# Logical extremes, beta, and the power of the test

James V. Pinto, Pin T Ng, David S Allen

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 of Statistics Education 11 1 Published - Mar 2003

Power Function
Extremes
Null
Type II error
Null hypothesis
Values
Logic
Alternatives

### Keywords

• Power function
• Simulations
• Type II error

### ASJC Scopus subject areas

• Statistics and Probability
• Education

### Cite this

In: Journal of Statistics Education, Vol. 11, No. 1, 03.2003.

Research output: Contribution to journalArticle

title = "Logical extremes, beta, and the power of the test",
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.",
keywords = "Power function, Simulations, Type II error",
author = "Pinto, {James V.} and Ng, {Pin T} and Allen, {David S}",
year = "2003",
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language = "English (US)",
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journal = "Journal of Statistics Education",
issn = "1069-1898",
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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

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