Cohen's d Calculator
Calculate standardized mean difference effect size Cohen's $d = \frac{\bar{x}_1 - \bar{x}_2}{s_{\text{pooled}}}$, Hedges' $g$, Glass's $\Delta$, and effect magnitude ratings.
Calculate Standardized Effect Size Cohen's d
Enter sample mean, SD, and size for Group 1 and Group 2.
Calculation Results
Calculated using Cohen\'s effect size standard: d = \frac{\bar{x}_1 - \bar{x}_2}{s_{\text{pooled}}}, \quad s_{\text{pooled}} = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}
Quick Summary
The Cohen's d Calculator evaluates standardized mean difference effect size ($d$), Hedges' $g$ small-sample correction, Glass's $\Delta$, and qualitative magnitude ratings.
Formula Explanation
d = \frac{\bar{x}_1 - \bar{x}_2}{s_{\text{pooled}}}
\text{Hedges\' g} = d \cdot \left(1 - \frac{3}{4(n_1 + n_2) - 9}\right)How It Works
Cohen's $d$ expresses the difference between two sample means in units of standard deviation. The Cohen's d Calculator pools standard deviations $s_1$ and $s_2$ to compute standardized effect sizes.
Step-by-Step Worked Example
Practical Problem: Treatment Group 1 ($\bar{x}_1 = 85, s_1 = 12, n_1 = 30$) vs Control Group 2 ($\bar{x}_2 = 75, s_2 = 10, n_2 = 30$). Calculate Cohen's $d$.
- Step 1: Calculate mean difference ($\bar{x}_1 - \bar{x}_2$): $85 - 75 = \mathbf{+10.0000}$.
- Step 2: Calculate pooled variance ($s_{\text{pooled}}^2$): $\frac{(29 \times 144) + (29 \times 100)}{58} = \frac{4176 + 2900}{58} = \frac{7076}{58} = \mathbf{122.0000}$.
- Step 3: Calculate pooled standard deviation ($s_{\text{pooled}}$): $\sqrt{122.0} = \mathbf{11.0454}$.
- Step 4: Divide mean difference by $s_{\text{pooled}}$: $d = 10.0 / 11.0454 = \mathbf{+0.9054}$.
- Step 5: Determine Magnitude Rating: Since $d = 0.9054 \ge 0.80$, it is classified as a **Large Effect Size**.
Real-World Calculation Examples
Scenario 1: Educational Tutoring Program
Parameters: x̄1 = 85, x̄2 = 75, n = 30
Result: d = +0.9054 (Large positive treatment effect).
Scenario 2: Clinical Drug Trial Blood Pressure Reduction
Parameters: Drug vs Placebo
Result: Standardized clinical effect size comparison.
Scenario 3: Psychological Therapy Intervention
Parameters: Pre-post or control group trial
Result: Cohen's d effect size.
Scenario 4: Meta-Analysis Synthesis across 10 Studies
Parameters: Standardized metric pooling
Result: Hedges' g small sample corrected pooling.
Key Benefits of Using This Calculator
Sample-Size Independent Metric
Measures practical effect magnitude without distortion from sample size scale.
Hedges' g Small Sample Bias Correction
Includes Hedges' g correction factor $J$ for small sample studies ($n < 20$).
Glass's Delta Output
Provides Glass's $\Delta$ using control group standard deviation $s_2$.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is Cohen's d?
Cohen's d is a standardized effect size measuring the distance between two sample means in units of standard deviation.
What are Cohen's benchmarks for effect size?
Small: $d = 0.20$; Medium: $d = 0.50$; Large: $d = 0.80$; Very Large: $d \ge 1.20$.
What is difference between Cohen's d and Hedges' g?
Hedges' g applies a small-sample correction factor $J = 1 - \frac{3}{4(n_1+n_2)-9}$ to remove slight positive bias in Cohen's d for small samples.
What is Glass's Delta ($\Delta$)?
Glass's Delta standardizes mean difference using ONLY control group standard deviation $s_2$, useful when treatment affects variance.
How do I calculate Cohen's d in Excel?
Calculate `(xBar1 - xBar2) / s_pooled` using pooled variance formula.
Why is effect size important alongside p-values?
Statistical significance ($p < 0.05$) proves an effect EXISTS, while effect size ($d$) measures HOW BIG or PRACTICALLY IMPORTANT the effect is.
Can Cohen's d be negative?
Yes — negative $d$ indicates that Group 1 mean is smaller than Group 2 mean.
How do I convert Cohen's d to Pearson correlation r?
$r = \frac{d}{\sqrt{d^2 + 4}}$ (assuming equal sample sizes).
What is Cohen's d for a Paired t-test?
$d = \frac{\bar{d}}{s_d}$, standardizing paired difference mean by SD of differences.
How is Cohen's d used in Meta-Analysis?
Meta-analyses pool standardized effect sizes ($d$ or $g$) across multiple independent studies to synthesize overall intervention impact.