Glass's Delta Calculator

Standardise the treatment effect using the control group's variability. Enter summary statistics to obtain Glass's delta, an approximate confidence interval, and qualitative interpretation of the effect magnitude.

1. Supply Group Statistics

Control SD anchors the standardisation

Treatment group

Control group

Uses an approximate variance for Glass's delta following Hedges and Olkin (1985).

Changing the direction flips the sign of delta.

Formula Reference

Glass's delta

\\[ \Delta = \frac{\bar{x}_{\text{treatment}} - \bar{x}_{\text{control}}}{s_{\text{control}}} \\]

Only the control group's standard deviation anchors the denominator.

Approximate variance

\\[ \text{Var}(\Delta) \approx \frac{n_t + n_c}{n_t n_c} + \frac{\Delta^2}{2(n_c - 1)} \\]

Variance reflects the use of the control variance estimator.

Step-by-Step Guide

  1. Compute the mean difference between treatment and control groups.
  2. Divide by the control group's standard deviation to obtain Glass's delta.
  3. Estimate the variance using the sample sizes and the squared delta term.
  4. Translate the delta value into magnitude descriptors and overlap metrics.
  5. Report delta alongside raw means and standard deviations for transparency.

References

  • Glass, G. V. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5(10), 3-8.
  • Hedges, L. V., & Olkin, I. (1985). Statistical Methods for Meta-Analysis. Academic Press.
  • Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science. Frontiers in Psychology, 4, 863.