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There is no universal sample count: choose the largest false-positive rate you are willing to accept and the confidence level you need. If your validation requires zero false positives, the sample size is n = log(α) / log(1 − p), rounded up, where p is the rate limit and 1 − α is the confidence level. Under that rule, 59 known-negative samples with zero false positives support a below-5% rate at 95% confidence; a below-1% claim at the same confidence requires 299.
What does a false-positive budget mean?
Before counting samples, define the budget. It can refer to the maximum false-positive probability allowed, the confidence required for a claim about that rate, or the maximum number of errors the validation will accept. These choices determine the design together; a sample count by itself does not establish a meaningful performance claim.
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- Rate threshold: the maximum false-positive rate you want to rule out, such as 5%.
- Confidence or acceptable risk: how strong the evidence must be, such as 95% confidence.
- Acceptance rule: whether the validation passes only if it sees zero false positives, or permits some errors.
- Population: what qualifies as a known-negative case and which intended-use population, samples, devices, or conditions the result represents.
The false-positive rate is the proportion of known-negative cases incorrectly called positive. In the NIST method-performance example, it is the complement of specificity: NIST method-performance discussion.
How many samples are needed if zero false positives are allowed?
For a zero-acceptance design, every tested known-negative sample must produce a negative result. FDA guidance gives the formula n = log(α) / log(1 − p), where p is the maximum false-positive rate being bounded and α is the remaining risk. For example, 95% confidence means α = 0.05. Round the calculated sample count up to the next whole sample.
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This is a binomial calculation for independent, representative trials with zero observed false positives. FDA’s 2023 guidance provides these minimum counts for its zero-acceptance criteria; the figures apply to the stated rate and confidence combination, not as universal validation requirements. Source: FDA, Guidelines for the Validation of Analytical Methods Using Nucleic Acid Sequenced-Based Technologies, Appendix 3.
| Maximum false-positive rate | 80% confidence | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|---|
| Below 1% | 161 | 230 | 299 | 459 |
| Below 2% | 80 | 114 | 149 | 228 |
| Below 5% | 32 | 45 | 59 | 90 |
| Below 10% | 16 | 22 | 29 | 44 |
The 59-sample result has a direct probability interpretation: if the true false-positive probability were 5%, the chance of seeing no false positives in 59 independent trials would be about 5%. Thus, zero errors in that sample is the boundary for a one-sided 95% upper bound near 5%. FDA states that the minimum count depends on both the defect-rate criterion and statistical confidence.
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What changes if the study allows errors or estimates a rate?
The zero-acceptance formula cannot be reused when one or more false positives are allowed. The acceptance rule and sample count must be designed together for the permitted error count; the zero-error calculation does not answer that question.
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One free scan finds every outdated or missing driver and matches the right update for your exact hardware.Free scan · exact hardware matchIf the purpose is to estimate the false-positive rate, or if errors occur, report the number of false positives and the number of known-negative samples, then calculate an appropriate binomial confidence interval or bound. NIST’s instrument-performance technical note covers estimates and confidence bounds for false-alarm rates and binomial proportions: NIST Technical Note 2106. The NIST/SEMATECH handbook also discusses proportion tests and notes that normal approximations require sufficiently large samples; for rare events or sparse counts, exact or score-based binomial methods are often preferable: NIST/SEMATECH handbook, tests for proportions.
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Will the sample count support the claim you want to make?
The calculation only supports the population and conditions represented by the validation samples. For diagnostic-test studies, FDA guidance calls for comparison with a reference standard, subjects representative of intended use, and confidence intervals for performance measures. Its stated assumptions exclude multiple samples from the same patient. See FDA guidance on reporting diagnostic-test study results.
If samples come from different matrices, sites, instruments, users, or subgroups, decide whether a single pooled rate answers the intended question. Separate claims or stratified analyses can require separate sample-size calculations. Repeated observations sharing a source may not be independent, so counting each as a fully independent trial can overstate the information in the data.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How to set the design before testing
- Define the negative case and reference standard. Specify what counts as a false positive and the intended-use population represented by the known-negative samples.
- Choose the maximum rate and confidence. These two values determine the zero-acceptance count; FDA’s table illustrates how changing either changes the required n.
- Set the acceptance rule. Decide whether zero errors are required. If the study permits errors or aims for a precision target, use a design for that objective instead.
- Check independence and coverage. Review repeated samples, subgroup representation, and relevant operating conditions before treating the trials as one binomial sample.
- Predefine the analysis and report the counts. State the numerator, denominator, interval or bound, and the claim the design was intended to support.
NIST’s guidance on confirming a binary performance threshold frames sample-size planning around the threshold and acceptable risk or required confidence: NIST, Confirming a Performance Threshold with a Binary Experimental Response.
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