Choose the false-positive budget before examining the results. Set an alpha level for the primary hypothesis, define which other tests belong to the same family, specify how you will handle multiple comparisons, and plan sample size around a meaningful effect and a target power. There is no universally correct alpha: the right choice depends on the consequences of a false alarm and the purpose of the analysis.
What a false-positive budget means
In hypothesis testing, alpha (α) is the probability of rejecting a null hypothesis that is true, assuming the test’s design and analysis conditions hold. The National Academies’ Reference Manual on Scientific Evidence, Fourth Edition (2025) describes this as the chance of falsely rejecting the null when it is true. Alpha is a rule for long-run error control—not the probability that a particular significant finding is false.
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Alpha is related to, but distinct from, power. Power is the probability of detecting an effect of a specified size when that effect exists under the planned assumptions. At a fixed sample size, reducing alpha generally makes it harder to reject the null and can reduce power. A non-significant result therefore does not prove there is no effect, just as a significant result is not automatically true. Interpretation also depends on effect size, uncertainty, study design, prior plausibility, and independent evidence. See the Indian Journal of Anaesthesia primer on Type I and Type II errors (2010).
Choose the error target before choosing a number
Start with the decision the analysis will support. Consider both the harm of a false alarm and the harm of missing a real effect. Then select an alpha for the primary confirmatory question and document why that level is appropriate to the decision.
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Values such as α = 0.05 and power = 0.80 are common conventions, not universal requirements. A 2010 primer in the Indian Journal of Anaesthesia describes them as common while noting that choices should reflect the relative importance of the two kinds of error.
For multiple confirmatory hypotheses, decide whether your budget should control:
- Family-wise error rate (FWER): the probability of making at least one false rejection across a defined family of tests.
- False discovery rate (FDR): the expected proportion of false discoveries among the results declared significant.
These answer different questions. Define the family and error target first; do not treat a per-test alpha as if it automatically controls the chance of any false positive across a larger analysis.
Define the family of tests
A test family is the set of opportunities to declare a result significant that your chosen error-control rule is intended to cover. Write down its boundaries before looking at outcomes. Depending on the study, it may include primary and secondary endpoints, multiple comparisons or contrasts, subgroup analyses, and planned interim looks. The 2018 Korean Journal of Anesthesiology article on multiple comparisons and a 2016 Indian Journal of Anaesthesia article on multiple testing pitfalls explain why considering only each test’s individual alpha can understate the chance of a false positive across an analysis.
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For four independent tests, each run at α = 0.05, the probability of at least one false rejection is 1 − (1 − 0.05)4 = 18.5%. The 2018 Korean Journal of Anesthesiology article reports this example using the independent-tests formula. It is not a universal answer: dependence between tests changes the exact family-wise error rate.
Choose a multiplicity procedure that matches the plan
Once the family and error target are clear, select a procedure that fits the number, structure, and dependence of the tests. Bonferroni is straightforward to explain and can be conservative. Holm or Benjamini–Hochberg may be appropriate alternatives in some settings; the choice depends on whether the goal is FWER or FDR and on the test structure. The 2022 International Journal of Behavioral Medicine guideline on adjusting Type I error in multiple testing discusses multiplicity adjustment.
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Do not choose or switch procedures after seeing which one produces a preferred result. Prespecify the method, the family it covers, and the rationale. When the design has unusual dependence, grouped or ordered hypotheses, or other constraints, the method should be chosen with that structure in view rather than by applying a familiar correction mechanically.
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Before data collection, specify a meaningful effect size and a target power, then calculate the sample size for the planned design and analysis. The calculation should use the alpha level and multiplicity procedure that you intend to apply: an adjustment for multiple comparisons can affect the sample size needed to reach the target power.
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Record the assumptions behind the calculation, including how the outcome is measured and which design features affect precision. A nominal power target is useful only in relation to a particular effect size and set of assumptions; it is not a general guarantee that the study will detect every real effect.
Prespecify the analysis
Write the decision rules before inspecting outcome data. The National Academies’ 2019 discussion of improving reproducibility and replicability explains how preregistration can make analytic decisions transparent and help ensure the stated alpha corresponds to the planned test.
A practical plan should record:
- The primary hypothesis, outcome, and whether the test is one-sided or two-sided.
- The primary-test alpha and why it fits the consequences of the decision.
- All confirmatory endpoints, comparisons, contrasts, subgroups, and planned interim looks.
- The boundary of each test family, its FWER or FDR target, and the named adjustment procedure.
- The meaningful effect size, power target, sample-size calculation, and assumptions.
- The stopping rule, handling of missing data, and exclusion criteria.
- How deviations, changed analyses, and exploratory findings will be identified and reported.
If you change the plan, report the deviation. Analyses selected after examining the results should be labeled exploratory rather than presented as if they were prespecified confirmatory tests.
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