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Data Labeling Sample Size Estimator

The Data Labeling Sample Size Estimator calculates how many labeled items to inspect when estimating a binary labeling-quality proportion, such as the share of annotations that pass an audit. It is useful for QA sampling when reviewing an entire labeled dataset is impractical but you still want a defined precision target. Choose the confidence level, margin of error, and expected pass proportion. If the labeling batch has a known finite size, enter that population to apply a finite-population correction. The calculator rounds the requirement upward so the suggested audit sample does not fall below the formula result.

Audit sampling target

%
%
Result
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Recommended audit sample
Large-population sample—
Target margin—
Expected pass proportion—
Population assumption—

1. Choose the audit outcome
Define one binary result, such as pass/fail against an annotation guideline.

2. Set confidence
Choose how much confidence the audit estimate should target.

3. Set the margin
Enter the maximum sampling margin of error you want for the proportion estimate.

4. Estimate expected quality
Use prior audit information when available; otherwise a more conservative value can protect against underestimating the needed sample.

5. Enter the batch size if known
Provide the finite labeled-item population for a bounded batch, or use 0 for a large or unspecified population.

6. Draw the sample
Use a sampling method that represents label classes, annotators, sources, and other relevant strata rather than selecting only convenient items.

n₀ = z² × p × (1 − p) / e²Finite-population n = n₀ / (1 + (n₀ − 1) / N)

Where:

• n₀ = large-population sample requirement
• z = confidence-level critical value
• p = expected audit pass proportion
• e = target margin of error
• N = total labeled-item population when entered

Assumptions: The calculation is for a binary proportion under simple random sampling. Stratified or clustered audit designs may need allocation rules or a design-effect adjustment.

What the result means

The result is the rounded-up number of labeled items to audit under the stated statistical assumptions.

Sampling enough items does not compensate for an audit set that systematically misses difficult classes, annotators, or edge cases.

Given: 95% confidence, ±4% margin of error, expected pass proportion 90%, and 12,000 labeled items.

Calculation: n₀ = 1.959964² × 0.90 × 0.10 / 0.04² ≈ 216.08. Applying the finite-population correction gives about 212.27.

Result: Round up to 213 audited items.

Interpretation: Under simple random sampling, an audit of 213 items targets the stated precision for a batch of 12,000 when the expected pass rate is about 90%.

Should I sample the same number from every label class?

Not necessarily. Equal class sampling can be useful for class-specific QA, while population-proportional sampling better represents the overall dataset. Choose the design to match the metric you plan to report.

What expected proportion should I use without prior audit data?

A 50% planning value produces the largest variance and therefore the most conservative sample for this formula. If credible prior data exists, you can use a more specific estimate.

Does the finite-population correction matter for very large datasets?

Its effect becomes small when the required sample is tiny relative to the total population. It matters more when you are sampling a substantial fraction of a bounded batch.

Can this sample prove every rare error type is covered?

No. A sample sized for an overall proportion can miss rare but important errors. Add targeted or stratified checks when specific failure modes require coverage.

How is this different from inter-annotator agreement?

This estimator determines audit sample size for a pass proportion. Agreement metrics measure consistency between annotators and require paired or repeated labels.