Statistics Tool

Standardized Mean Difference Calculator

Estimate effect size from two groups quickly. Get corrected metrics, bounds, overlap, and interpretation notes. Use robust outputs for studies, dashboards, reviews, and reports.

Enter Group Statistics

Use summary statistics for two independent groups. The calculator computes pooled and corrected effect size measures from the values you enter.

Example Data Table

This worked example shows how the tool behaves with two independent groups.

Scenario Group 1 Mean Group 1 SD Group 1 n Group 2 Mean Group 2 SD Group 2 n Cohen's d Hedges' g 95% CI for g
Training score comparison 82.0000 10.0000 40 74.0000 12.0000 38 0.7260 0.7188 0.2646 to 1.1730

Formula Used

1) Mean Difference
Mean Difference = Mean1 − Mean2
2) Pooled Standard Deviation
SDpooled = √[ ((n1 − 1)SD12 + (n2 − 1)SD22) / (n1 + n2 − 2) ]
3) Cohen's d
d = (Mean1 − Mean2) / SDpooled
4) Hedges' g
J = 1 − 3 / (4(n1 + n2) − 9)
g = J × d
5) Glass Delta
Δ = (Mean1 − Mean2) / SDcontrol
6) Variance and Confidence Interval
Var(d) = (n1 + n2) / (n1n2) + d2 / [2(n1 + n2 − 2)]
Var(g) = J2 × Var(d)
CI = g ± z × SE(g)

The calculator also estimates probability of superiority, U3 percentile, and distribution overlap using a normal approximation.

How to Use This Calculator

  1. Enter the mean, standard deviation, and sample size for Group 1.
  2. Enter the same three values for Group 2.
  3. Choose a confidence level for the interval around Hedges' g.
  4. Select which group standard deviation should act as the control for Glass delta.
  5. Press the calculate button to display results above the form.
  6. Review Hedges' g as the corrected primary effect size.
  7. Use CSV for spreadsheets and PDF for reporting or sharing.
  8. Check the stability note when the group standard deviations differ noticeably.

FAQs

1) What does standardized mean difference measure?

It measures the difference between two group means after scaling that gap by variability. This makes results easier to compare across studies, outcomes, or reporting formats.

2) Why does the calculator show both Cohen's d and Hedges' g?

Cohen's d is a common raw effect size. Hedges' g applies a small sample correction, so it is often preferred when total sample size is modest.

3) When should I look at Glass delta?

Glass delta is useful when one group acts as a control and the standard deviations differ meaningfully. It standardizes the mean gap using only the selected control group's variation.

4) What is a good interpretation for effect size magnitude?

A common guide is negligible below 0.20, small near 0.20, medium near 0.50, and large near 0.80. Context still matters.

5) Why is the confidence interval important?

The interval shows the likely range of the corrected effect size. Narrow intervals suggest better precision, while wide intervals indicate more uncertainty in the estimate.

6) What does probability of superiority mean?

It estimates how often a randomly selected value from Group 1 would exceed a randomly selected value from Group 2, assuming the model assumptions are reasonable.

7) Can I use this calculator for paired samples?

No. This version is designed for two independent groups using summary statistics. Paired or repeated measures designs require a different effect size method.

8) What should I do if standard deviations are very different?

Inspect Glass delta, review the SD ratio, and consider whether the groups truly share comparable variability. Large SD gaps can affect the meaning of pooled measures.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.