Cohen's D Calculator

Calculate Cohen's d effect size to measure standardized differences between two groups

Calculate Cohen's D Effect Size

Statistics will be calculated automatically

Statistics will be calculated automatically

Cohen's D Results

0.000
Cohen's d
0.000
Pooled Standard Deviation

Group 1:

Mean = 0.000

SD = 0.000

n = 0

Group 2:

Mean = 0.000

SD = 0.000

n = 0

Formula: d = (M₁ - M₂) / s_pooled

Calculation: d = (0.000 - 0.000) / 0.000 = 0.000

Validation Notes

⚠️ Group 1 needs at least 2 data points to calculate standard deviation.
⚠️ Group 2 needs at least 2 data points to calculate standard deviation.

Example Calculation

Study Example

Treatment Group A: [5, 9, 3, 4, 8] (n=5, M=5.8, SD=2.49)

Control Group B: [8, 9, 12, 15, 7] (n=5, M=10.2, SD=3.27)

Step-by-Step Calculation

1. Calculate pooled SD: s_p = √[((5-1)×2.49² + (5-1)×3.27²) / (5+5-2)] = 2.92

2. Calculate Cohen's d: d = (5.8 - 10.2) / 2.92 = -1.51

Result: Large negative effect (Group B > Group A)

Cohen's D Interpretation

Very Small (< 0.2)

Negligible effect

Little practical significance

Small (0.2 - 0.5)

Small effect size

Minimal practical significance

Medium (0.5 - 0.8)

Medium effect size

Moderate practical significance

Large (0.8 - 1.2)

Large effect size

Substantial practical significance

Very Large (> 1.2)

Very large effect size

High practical significance

Common Applications

Clinical trial effectiveness

Educational intervention studies

Psychology research

A/B testing analysis

Meta-analysis studies

Treatment comparison

Key Points

Cohen's d measures practical significance

Independent of sample size

Assumes equal variances

Can be positive or negative

Complements statistical significance

Understanding Cohen's D Effect Size

What is Cohen's D?

Cohen's d is a standardized effect size measure that quantifies the difference between two group means in terms of standard deviation units. It provides a scale-free measure of the practical significance of a difference, complementing statistical significance testing.

Why Use Cohen's D?

  • Measures practical significance beyond p-values
  • Enables comparison across different studies
  • Independent of sample size effects
  • Standardized interpretation guidelines

Calculation Steps

Step 1: Calculate Group Means

M₁ = Σx₁/n₁, M₂ = Σx₂/n₂

Find the average value for each group

Step 2: Calculate Standard Deviations

SD = √[Σ(x-M)²/(n-1)]

Calculate sample standard deviation for each group

Step 3: Pooled Standard Deviation

s_p = √[((n₁-1)SD₁² + (n₂-1)SD₂²) / (n₁+n₂-2)]

Combine variability from both groups

Step 4: Cohen's d

d = (M₁ - M₂) / s_p

Standardize the mean difference

Interpretation Guidelines

Statistical vs Practical Significance

A statistically significant result (p < 0.05) doesn't guarantee practical importance. Cohen's d helps assess real-world relevance.

Context Matters

Effect size interpretation can vary by field. A small effect in medicine might be clinically significant, while larger effects may be needed in education.

Direction of Effect

Negative Cohen's d indicates Group 2 has higher mean than Group 1. The sign shows direction, absolute value shows magnitude.

Assumptions and Limitations

Equal Variances

Cohen's d assumes similar variability between groups. For unequal variances, consider Glass's delta or Hedges' g.

Normal Distribution

Best suited for normally distributed data. Non-normal data may require non-parametric alternatives.

Sample Size Considerations

Small samples can lead to biased estimates. Hedges' g provides bias correction for small samples.