Hedges' g
A standardised mean-difference effect size that adjusts Cohen's d for small-sample upward bias. Hedges (1981) showed that the standard d-style estimator is biased upward in small samples and derived a correction factor, often written J(df), that approaches 1 as sample size grows. Hedges' g is computed as g = J × d, where J ≈ 1 − 3 / (4·df − 1) for the two-sample case.
Why the Correction Matters
The bias is small once total sample size exceeds roughly 50 but becomes non-trivial at sizes typical of classroom studies. Cohen's d in a study with two groups of fifteen learners can overstate the population effect by several percent — large enough to nudge a result across conventional thresholds. Because the correction factor is multiplicative and always less than 1, g is always slightly smaller in absolute value than the corresponding d.
Standard in Meta-Analysis
Meta-analyses in applied linguistics typically prefer Hedges' g as the input metric. Its small-sample correction makes pooled estimates less sensitive to the size of any single study, and modern meta-analytic software (metafor, Comprehensive Meta-Analysis, psychmeta) computes g and its sampling variance directly from group means, SDs, and sample sizes. Plonsky and Oswald's (2014) L2 benchmarks for d apply, in practice, equally to g once samples are reasonably sized, and reviews routinely treat the two metrics as interchangeable for interpretive purposes while recommending g for computation.
Reporting
A g value should be reported with sample sizes, the SD denominator used (pooled, control, or other), and a Confidence Interval. Where original studies report only d, g can be back-computed from d and df without re-accessing raw data, which is the usual route in retrospective syntheses.
References
- Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107–128.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Plonsky, L., & Oswald, F. L. (2014). How big is "big"? Interpreting effect sizes in L2 research. Language Learning, 64(4), 878–912.
- Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. Chichester: Wiley.