Minimum Detectable Effect (MDE) Calculator

StatisticsLast updated: August 22, 2026

The minimum detectable effect (MDE) is the smallest effect size a study can catch with a given sample size, power, and significance level. It turns the usual question around: instead of "how many participants do I need to see this effect?" it answers "what is the smallest effect I can see with the sample I have?" That makes it useful both at the design stage, when the budget is fixed, and after the study, when a non-significant result has to be interpreted.

When no significant difference is found, the question to ask is not "what was my power?" but "how sensitive was this study — what size of effect could it have seen?" Because the MDE rests on the design alone and not on the observed effect size, it avoids the circular reasoning of post-hoc power analysis. This calculator computes the MDE in terms of Cohen's d for two independent groups and for one-sample/paired designs, converts it to raw measurement units when a standard deviation is supplied, and produces an effect-power table together with two separate curves.

In a two-group design the effective sample size is n/2; in a one-sample design it is n.
In a two-group design, the number of observations PER GROUP; in a one-sample/paired design, the total number of observations (pairs).
%
The standard benchmark in the literature is 80%; sensitivity analyses usually use this value.
Sets the false positive risk. In the social sciences 5% is the common choice.
The two-tailed test is the standard; a one-tailed test makes a smaller effect detectable with the same sample.
If supplied, the effect size is converted to raw measurement units: Δ = d · σ (points, mmHg, currency units...).

Minimum Detectable Effect (MDE)

Two independent groups: d_min = (z₍α/₂₎ + z₍β₎) · √(2 / n)      (n = per group)
One-sample/paired:      d_min = (z₍α/₂₎ + z₍β₎) · √(1 / n)
In raw units:           Δ_min = d_min · σ
z₍α/₂₎: α = 0.05 → 1.960 · α = 0.01 → 2.576   (one-tailed z₍α₎: 1.645 · 2.326)
z₍β₎: power 80% → 0.842 · 90% → 1.282 · 95% → 1.645
Inverse relation:  n = 2 · (z₍α/₂₎ + z₍β₎)² / d_min²
Benchmark:  d_min ≤ smallest practically meaningful difference → the design is sensitive enough

The formula is the sample size formula solved for d, and it rests on the normal (z) approximation. d_min is inversely proportional to the square root of the sample size: quadrupling the sample halves the smallest detectable effect.

How to Calculate

  1. Choose your study design: two independent groups, or a one-sample/paired measurement?
  2. Enter the sample size you have (or can reach) — in a two-group design, write the number of observations per group.
  3. Set the power you are targeting; 80% is the standard choice in sensitivity analyses.
  4. Choose the significance level (α) and the test direction.
  5. If you know the standard deviation of your scale, enter it; the result is then also reported in raw units such as points, mmHg, or currency units.
  6. Compare the resulting d_min with the smallest difference considered meaningful in your field: if d_min is larger than that threshold, the design is not sensitive enough.

Worked Examples

A typical study with 30 per group

With 30 participants per group, d_min = (1.9600 + 0.8416) · √(2/30) = 0.723. This study can therefore catch only medium and larger differences with 80% power; smaller true effects are likely to be missed. Raising the power target to 90% pushes the smallest detectable effect up to 0.837.

Smallest detectable effect (d): 0.723 · Effect size class: Medium · z₍α/₂₎ critical value: 1.9600

Converting to raw units: groups of 100, σ = 10

With 100 participants per group, d_min = (1.9600 + 0.8416) · √(2/100) = 0.396, and since σ = 10.00 this corresponds to a difference of 3.96 points on the raw scale. With the same sample, a power target of 90% raises the smallest detectable effect to 0.458, or 4.58 units on the raw scale.

Smallest detectable effect (d): 0.396 · Smallest difference in raw units (Δ): 3.96 · Effect size class: Small

Paired design, 25 pairs, 90% power

In a pre-post design with 25 pairs and a 90% power target, d_min = (1.9600 + 1.2816) · √(1/25) = 0.648. Lowering the power target to 80% with the same sample brings d_min down to 0.560: at lower power, smaller effects count as "detectable" simply because the benchmark has been relaxed.

Smallest detectable effect (d): 0.648 · Effect size class: Medium · z₍α/₂₎ critical value: 1.9600

Frequently Asked Questions

Why is post-hoc power analysis problematic?
Power computed after the study from the OBSERVED effect size is a one-to-one transformation of the p-value: as p grows, post-hoc power mechanically shrinks. So "it was not significant because our power was low" amounts to saying "it was not significant because it was not significant" and adds no new information. Hoenig and Heisey (2001) called this the observed power fallacy, and many journals and editorial guidelines explicitly advise against reporting post-hoc power.
What should I report instead of post-hoc power?
There are two sound options. The first is to report the effect size with its confidence interval: if the interval is narrow and centered near zero, you can conclude the effect really is small; if it is wide and covers large values, the study is inconclusive. The second is to report the minimum detectable effect (a sensitivity analysis), as this calculator does. Because the MDE is computed from the design rather than the observed data, it is not circular and gives an honest answer to "what could my study have seen?"
How is the MDE related to a sample size calculation?
They are the same equation solved for different unknowns. A sample size calculation takes d and returns n (n = 2(z₍α/₂₎+z₍β₎)²/d²); an MDE calculation takes n and returns d. That is why feeding the result of one tool into the other brings you back to the number you started with, up to rounding.
How much does the detectable effect shrink if I double the sample?
Because d_min is inversely proportional to the square root of the sample size, doubling it shrinks d_min by a factor of about √2 ≈ 1.41, that is by 29%. To halve the detectable effect you have to quadruple the sample. A d_min of 0.723 at 30 per group falls to 0.362 at 120 per group.
Is the MDE always a hard "undetectable" cutoff?
No; it is not a cutoff but the point corresponding to the power you targeted. Effects slightly below d_min can still be detected, only with a probability lower than 80% (or whatever power you chose). The effect-power table shows this transition: with the same sample, much smaller effects look "detectable" at 50% power, but at that level it is no better than a coin flip.
How do I run this calculation in G*Power?
In G*Power, select the relevant test and then choose "Sensitivity: Compute required effect size" as the type of power analysis; entering α, power, and the sample sizes returns the smallest detectable d. Because G*Power uses the noncentral t distribution, its result is slightly larger than this calculator's; the gap is a few percent in small samples and negligible around n ≥ 30.
Can I interpret my non-significant result as "no effect"?
No. In classical hypothesis testing, a non-significant result shows only that the null hypothesis could not be rejected; it does not mean the null hypothesis has been confirmed. If you want to demonstrate the absence of an effect, use a method designed for that, such as an equivalence test (TOST), and set an equivalence margin in advance. The MDE is where that conversation starts: it states honestly which effect sizes your study was able to rule out.