Minimum Detectable Effect Calculator

Work out minimum detectable effect instantly with clear inputs, formula shown and shareable results.

About Minimum Detectable Effect Calculator

The minimum detectable effect is the smallest true effect a design can find reliably. With 100 per group at 80% power and alpha 0.05, it is d = 0.397 - so smaller genuine effects will usually be missed. Halving that threshold to 0.199 needs 397 per group, since sample size scales with the inverse square of the effect.

Formulas

Minimum detectable effect

MDE = (z(alpha/2) + z(power)) x sqrt(2/n)

Sample scaling

halving the MDE requires four times the sample

Worked example

With the default values below, Minimum Detectable Effect Calculator returns Minimum Detectable Effect of 0.3962. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample size per groupminimum 2: 100
Desired poweraccepts 50–99 %: 80 %
Significance levelaccepts 0.1–20 %: 5 %

Results

Minimum Detectable Effect: 0.3962 d
Sample Per Group To Halve That Effect: 400
Sum Of The Critical Values: 2.8016
What This Study Can Detect: Small effects detectable

Step by step

1Values used
2Minimum detectable effect
3Sample scaling
4Minimum Detectable Effect= 0.3962 d
5Sample Per Group To Halve That Effect= 400
6Sum Of The Critical Values= 2.8016
7What This Study Can Detect= Small effects detectable

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why compute MDE rather than power?

Because it answers the more useful question: given the sample I can actually recruit, what is the smallest effect worth designing for?

Why does halving the effect quadruple the sample?

Because the effect enters squared in the sample size formula, which is the fundamental cost of chasing small effects.