cthreshold: Familywise type I error rate

Description

Function to calculate the testwise type I error rate threshold corresponding to a give familywise threshold.

Usage

cthreshold(alpha, nbtest)

Arguments

alpha

The familywise type I error threshold.

nbtest

The number of tests performed.

Value

The threshold that have to be used for individual tests.

encoding

utf8

Details

Type I error rate inflation occurs when a single hypothesis is tested indirectly using inferences about two or more (i.e. a family of) sub-hypotheses. In such situation, the probability of type I error (i.e. the probability of incorrectly rejecting the null hypothesis) of the single, familywise, hypothesis is higher than the lowest, testwise, probabilities. As a consequence, the rejection of null hypothesis for one or more individual tests does not warrant that the correct decision (whether to reject the the null hypothesis on a familywise basis) was taken properly. This function allows to obtain correct, familywise, alpha thresholds in the context of multiple testing. It is base on the Sidak inegality.

References

Sidak, Z. 1967. Rectangular Confidence Regions for Means of Multivariate Normal Distributions J. Am. Stat. Assoc. 62: 626-633 Wright, P. S. 1992. Adjusted p-values for simultaneous inference. Biometrics 48: 1005-1013

Examples

Run this code

# For a familywise threshold of 5\% with 5 tests:
cthreshold(c(0.05),5)   # The corrected threshold for each test is 0.01020622

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