cthreshold | R Documentation |

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

```
cthreshold(alpha, nbtest)
```

`alpha` |
The familywise type I error threshold. |

`nbtest` |
The number of tests performed. |

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.

The threshold that have to be used for individual tests.

Guillaume Guenard and Pierre Legendre, Bertrand Pages Maintainer: Guillaume Guenard <guillaume.guenard@gmail.com>

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

Legendre, P. and Legendre, L. 1998. Numerical Ecology. Elsevier Science B.V., Amsterdam, The Neatherlands. p. 18

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

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