Hedges' g is a bias-corrected version of Cohen's d that adjusts for small sample sizes. It provides a more accurate estimate of effect size when working with small samples (typically n < 50).

When should I use Hedges G instead of Cohen's d?

Use Hedges' g when you have small sample sizes (n < 50 per group). Hedges' g applies a correction factor that reduces the positive bias found in Cohen's d for small samples.

Hedges' g Calculator

Q: When should I use Hedges G instead of Cohen's d?

Use Hedges' g when you have small sample sizes (n < 50 per group). Hedges' g applies a correction factor that reduces the positive bias found in Cohen's d for small samples.

Calculate bias-corrected effect sizes for small samples. Pre-loaded with example data - try it now!

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Enter Group Statistics

Independent samples with bias correction

Group 1 (Treatment/Experimental)

Mean (M₁)

Standard Deviation (SD₁)

Sample Size (n₁)

Group 2 (Control/Comparison)

Mean (M₂)

Standard Deviation (SD₂)

Sample Size (n₂)

Confidence level (%)

Most common: 95% (standard in research)

Difference reported as

Flipping changes the sign of g

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Your Effect Size Results

✓ Calculation complete

Hedges' g (Bias-Corrected)

0.65

Medium Effect Size

95% CI: [0.42, 0.88]

Effect Size Visualization

Key Values

Hedges' g: 0.65
95% CI: [0.42, 0.88]
Correction J: 0.983
Cohen's d: 0.66

Interpretation

Magnitude: Medium
r (correlation): 0.31
Overlap %: 73.1%
Significance: ✓ CI excludes 0

Narrative

Group 1 scored 0.65 standard deviations higher than Group 2, representing a medium positive effect.

APA 7th Edition Reporting

Ready-to-use text for your research paper:

The treatment group (M = 85.5, SD = 12.3, n = 42) showed significantly higher scores than the control group (M = 77.2, SD = 11.8, n = 38), with a medium effect size, Hedges' g = 0.65, 95% CI [0.42, 0.88].

Effect Size Interpretation Guide (Cohen, 1988)

Small

0.20

Subtle difference, hard to notice

Medium

0.50

Noticeable difference, typical in research

Large

0.80

Obvious difference, practically significant

Hedges' g is a bias-corrected version of Cohen's d that adjusts for small sample sizes. When you calculate Cohen's d with small samples (typically n < 50), there's a slight positive bias - the effect size tends to be overestimated. Hedges' g corrects this by multiplying Cohen's d by a correction factor J.

Key Formula: g = J × d, where J = 1 - 3/(4(n₁ + n₂) - 9)

For large samples (n > 50), J ≈ 1, so Hedges' g and Cohen's d are nearly identical. For small samples, the correction becomes important.

Use Hedges' g when:

You have small sample sizes (n < 50 per group)
You're conducting meta-analysis (standard in the field)
You want to report the most accurate, unbiased effect size
You're comparing studies with different sample sizes

Use Cohen's d when:

You have large sample sizes (n > 50 per group)
Your field traditionally uses Cohen's d (e.g., some psychology subfields)
The difference between g and d is negligible (< 0.01)

Hedges' g	Magnitude	Interpretation
0.00 - 0.20	Negligible/Very Small	Minimal practical significance
0.20 - 0.50	Small	Subtle but measurable difference
0.50 - 0.80	Medium	Noticeable, typical in research
0.80+	Large	Obvious, practically significant

Important: These are Cohen's (1988) general guidelines. Context matters - a "small" effect in education might be more practically significant than a "large" effect in physics.

Education: Reading Intervention (g = 0.42)

Students receiving a new reading program (M = 73.2, SD = 15.4, n = 55) scored 0.42 standard deviations higher than control group (M = 68.9, SD = 14.8, n = 52). This is a small-to-medium effect, typical for education interventions.

Medicine: Treatment Effect (g = 1.2)

Patients receiving new treatment (M = 92.5, SD = 10.2, n = 30) showed 1.2 standard deviations improvement vs control (M = 75.3, SD = 11.5, n = 28). This is a large effect - highly clinically significant.

Psychology: Therapy Outcome (g = 0.65)

Therapy group (M = 85.5, SD = 12.3, n = 42) vs control (M = 77.2, SD = 11.8, n = 38) showed g = 0.65 - a medium effect. This is above average for psychological interventions.

