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Visual Guides/Statistical Power & Effect Size
Statistics

Statistical Power & Effect Size

Discover how effect size, sample size, and significance threshold jointly determine whether your study can detect a true signal. Tune the parameters and watch the overlapping distributions shift in real time.

Effect size adjusted
Sample size adjusted
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Power Visualization

αPowerβ
-4-3-2-10123456H₀ (μ=0)H₁ (μ = d·√(n/2) = 2.83)z (test statistic scale)α=0.050β=0.19Power=0.81
Larger d or larger n pushes the curves apart → more power (green area grows, gray area shrinks)

Effect Size (Cohen's d)

Medium0.5
Small
Medium
Large
Very Large
Cohen's d measures the standardized difference between two group means: d = (μ₂ − μ₁) / σ. A value of 0.5 means the groups differ by half a standard deviation.

Sample Size per Group

Power = 0.81n = 64

Total participants = n × 2 (two groups). Every power number in this guide is for the two-sample comparison; a one-sample test with the same n has different power, so do not reuse these values for it.

Significance Level (α)

Standard significance threshold: 5% false positive rate

Two-tailed test

Two-tailed tests are more conservative: they split α across both tails. Use one-tailed only when the direction of effect is known in advance.

Power Analysis Results

0.81

Statistical Power

Good

Significance (α)

0.05

Type II Error (β)

0.19

Effect Size (d)

0.50 (Medium)

n per group

64

Meets the conventional 80% power threshold. The standard recommendation for confirmatory studies. β = 1 − power = risk of missing a real effect.

Effect Size Calculator

Cohen's d = |μ₂ − μ₁| / σ

|110 − 100| / 15 = 0.667

Medium

Sample Size Planner

Target Power

Effect Size (d)

Medium

Significance Level

Power at varying n (d = 0.50, α = 0.05)

n per groupPowerβ
100.2010.799
200.3520.648
300.4910.509
500.7050.295
640.8070.193
1000.9420.058
2000.9990.001

Type I Error (α)

The probability of rejecting a true null hypothesis: a false positive. You control this directly by choosing α.

Type II Error (β)

The probability of failing to reject a false null hypothesis: a false negative. β = 1 − Power.

Power = 1 − β

The probability of correctly detecting a real effect. Power ≥ 0.80 is the standard convention for confirmatory research.

← P-Values DemystifiedMultiple Testing & False Discovery →