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A false-positive budget is the prespecified amount of Type I error risk a defined testing plan is willing to tolerate. It is not the probability that a hypothesis is true, nor a guarantee that a statistically significant result is correct. A sound plan connects the question, a meaningful effect, the significance threshold, desired power, sample size, and any multiple-testing adjustments; interpretation then considers the effect estimate, its uncertainty, and the study’s design—not a cutoff alone.
What does “false-positive budget” mean?
It is a plain-language way to describe the Type I error risk tolerated across a particular testing procedure. The phrase is not a universal statistical quantity with one standard numeric value. To make it meaningful, define which hypotheses or comparisons belong to the testing family, what procedure will be used, and what decision the analysis is meant to inform.
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A Type I error occurs when a test rejects a true null hypothesis. The significance level, often written as alpha, is a prespecified decision threshold used to limit that error under the stated model and testing procedure. The threshold should reflect the purpose of the study and the consequences of incorrect decisions; a familiar convention is not, by itself, a justification. The American Statistical Association’s 2021 guidance discusses thresholds, uncertainty, multiplicity, design, and reporting: ASA President’s Task Force statement.
What a p-value and statistical significance do—and do not—tell you
A p-value describes how incompatible the observed data are with a specified statistical model. It does not state the probability that the null hypothesis is true, the probability that the alternative is true, or the probability that the result arose from “chance alone.” The ASA’s 2016 statement says, “By itself, a p-value does not provide a good measure of evidence regarding a model or hypothesis.” Its principles explain the limits of p-values and their interpretation: ASA Statement on Statistical Significance and P-Values.
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Statistical significance is also not the same as effect size or practical importance. A larger sample can make the same estimated effect yield a smaller p-value. Whether that effect matters scientifically, clinically, or operationally depends on the question and context, not the threshold alone. As ASA executive director Ron Wasserstein put it in the association’s March 7, 2016 release, “The p-value was never intended to be a substitute for scientific reasoning”: ASA release and statement.
How power and sample size fit the error budget
Power is the probability that a planned procedure will detect a specified effect under the assumptions and alternative used for planning. Its counterpart, Type II error, is failing to reject a false null hypothesis. Choosing a more stringent Type I error threshold or seeking higher power can affect the sample size required, but there is no sample size that works for every question and design.
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- This guide is a perfect overview for the topics covered in introductory statistics courses.
Planning requires a scientifically meaningful target effect, the outcome’s expected variability, the study design and sampling structure, the Type I and Type II error tolerances, and the planned analysis. An explanatory article on sample-size planning describes using a relevant effect size along with appropriate alpha and beta values: Sample size calculations: basic principles. Without concrete design inputs, a numeric sample-size recommendation would be misleading.
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- Define the question and analysis. State the primary question, null and alternative hypotheses, outcome, and planned analysis before examining results.
- Choose a meaningful effect. Decide what size of effect would matter for the scientific or practical decision, and use that target—not an arbitrary observed result—for planning.
- Set error tolerances deliberately. Choose the Type I error threshold and desired power in light of the costs of false-positive and false-negative decisions. Prespecify and justify the choices.
- List planned comparisons. Identify the number of tests and state how multiplicity will be handled. Adjustments can reduce false-positive risk while also reducing power. Selective reporting or unreported tests can conceal the real testing context.
- Report results in context. Provide effect estimates and uncertainty alongside p-values, and describe the design, assumptions, limitations, and practical meaning of the findings.
The ASA’s guidance emphasizes study design, transparency, full reporting, and careful interpretation rather than treating a threshold as a standalone verdict: 2016 ASA statement and 2021 ASA task force statement.
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What to check when reading a statistically significant result
- Was the question and analysis specified in advance, or were many analyses tried?
- What is the estimated effect, and how uncertain is it?
- Does the effect meet a meaningful scientific or practical threshold?
- How were multiple comparisons handled, and which tests were reported?
- Do the design and assumptions support the conclusion being drawn?
A threshold can help structure a decision, but it cannot substitute for these checks. The conclusion should reflect the estimate, uncertainty, design quality, and the costs of being wrong.
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