What is Hedges' g? Understanding Bias-Corrected Effect Size

Definition and Purpose

Hedges' g is a standardized measure of effect size used in meta-analysis and statistical research to quantify the magnitude of difference between two groups. It represents a bias-corrected version of Cohen's d, specifically designed to provide more accurate estimates when working with small sample sizes (typically n < 50 per group). The correction factor, known as the J correction or Hedges' correction, addresses the slight positive bias inherent in Cohen's d calculations for small samples.

Unlike Cohen's d, which tends to overestimate the true population effect size in small samples, Hedges' g applies a multiplicative correction factor that shrinks the estimate toward zero. This correction becomes negligible with large samples but can substantially improve accuracy in typical research scenarios. Hedges' g is particularly valuable in meta-analyses where studies with varying sample sizes need to be combined, as it provides a more consistent estimate of standardized mean differences across studies.

Key Characteristics of Hedges' g:

Bias correction: Removes positive bias present in Cohen's d for small samples
Standardized metric: Expresses effect size in standard deviation units, making it interpretable across different measurement scales
Meta-analysis friendly: Preferred in systematic reviews and meta-analyses due to statistical properties
Comparable across studies: Allows direct comparison of effects from different research contexts
Approximately unbiased: Provides nearly unbiased estimates of population effect size

When to Use Hedges' g vs Cohen's d

The choice between Hedges' g and Cohen's d depends primarily on sample size and research context. Use Hedges' g when: (1) total sample size is less than 100 (n₁ + n₂ < 100), (2) conducting meta-analysis or systematic review, (3) combining effect sizes from multiple studies with varying sample sizes, or (4) publishing in journals that require bias-corrected estimates. Cohen's d remains acceptable for large samples (n > 50 per group) where the correction factor J ≈ 1.000, making the two measures virtually identical.

For small samples, the difference can be meaningful. For example, with n₁ = 15 and n₂ = 15 (total N = 30), the correction factor J ≈ 0.960, reducing a Cohen's d of 0.80 to Hedges' g of 0.77. While this 3% reduction may seem small, it accumulates across meta-analyses and can affect conclusions about clinical or practical significance.

Hedges' g Calculation Formulas

Step-by-Step Calculation

Step 1: Calculate Pooled Standard Deviation

Pooled SD Formula:

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

The pooled standard deviation combines the variability from both groups, weighted by their respective sample sizes. It provides a single estimate of population standard deviation under the assumption of homogeneity of variance (homoscedasticity).

Step 2: Calculate Cohen's d

Cohen's d Formula:

d = (Mean₁ - Mean₂) / s_pooled

Cohen's d represents the standardized mean difference, expressing the difference between groups in terms of their pooled standard deviation. A positive d indicates Group 1 scores higher than Group 2.

Step 3: Apply Hedges' Correction Factor

Correction Factor J:

J = 1 - [3 / (4 × (n₁ + n₂ - 2) - 1)]

Hedges' g Formula:

g = J × d

The J correction factor is always less than 1.0 for finite samples, approaching 1.0 as sample size increases. For very large samples (N > 200), J ≈ 0.999, making the correction negligible. For small samples, the correction is more substantial.

Confidence Interval Calculation

Standard Error Formula:

SE_g = √[(n₁ + n₂) / (n₁ × n₂) + g² / (2 × (n₁ + n₂))]

95% Confidence Interval:

CI_95% = [g - 1.96 × SE_g, g + 1.96 × SE_g]

The confidence interval indicates the precision of the effect size estimate. A narrow CI suggests high precision, while a wide CI indicates greater uncertainty. If the CI excludes zero, the effect is statistically significant at α = 0.05.

Worked Example

Example: Educational Intervention Study

Given Data:

Group 1 (Treatment): Mean₁ = 85.5, SD₁ = 12.3, n₁ = 42
Group 2 (Control): Mean₂ = 77.2, SD₂ = 11.8, n₂ = 38

Calculation Steps:

Pooled SD:
s_pooled = √[((42-1) × 12.3² + (38-1) × 11.8²) / (42+38-2)]
= √[(41 × 151.29 + 37 × 139.24) / 78]
= √[(6,202.89 + 5,151.88) / 78] = √145.58 = 12.07
Cohen's d:
d = (85.5 - 77.2) / 12.07 = 8.3 / 12.07 = 0.688
Correction Factor J:
J = 1 - [3 / (4 × 78 - 1)] = 1 - [3 / 311] = 1 - 0.00965 = 0.9904
Hedges' g:
g = 0.9904 × 0.688 = 0.681
Standard Error:
SE = √[(80/1,596) + 0.681² / (2 × 80)] = √[0.0501 + 0.0029] = 0.230
95% CI:
[0.681 - 1.96 × 0.230, 0.681 + 1.96 × 0.230] = [0.230, 1.132]

Interpretation: The treatment group scored 0.68 standard deviations higher than the control group, representing a medium-to-large positive effect. The 95% CI [0.23, 1.13] excludes zero, indicating statistical significance (p < 0.05).

