Teaching · For Teachers

How big was the difference,
in a number others can read.

Enter the means, SDs and sizes of two groups, or paste the scores. The calculator gives Hedges’ g with its confidence interval, the improvement index in percentile points and an honest label for an education study, and handles before-and-after data from one class without overstating it.

Calculate an effect sizeWhat you get
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Included with Caveat Classroom and Whole-school licenses. Or get it in the For Teachers toolkit, $79 for 72 items.

The effect size calculator

The worked example is made up: an intervention group and a comparison group on a spring reading test. A second saved example has one class’s fluency before and after. Nothing you enter leaves this browser.

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What you get

Teaching · For Teachers$12 · included with Classroom and Whole-school licenses

What you finish with
For two groups: Hedges’ g with a 95% confidence interval, Cohen’s d, Glass’s delta, the pooled SD, U3 and the improvement index, the probability of superiority and the overlap, each labelled against benchmarks for education studies and Cohen’s general rule, with a picture of the two distributions and a plain-language sentence. For one group before and after: gav, dav and dz with an interval, and a clear note on why it is not a program effect. Analyses are saved, compared in a list, printed as a report and downloaded together.
Who it is for
Teachers doing action research, instructional leaders and intervention teams reporting results, graduate students in education, and anyone reading a study who wants to check its effect size.
Format
Browser tool. Works on a phone, tablet or computer; results recalculate as you type. Summary statistics or pasted scores. Prints a one-page report; downloads every saved analysis as a spreadsheet (.csv); export and import a file.
Access
$12 one-time, yours on every device you sign in on; the tool opens once you are signed in with it. Included with Caveat Classroom and Whole-school licenses. Also in the For Teachers toolkit ($79) and the Teaching Suite pass ($199), and 1 more bundle. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The For Teachers space in Caveat Teaching.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Choose the design: two separate groups, or the same students measured before and after.
  2. Enter each group’s mean, SD and size, or switch to Paste scores and paste a column from a spreadsheet.
  3. Read g and its interval first. If the interval crosses zero, the groups may not differ at all.
  4. Read the label for an education study, the improvement index and the plain-language sentence, and look at the two curves.
  5. Name and save the analysis, then print the report or download all saved analyses.

Calculate an effect size

How the effect sizes are worked out

Standard formulas, shown on the worked example.

1 Difference in means, in standard deviationsDifference8.1 points213.2 − 205.1Pooled SD14.60SDs 14.2 and 15.0, weightedCohen's d0.5558.1 ÷ 14.602 Correct for small samples, then give the rangeCorrection J0.99181 − 3 ÷ (4 × 94 − 9)Hedges' g0.5595% CI 0.14 to 0.963 Say it in percentilesU370.9%of the intervention group aboveImprovement index+20.9percentile points (U3 − 50)1 Difference in SDsDifference8.1 points213.2 − 205.1Pooled SD14.60weighted by nCohen's d0.5558.1 ÷ 14.602 Small-sample correctionCorrection J0.99181 − 3 ÷ 367Hedges' g0.55CI 0.14 to 0.963 In percentilesU370.9%above the meanImprovement+20.9percentile points
The worked example: an intervention group of 48 averaged 213.2 and a comparison group of 46 averaged 205.1. The 8.1-point gap is 0.55 pooled standard deviations; corrected for sample size, g = 0.55.

Two groups

Cohen’s d divides the difference in means by the pooled standard deviation, the two SDs weighted by their degrees of freedom. Hedges’ g multiplies d by J = 1 − 3 ÷ (4(n1 + n2) − 9), which removes the small upward bias of d in small samples; the What Works Clearinghouse reports g. The 95% interval is g ± 1.96 standard errors, the usual normal approximation. Glass’s delta uses only the comparison group’s SD. U3 is the share of the first group above the comparison mean, assuming normal scores, and the improvement index is U3 minus 50 percentile points.

Before and after, and the benchmarks

For one group measured twice, dz divides the average gain by the SD of the gains, and dav divides it by the average of the two SDs (Lakens, 2013); gav applies the small-sample correction. These describe change, not the effect of a program, because students grow and retake tests anyway. Cohen called 0.2, 0.5 and 0.8 small, medium and large as a general rough guide. Kraft (2020) found effects in education studies are usually far smaller and proposed under 0.05 small, 0.05 to under 0.20 medium and 0.20 or more large for causal studies with standardized achievement outcomes; the page uses Kraft’s labels only for two-group designs.

Sources

  1. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
  2. Hedges, L. V. (1981). Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107–128.
  3. Kraft, M. A. (2020). Interpreting effect sizes of education interventions. Educational Researcher, 49(4), 241–253.
  4. 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.
  5. What Works Clearinghouse. Procedures and Standards Handbook, Version 5.0 (2022). Institute of Education Sciences: Hedges’ g and the improvement index.
  6. Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. Wiley: variance of d and g.

The worked examples are made up. Effect sizes describe a difference; they do not show what caused it, and a single-group gain is not a program effect. Intervals use the normal approximation and are rough with very small groups. Your data stay in this browser. Support: team@caveatacademic.com.