False positive rate
Encyclopedia
When performing multiple comparisons
in a statistical
analysis, the false positive rate is the probability of falsely rejecting the null hypothesis
for a particular test among all the tests performed. If the false positive rate is a constant α for all tests performed, it can also be interpreted as the expected proportion among all tests performed that are false positives (also known as type 1 errors).
In the setting of analysis of variance
(ANOVA), the false positive rate is referred to as the comparisonwise error rate or pairwise error rate. When three or more treatments are studied in parallel, a comparison can be made for each pair of treatments to assess whether one of the treatments is superior to the other. For example, if three treatments are studied, there are three pairwise comparisons among them.
The false positive rate is very different from the familywise error rate
, which is the probability that at least one of the tests that are performed results in a type I error. As the number of tests grows, the familywise error rate generally tends to 1 even while the false positive rate remains fixed.
Multiple comparisons
In statistics, the multiple comparisons or multiple testing problem occurs when one considers a set of statistical inferences simultaneously. Errors in inference, including confidence intervals that fail to include their corresponding population parameters or hypothesis tests that incorrectly...
in a statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
analysis, the false positive rate is the probability of falsely rejecting the null hypothesis
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
for a particular test among all the tests performed. If the false positive rate is a constant α for all tests performed, it can also be interpreted as the expected proportion among all tests performed that are false positives (also known as type 1 errors).
In the setting of analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
(ANOVA), the false positive rate is referred to as the comparisonwise error rate or pairwise error rate. When three or more treatments are studied in parallel, a comparison can be made for each pair of treatments to assess whether one of the treatments is superior to the other. For example, if three treatments are studied, there are three pairwise comparisons among them.
The false positive rate is very different from the familywise error rate
Familywise error rate
In statistics, familywise error rate is the probability of making one or more false discoveries, or type I errors among all the hypotheses when performing multiple pairwise tests.-Classification of m hypothesis tests:...
, which is the probability that at least one of the tests that are performed results in a type I error. As the number of tests grows, the familywise error rate generally tends to 1 even while the false positive rate remains fixed.