Interpreting Hedges' g: Guidelines and Benchmarks

Cohen's Conventional Benchmarks

Jacob Cohen (1988) proposed conventional benchmarks for interpreting standardized effect sizes, which remain widely used despite his cautionary note that these are arbitrary guidelines that should be contextualized within specific research domains.

\|g\| Range	Classification	Interpretation	Overlap %
< 0.20	Negligible	Very small difference, difficult to detect	92%
0.20 - 0.50	Small	Noticeable difference, visible to careful observer	85%
0.50 - 0.80	Medium	Moderate difference, typical in behavioral research	67%
≥ 0.80	Large	Substantial difference, grossly perceptible	53%

Note on Overlap %: This represents the percentage of overlap between the two distributions. For example, at g = 0.80, 53% of the two distributions still overlap, meaning a randomly selected individual from the higher-scoring group has a 47% chance of scoring above the mean of the lower-scoring group.

Field-Specific Benchmarks

Cohen's benchmarks should be contextualized within specific research domains. What constitutes a "large" effect in physics might be considered "negligible" in educational research. Below are empirically-derived benchmarks from meta-analyses in various fields:

Psychology & Psychiatry

• Small: g ≈ 0.20 (e.g., subtle cognitive improvements)
• Medium: g ≈ 0.50 (e.g., therapeutic interventions)
• Large: g ≈ 0.80 (e.g., medication vs. placebo)

Education

• Small: g ≈ 0.15 (e.g., minor curriculum changes)
• Medium: g ≈ 0.40 (e.g., new teaching methods)
• Large: g ≈ 0.60+ (e.g., intensive interventions)

Medicine & Health

• Small: g ≈ 0.30 (e.g., lifestyle interventions)
• Medium: g ≈ 0.60 (e.g., drug treatments)
• Large: g ≈ 1.00+ (e.g., surgical procedures)

Organizational & I-O Psychology

• Small: g ≈ 0.25 (e.g., training programs)
• Medium: g ≈ 0.50 (e.g., selection procedures)
• Large: g ≈ 0.75+ (e.g., major org changes)

⚠️ Important Considerations

Effect size alone doesn't determine clinical or practical significance
Consider cost-effectiveness, feasibility, and implementation challenges
A small effect in a large population can have substantial real-world impact
Statistical significance (p-value) is separate from effect size magnitude
Always report confidence intervals alongside point estimates

Excel Formulas for Hedges' g Calculation

Step-by-Step Excel Implementation

You can calculate Hedges' g directly in Microsoft Excel using the following formulas. Assume your data is organized with Group 1 statistics in cells B2:B4 and Group 2 statistics in cells C2:C4.

Excel Data Setup:

Cell	Label	Group 1	Group 2
A2/B2/C2	Mean	85.5	77.2
A3/B3/C3	SD	12.3	11.8
A4/B4/C4	n	42	38

Formula 1: Pooled Standard Deviation (Cell D6)

=SQRT(((B4-1)*B3^2+(C4-1)*C3^2)/(B4+C4-2))

This calculates the pooled SD using the weighted variance formula.

Formula 2: Cohen's d (Cell D7)

=(B2-C2)/D6

Divides the mean difference by the pooled SD.

Formula 3: Degrees of Freedom (Cell D8)

=B4+C4-2

Total sample size minus 2.

Formula 4: Correction Factor J (Cell D9)

=1-(3/(4*D8-1))

Hedges' bias correction factor.

Formula 5: Hedges' g (Cell D10)

=D7*D9

Bias-corrected effect size.

Formula 6: Standard Error (Cell D11)

=SQRT((B4+C4)/(B4*C4)+(D10^2)/(2*(B4+C4)))

Standard error of Hedges' g.

