Cohen's d Calculator

Cohen's d Calculator

Calculate standardized effect size between two groups using Cohen's d, Hedges' g, and Glass's delta.

Last updated: March 2026

Group Statistics

Effect Size Measures

Cohen's d
0.4527
Hedges' g
0.4468
Glass's Δ
0.4167
Pooled SD
11.0454
Effect Size Interpretation
Small

Based on |d| = 0.453

Cohen's d Effect Size Interpretation

d Value RangeMagnitudePractical MeaningPercentile Overlap
|d| < 0.2NegligibleBarely noticeable difference>92%
0.2 ≤ |d| < 0.5SmallNoticeable but still small85–92%
0.5 ≤ |d| < 0.8MediumClearly visible difference69–85%
|d| ≥ 0.8LargeSubstantial, meaningful difference<69%

What is Cohen's d?

Cohen's d is a standardized measure of effect size that quantifies the difference between two group means in units of standard deviation. Unlike t-tests (which test whether a difference exists), Cohen's d measures how large or meaningful that difference is, independent of sample size.

Cohen's d is calculated as: d = (μ₁ - μ₂) / σ_pooled, where μ₁ and μ₂ are the group means and σ_pooled is the pooled standard deviation. Related measures include Hedges' g (a bias-corrected version) and Glass's delta (which uses only the control group's standard deviation).

Effect sizes are crucial for research interpretation. A statistically significant result (low p-value) might involve a tiny, practically meaningless effect size, while a non-significant result might have a large practical effect size due to low sample size.

How to Calculate Cohen's d

Step-by-Step Process:

Step 1: Collect means, SDs, and n for both groups
Step 2: Calculate pooled SD = √[((n₁-1)s₁² + (n₂-1)s₂²) / (n₁+n₂-2)]
Step 3: Calculate d = (M₁ - M₂) / σ_pooled
Step 4: For Hedges' g, apply bias correction: g = d × [1 - 3/(4df-1)]
Step 5: For Glass's Δ, use control group SD: Δ = (M₁ - M₂) / s₂

Cohen's Interpretation Guidelines:

|d| < 0.2
Negligible
0.2 ≤ |d| < 0.5
Small
0.5 ≤ |d| < 0.8
Medium
|d| ≥ 0.8
Large

Three Effect Size Measures:

  • Cohen's d: Most common; uses pooled SD; assumes equal variances
  • Hedges' g: Bias-corrected version of Cohen's d; better for small samples
  • Glass's Δ: Uses only the control group SD; useful when variances are unequal or group sizes differ

Example: Treatment vs. Control

Did a training program improve test scores?

Control:
Mean = 70, SD = 12, n = 30
Treatment:
Mean = 75, SD = 10, n = 30
Pooled SD:
√[((29)(12)² + (29)(10)²) / (58)] = 11.048
Cohen's d:
(75 - 70) / 11.048 = 0.452
Interpretation:
d = 0.452 indicates a small to medium effect size. The training program improved scores meaningfully, even though the absolute difference (5 points) seems small.

Frequently Asked Questions

Why use effect size instead of p-values?

P-values only tell you if a difference exists, not how meaningful it is. Effect sizes quantify the magnitude of the difference, which is crucial for practical decision-making.

Can effect size be negative?

Yes, Cohen's d can be negative (indicating Group 2 is higher). The sign indicates direction; the absolute value indicates magnitude. Conventionally, we interpret |d|.

When should I use each measure?

Use Cohen's d when variances are equal. Use Hedges' g for small samples or when correcting bias. Use Glass's Δ when one group is a control and variances differ.

What if the effect size is very large?

A large effect size indicates a substantial, meaningful difference. In research, this suggests strong practical significance, even if sample size or p-values might vary.

How does effect size relate to sample size?

Effect size is independent of sample size. A large sample can detect small effects (low p-value), but that doesn't mean the effect is large—check Cohen's d.

Is medium effect size always acceptable?

Context matters. In experimental research, medium effects are often satisfactory. In clinical settings, even small effects might be meaningful; in other fields, large effects might be required.

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