Minimum Detectable Effect Calculator

What Is the Minimum Detectable Effect?

The minimum detectable effect (MDE) is the smallest effect size your study can reliably detect with specified power and significance level. Given your sample size, MDE answers: "How small an effect can I find?"

High sample → small MDE (can detect subtle effects) Low sample → large MDE (only detect obvious effects)

Why MDE Matters

Before running an experiment:

• "Is my sample large enough to detect a meaningful effect?"
• "Can I detect an effect small enough to be practically important?"

If your MDE is larger than what would be practically meaningful, the study can't distinguish important effects from noise.

The Calculation

MDE is derived from the power equation, solved for effect size:

For a two-sample t-test:

MDE ≈ (z₁₋α/₂ + z₁₋β) × √(2/n)

Where:

• z₁₋α/₂ = critical z for significance level
• z₁₋β = critical z for power
• n = sample size per group

Example: n = 100 per group, α = 0.05 (two-tailed), power = 0.80

MDE ≈ (1.96 + 0.84) × √(2/100) = 2.80 × 0.141 = 0.40

You can detect effects of d = 0.40 or larger.

Interpreting MDE

In Context of Cohen's d

In Original Units

Convert standardized MDE to original units:

Raw MDE = MDE × σ

If MDE = 0.40 and σ = 15 (e.g., IQ points): Raw MDE = 0.40 × 15 = 6 points

MDE for Proportions

For comparing two proportions:

MDE depends on baseline proportion p₁ and sample size n.

Example:

• Baseline conversion = 10%
• n = 1,000 per group
• α = 0.05, power = 0.80

MDE ≈ 2.5 percentage points (can detect change to 12.5% or 7.5%)

Applications

A/B Testing

"With 10,000 users per variant, what's the minimum lift we can detect?"

Baseline: 5% conversion MDE ≈ 0.75 percentage points (15% relative lift)

If you need to detect 5% relative lifts, you need more users.

Clinical Trials

"Given our enrolled patients, what's the smallest treatment effect we can claim?"

If MDE = 8 mmHg blood pressure reduction, effects smaller than 8 mmHg would likely be missed.

Educational Research

"Can we detect a half-grade improvement with our sample?"

If MDE corresponds to 0.7 grade points, half-grade effects won't be reliably detected.

Sensitivity Analysis

Calculate MDE across different scenarios:

This helps budget sample size against sensitivity needs.

MDE and Study Planning

Forward Planning

1. Determine the smallest practically meaningful effect
2. Calculate MDE for available sample size
3. If MDE > meaningful effect, increase sample or reconsider

Go/No-Go Decision

If your MDE is larger than effects reported in similar studies, your study may be futile.

Resource Allocation

MDE helps compare designs:

• Design A: n = 200, MDE = 0.28
• Design B: n = 100 with reduced variance (clustering), MDE = 0.30

Despite fewer subjects, Design B may be preferable if cost-effective.

MDE vs. Expected Effect

These are different concepts:

Expected effect: What you think the true effect is MDE: Smallest effect you can detect

Ideally: MDE < Expected effect

If MDE > Expected effect, you'll likely miss the effect even if it exists.

Relationship to Power

Power and MDE are inversely related (given fixed n and α):

• Target larger MDE → higher power
• Target smaller MDE → lower power

The Statistical Power Calculator finds power for a specified effect size.

One-Tailed vs. Two-Tailed

One-tailed tests have smaller MDE:

But one-tailed tests require prior justification.

MDE for Different Designs

Paired/Within-Subjects

MDE is smaller due to reduced variance:

MDE_paired ≈ MDE_independent × √(1 - ρ)

Where ρ = correlation between paired observations.

Clustered Designs

MDE is larger due to design effect:

MDE_cluster ≈ MDE_simple × √(1 + (m-1)ρ)

Where m = cluster size, ρ = intraclass correlation.

Common Mistakes

Ignoring Practical Significance

MDE = 0.05 doesn't mean effects of 0.04 are unimportant—just that your study can't reliably detect them.

Confusing MDE with Expected Effect

MDE is about detection capability, not prediction of what will happen.

Not Reporting MDE

Studies should report what they could and couldn't detect. "We found no effect" means more when MDE is stated.

Related Calculations

• Sample Size for Two Means — Find n for target MDE
• Sample Size for Two Proportions — For binary outcomes
• Statistical Power Calculator — Power for given effect size
• Cohen's d Calculator — Observed effect size
• A/B Test Sample Size Calculator — MDE for web testing

Summary

Minimum detectable effect reveals what your study can and cannot find. Given sample size, significance level, and power, MDE quantifies sensitivity. Studies with MDE larger than practically meaningful effects will miss important findings. Before running experiments, calculate MDE to ensure your design can answer your question. Report MDE in null results to help readers interpret what "no effect" means—whether you definitively ruled out meaningful effects or simply lacked sensitivity.