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Data Labeling Statistical Power Calculator

The Data Labeling Statistical Power Calculator estimates how likely a two-group proportion comparison is to detect a planned improvement in labeling quality. You can use it when comparing two annotation workflows, guideline versions, model-assisted labeling methods, or vendor processes using a binary audit outcome such as pass versus fail. Enter the baseline pass rate, the minimum absolute percentage-point lift worth detecting, the audited sample size per group, and the significance level. The result is an approximate two-sided test power under independent, equally sized groups.

Comparison assumptions

%
pp
Result
—
Approximate statistical power
Alternative pass rate—
Absolute lift—
Total audited items—
Significance level—

1. Enter the baseline pass rate
Use the expected or historical audit pass proportion for the current labeling process.

2. Set a meaningful lift
Enter the smallest absolute percentage-point improvement that would justify calling the new process better.

3. Set audited items per group
Use the number of independent audit outcomes planned for both baseline and comparison groups.

4. Choose significance
Select the two-sided false-positive threshold for the planned test.

5. Evaluate power
If power is too low, increase the audit sample or revisit the minimum difference the study must reliably detect.

p₂ = p₁ + liftSE₀ = sqrt(2 × p̄ × (1 − p̄) / n)SE₁ = sqrt((p₁(1 − p₁) + p₂(1 − p₂)) / n)Power ≈ Φ((|p₂ − p₁| − zα × SE₀) / SE₁)

Where:

• p₁ = baseline audit pass proportion
• p₂ = improved pass proportion
• p̄ = average group proportion
• n = audited items per group
• zα = two-sided normal critical value
• Φ = standard normal cumulative distribution

Assumptions: The calculation assumes two independent, equally sized groups and a normal approximation to the difference in proportions. If the same items or annotators are paired across conditions, a paired design may be more efficient and requires different power logic.

What the result means

The power percentage estimates the probability of detecting the stated pass-rate improvement if that improvement is truly present.

A powered comparison still requires representative audits and a stable quality definition. Changing the rubric between groups can invalidate the interpretation.

Given: an 88% baseline audit pass rate, a +4 percentage-point minimum lift, 700 audited items per group, and a 5% significance level.

Calculation: p₁ = 0.88 and p₂ = 0.92. The calculator estimates pooled and alternative standard errors, then evaluates the 0.04 difference against the two-sided 1.959964 critical value.

Result: Approximate statistical power is 74.5% with 1,400 total audited items.

Interpretation: Use the power estimate to judge whether the planned audit is large enough to distinguish a practically important change from random sample variation.

Can I use relative improvement instead of percentage points?

Convert it to the resulting absolute pass-rate difference first. For example, improving 88% by about 4.55% relatively produces 92%, which is a 4 percentage-point lift.

Why does a larger effect need less sample for the same power?

Larger differences are easier to distinguish from sampling noise. Small improvements require more observations to separate them reliably from random variation.

Can I compare two vendors with different audit sample sizes?

This version assumes equal samples per group. Use a two-proportion power method that supports unequal allocation if the audited counts differ materially.

Does annotator dependence matter?

Yes. If many audited items share the same annotator and errors are correlated, the effective sample may be smaller than the raw item count.

What if I only need to estimate one vendor’s quality level?

Use a confidence-interval or sample-size estimator for a single proportion. Power analysis is designed for detecting a difference between conditions or groups.