Minimum Detectable Effect Calculator

Minimum detectable Cohen's d

What this answers

This calculator answers the inverse question to sample size planning: "given a sample size I already have (perhaps due to budget or timeline constraints), what is the smallest real effect I could reliably detect?" This is especially useful for evaluating a study that already happened, or one whose sample size is fixed by practical limits, to be honest about what it was actually capable of detecting.

How it is calculated

This is the mathematical inverse of the two-means sample size formula: instead of solving for n given a target effect size, it solves for the effect size given a fixed n, alpha, and target power, using the same normal-approximation design.

Worked example

For a planned sample of 63 per group, alpha of .05, and 80% power: the minimum detectable Cohen's d comes out to approximately .5, the exact inverse relationship confirmed by the Sample Size for Two Means engine, which recommends 63 per group specifically to detect a d of .5 at this alpha and power.

Assumption audit

Calculated from your data: the exact minimum detectable effect size given your stated n, alpha, and target power.

Evidence to review: compare this minimum detectable effect against what would actually be a meaningful, practically important effect size in your specific context. If the minimum detectable effect is larger than any effect you would actually care about, the study as planned may not be worth running.

You must verify: that the assumptions behind this calculation (equal variance, equal group sizes, a two-sided test) actually match your planned study design.

Common mistakes

A common mistake is treating the minimum detectable effect as the effect the study will find, rather than the smallest effect it could reliably find; the actual true effect, if one exists, could be larger, smaller, or in some unlucky samples still missed even above this threshold, since power is a probability, not a guarantee. Another is running this calculator after a study already found a null result and treating a large minimum detectable effect as proof the true effect is zero; it only shows the study was not equipped to detect a smaller effect, which is a different, more limited conclusion. A third is plugging in a per-group n that does not match how the actual study was run, such as a total n instead of a per-group figure.

Limitations

This calculator uses the same normal-approximation design as the Sample Size for Two Means engine, so its result is subject to the same approximation, close to but not identical to the more exact iterative noncentral-t solution.