Use a per-test false-positive rate (Type I error rate) to describe the chance that a test rejects a true null hypothesis. Use false discovery rate (FDR) control when testing a family of hypotheses and you want to limit the expected share of false results among the findings you report. Neither measure is a universal substitute for the other: the right choice depends on how many tests you ran and what kind of error matters most.
What each rate measures
The terms differ in both their denominator and the question they answer. In statistical hypothesis testing, a false positive is a rejection of a null hypothesis that is actually true. NIST describes this as a Type I error and explains that a test’s significance level is the risk of making that error when the null is true: NIST’s guide to statistical tests. The label “false positive” is also used in other fields, so the definition here is specifically about hypothesis tests; NIST’s glossary covers broader contexts at NIST’s false-positive entry.
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| Measure | What it asks | Denominator or conditioning |
|---|---|---|
| Per-test false-positive rate (Type I error probability) | How often does this test reject when its null hypothesis is true? | Among cases in which the null hypothesis is true, for one test procedure. |
| False discovery rate (FDR) | Among the findings declared significant, what is the expected share that are false rejections? | The total rejections in a defined family of tests. |
For a family of tests, let V be the number of false rejections and R the total number of rejections. FDR is the expected value of the false-discovery proportion, E[V/R], with the proportion defined as zero when there are no rejections. Benjamini and Hochberg introduced this criterion for multiple significance testing in their 1995 paper, “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing”.
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Why FDR is not the probability that any result is false
FDR does not tell you the probability that a particular significant finding is false, nor does it promise that no finding in your list is false. It controls an expected proportion across the procedure and the defined set of tests. The probability of at least one false rejection is a different criterion, called the familywise error rate (FWER).
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Benjamini and Hochberg note that FDR equals FWER when all tested null hypotheses are true and is smaller otherwise. That distinction matters: a procedure designed to limit the expected false share among discoveries is not a guarantee against even one false alarm.
Which measure to use for your analysis
One pre-specified test
For a single test chosen in advance, report the test and its significance level, and interpret that level as the test procedure’s Type I error risk under a true null. Do not describe it as the probability that a significant result is false; that is a different question and depends on factors such as how common true alternatives are in the tested setting.
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Several planned comparisons
Define which hypotheses form the family, then select a multiple-comparison procedure that matches the inference you need. The National Center for Education Statistics lists Bonferroni, FDR, Scheffé, and Tukey among procedures to consider for simultaneous inference in its 2002 Statistical Standard 5-1. These methods address different inferential goals; the name of a correction alone does not define the family or justify the choice.
Many exploratory candidates and a reported discovery list
FDR control can fit a setting where many hypotheses are tested and the goal is to manage the expected proportion of false findings among those declared. The original Benjamini–Hochberg procedure establishes FDR control for independent test statistics; do not assume that original result automatically applies to arbitrary dependence. If tests are dependent, identify that structure and use a procedure whose guarantee covers it.
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When any false rejection is costly
If the analysis requires stronger protection against making even one false claim across the family, consider a familywise error criterion rather than treating FDR control as a no-false-positives guarantee. The cost of a false alarm, the purpose of the analysis, and the consequences of missed findings all inform the appropriate target.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What to specify when reporting results
A useful report makes the error criterion interpretable, rather than naming a rate without context. State:
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- Which hypotheses belong to the testing family and why.
- Whether the analysis is exploratory or confirmatory.
- The target error level and the method used to control it.
- What assumptions the method makes about valid tests and dependence among test statistics.
- Whether the intended protection concerns each test, the expected false share among rejections, or the chance of any false rejection.
The original Benjamini–Hochberg guarantee cited above is specifically for independent test statistics. For other dependence structures or specialized designs, the procedure’s stated conditions must be checked rather than inferred from the word “FDR.”
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