Formula 7: 95% CI Lower Bound (Cell D12)

=D10-1.96*D11

Formula 8: 95% CI Upper Bound (Cell D13)

=D10+1.96*D11

💡 Pro Tip: Create a Reusable Template

Save this Excel file as a template (.xltx) for repeated use. You can also add data validation to ensure positive values for SD and n, and conditional formatting to highlight significant results (CI excludes 0).

LaTeX Formulas for Publications

Use these LaTeX codes to include Hedges' g formulas in your academic papers, presentations, or online publications.

Pooled Standard Deviation

s_p = \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}}

Cohen's d

d = \frac{\bar{X}_1 - \bar{X}_2}{s_p}

Hedges' Correction Factor J

J = 1 - \frac{3}{4df-1}

Hedges' g

g = J \times d

Standard Error of Hedges' g

SE_g = \sqrt{\frac{n_1+n_2}{n_1 n_2} + \frac{g^2}{2(n_1+n_2)}}

95% Confidence Interval

CI_{95\%} = g \pm 1.96 \times SE_g

📝 Complete LaTeX Equation Block

Copy this complete block to include all formulas in your document:

\begin{align}
s_p &= \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}} \\
d &= \frac{\bar{X}_1 - \bar{X}_2}{s_p} \\
J &= 1 - \frac{3}{4df-1} \\
g &= J \times d \\
SE_g &= \sqrt{\frac{n_1+n_2}{n_1 n_2} + \frac{g^2}{2(n_1+n_2)}} \\
CI_{95\%} &= g \pm 1.96 \times SE_g
\end{align}

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References and Further Reading

Primary Sources

Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107-128. https://doi.org/10.3102/10769986006002107
The foundational paper introducing the bias correction for standardized mean differences.
Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic Press.
Comprehensive textbook on meta-analysis methods, including detailed treatment of effect size estimation.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
Classic reference for Cohen's d and conventional effect size benchmarks.
Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to meta-analysis. Chichester, UK: Wiley. https://doi.org/10.1002/9780470743386
Modern comprehensive guide to meta-analysis with practical examples and software guidance.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
Accessible guide to effect size calculation and reporting in contemporary research.
Grissom, R. J., & Kim, J. J. (2012). Effect sizes for research: Univariate and multivariate applications (2nd ed.). New York: Routledge. https://doi.org/10.4324/9780203803233
Comprehensive coverage of effect size measures across various statistical tests.
Cumming, G., & Calin-Jageman, R. (2017). Introduction to the new statistics: Estimation, open science, and beyond. New York: Routledge. https://doi.org/10.4324/9781315708607
Modern approach emphasizing effect sizes and confidence intervals over p-values.
Durlak, J. A. (2009). How to select, calculate, and interpret effect sizes. Journal of Pediatric Psychology, 34(9), 917-928. https://doi.org/10.1093/jpepsy/jsp004
Practical guide for selecting and interpreting appropriate effect sizes in applied research.
Morris, S. B., & DeShon, R. P. (2002). Combining effect size estimates in meta-analysis with repeated measures and independent-groups designs. Psychological Methods, 7(1), 105-125. https://doi.org/10.1037/1082-989X.7.1.105
Advanced methods for combining effect sizes in complex meta-analytic designs.
Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48. https://doi.org/10.18637/jss.v036.i03
Comprehensive guide to meta-analysis using R software with practical examples.

Additional Resources

Comprehensive Meta-Analysis (CMA) Software - https://www.meta-analysis.com/
Cochrane Handbook for Systematic Reviews - https://training.cochrane.org/handbook
APA Guidelines on Effect Sizes - https://apastyle.apa.org/
Effect Size Calculator Validation Study - Lenhard, W., & Lenhard, A. (2016). Calculation of Effect Sizes. Psychometrica. Online Resource

📚 Recommended Reading for Different Audiences

Beginners: Cumming, G. (2012). Understanding the new statistics. New York: Routledge.
Intermediate: Ellis, P. D. (2010). The essential guide to effect sizes. Cambridge University Press.
Advanced: Kelley, K., & Preacher, K. J. (2012). On effect size. Psychological Methods, 17(2), 137-152.

Citation for This Calculator

Bhakuni, P. (2025). Hedges' g Calculator - Free Effect Size Calculator with Confidence Intervals. CalcArena. Retrieved from https://calcarena.com/calculators/hedges-g-calculator.html