Cohen’s d, Small-Sample Bias-Corrected Hedges’ g & Glass’s Δ Effect Size Calculator

Compute pooled Cohen’s d, Hedges’ g correction, Glass’s Δ, and variance explained r².

Pooled Cohen’s d Effect Size
0.693 SD units
Bias-Corrected Hedges’ g 0.68 SD units
Pooled Standard Deviation (s_p) 10.817 SD
Variance Explained (r² %) 10.73 %
Inputs
⚡ Scenarios:
M₁
Treatment / Group 1 Mean (M₁).
s₁
Treatment / Group 1 Standard Deviation (s₁).
n₁
Treatment / Group 1 Sample Size (n₁).
M₂
Control / Group 2 Mean (M₂).
s₂
Control / Group 2 Standard Deviation (s₂).
n₂
Control / Group 2 Sample Size (n₂).
Results & Graph
Pooled Cohen’s d Effect Size
0.693 SD units
Bias-Corrected Hedges’ g
0.68 SD units
Pooled Standard Deviation (s_p)
10.817 SD
Variance Explained (r² %)
10.73 %

Pooled Cohen’s d Effect Size

Graph 1 • Cohen’s d & Hedges’ g • Domain Architecture & Live Telemetry Maps Group1 Mean, Group1 Sd, Group1 N through Cohen’s d & Hedges’ g Formula.
Pooled Cohen’s d Effect Size: 0.693 SD units Cohen’s d & Hedges’ g • Invariants & Metrics Pooled Cohen’s d Effect Size 0.693 SD units Bias-Corrected Hedges’ g 0.68 SD units Pooled Standard Deviation (s 10.817 SD Variance Explained (r² %) 10.73 %
Graph 2 • Pooled Cohen’s d Effect Size Across Group1 Mean Sweep (40% → 160%) Evaluates s_pooled = √[ ((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2) ]; d = (M₁ − M₂) / s across 7 operating points (current input highlighted).
-3.66 SD uni 0.946 SD uni 5.55 SD uni -3.66 31.40M₁ -2.21 47.10M₁ -0.758 62.80M₁ 0.693 78.50M₁ 2.15 94.20M₁ 3.60 109.9M₁ 5.05 125.6M₁
Graph 3 • Joint Sensitivity: Group1 Mean × Group1 Sd Compares Pooled Cohen’s d Effect Size when Group1 Sd is shifted +25% (solid) vs. −25% (dashed).
-1.65 SD uni 0.930 SD uni 3.51 SD uni --- Group1 Sd @ 75% -1.33 -30% -0.354 -15% 0.620 +0% 1.59 +15% 2.56 +30%
Summary: Pooled SD is 10.817, Cohen’s d is 0.693, bias-corrected Hedges’ g is 0.68, and point-biserial correlation r is 0.328.
Summary: Pooled SD is 10.817, Cohen’s d is 0.693, bias-corrected Hedges’ g is 0.68, and point-biserial correlation r is 0.328.
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Formula & Mathematical Methodology: Cohen’s d & Hedges’ g Formula

spooled = ((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)
d = (M₁ − M₂) / spooled
g = d × [1 − 3/(4(n₁+n₂−2) − 1)]
s_pooled = √[ ((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2) ]; d = (M₁ − M₂) / s_pooled; g = d × [1 − 3/(4(n₁+n₂−2) − 1)]
  • group1Mean: Group1 Mean (M₁)
  • group1Sd: Group1 Sd (s₁)
  • group1N: Group1 N (n₁)
  • group2Mean: Group2 Mean (M₂)
  • group2Sd: Group2 Sd (s₂)
  • group2N: Group2 N (n₂)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: Cohen’s d & Hedges’ g

Compute pooled Cohen’s d, Hedges’ g correction, Glass’s Δ, and variance explained r².

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: s_pooled = √[ ((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2) ]; d = (M₁ − M₂) / s_pooled; g = d × [1 − 3/(4(n₁+n₂−2) − 1)].
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes Cohen’s d & Hedges’ g via s_pooled = √[ ((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2) ]; d = (M₁ − M₂) / s_pooled; g = d × [1 − 3/(4(n₁+n₂−2) − 1)].

Frequently Asked Questions

How does the Cohen’s d, Small-Sample Bias-Corrected Hedges’ g & Glass’s Δ Effect Size Calculator compute the solution?

It evaluates s_pooled = √[ ((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2) ]; d = (M₁ − M₂) / s_pooled; g = d × [1 − 3/(4(n₁+n₂−2) − 1)] directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Non-Parametric & Hypothesis Testing

Cohen’s d, Small-Sample Bias-Corrected Hedges’ g & Glass’s Δ Effect Size Calculator: inputs, method, and how to read the result

Compute pooled Cohen’s d, Hedges’ g correction, Glass’s Δ, and variance explained r².

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Group1 Mean: Treatment / Group 1 Mean (M₁).
  • Group1 Sd: Treatment / Group 1 Standard Deviation (s₁).
  • Group1 N: Treatment / Group 1 Sample Size (n₁).
  • Group2 Mean: Control / Group 2 Mean (M₂).

What the calculation includes

With the default values shown, Pooled Cohen’s d Effect Size is 0.693 SD units. The calculation follows Cohen’s d & Hedges’ g Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Group1 Mean from 78.5 M₁ to 86.35 M₁ changes Pooled Cohen’s d Effect Size from 0.693 SD units to 1.419 SD units. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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