |
| Medium | 0.5 | Moderate, practically significant |
| Large | 0.8 | Substantial, clearly meaningful |
| Very Large | > 1.0 | Exceptionally large difference |
Hedges' g Correction
For small sample sizes (typically n < 20 per group), Cohen's d can be biased. Hedges' g provides an unbiased estimate:
g = d × (1 - 3 / (4(n₁ + n₂) - 9))
When to Use Cohen's D
- Research Studies: Compare treatment vs. control groups
- Meta-Analysis: Combine results across studies
- Power Analysis: Determine required sample sizes
- Practical Significance: Assess if statistical differences matter
Cohen's D vs. P-Values
While p-values tell you if a difference is statistically significant, Cohen's d tells you how big that difference is:
- A tiny effect can be statistically significant with large samples
- Effect size helps determine practical importance
- Essential for understanding real-world impact
Frequently Asked Questions
Can Cohen's d be negative?
Yes! A negative d simply means Group 2 has a higher mean than Group 1. The absolute value indicates the magnitude.
What's a 'good' Cohen's d?
It depends on your field. In psychology, d = 0.5 is typical. In medicine, even small effects (d = 0.2) can be clinically important.
Should I use Cohen's d or Hedges' g?
Use Hedges' g when sample sizes are small (< 20 per group) or unequal. Otherwise, both give similar results.