### Abstract

There is a potential misuse of the power function under the logical extreme when the null hypothesis is true. The power function is defined to measure the probability of rejecting the null given any value of the parameter being tested. It can be used to obtain the power and the β values only under the alternative hypothesis. When the null is true, the power function can be used to obtain the size of the test. The power and the probability of committing a Type II error are, however, undefined and, hence, the power function should not be used to obtain these value.

Original language | English (US) |
---|---|

Journal | Journal of Statistics Education |

Volume | 11 |

Issue number | 1 |

State | Published - Mar 2003 |

### Fingerprint

### Keywords

- Power function
- Simulations
- Type II error

### ASJC Scopus subject areas

- Statistics and Probability
- Education

### Cite this

*Journal of Statistics Education*,

*11*(1).

**Logical extremes, beta, and the power of the test.** / Pinto, James V.; Ng, Pin T; Allen, David S.

Research output: Contribution to journal › Article

*Journal of Statistics Education*, vol. 11, no. 1.

}

TY - JOUR

T1 - Logical extremes, beta, and the power of the test

AU - Pinto, James V.

AU - Ng, Pin T

AU - Allen, David S

PY - 2003/3

Y1 - 2003/3

N2 - There is a potential misuse of the power function under the logical extreme when the null hypothesis is true. The power function is defined to measure the probability of rejecting the null given any value of the parameter being tested. It can be used to obtain the power and the β values only under the alternative hypothesis. When the null is true, the power function can be used to obtain the size of the test. The power and the probability of committing a Type II error are, however, undefined and, hence, the power function should not be used to obtain these value.

AB - There is a potential misuse of the power function under the logical extreme when the null hypothesis is true. The power function is defined to measure the probability of rejecting the null given any value of the parameter being tested. It can be used to obtain the power and the β values only under the alternative hypothesis. When the null is true, the power function can be used to obtain the size of the test. The power and the probability of committing a Type II error are, however, undefined and, hence, the power function should not be used to obtain these value.

KW - Power function

KW - Simulations

KW - Type II error

UR - http://www.scopus.com/inward/record.url?scp=3042531144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042531144&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3042531144

VL - 11

JO - Journal of Statistics Education

JF - Journal of Statistics Education

SN - 1069-1898

IS - 1

ER -