### Abstract

Homogeneity of variance test has been studied by Bartlett (1937), Hartley (1950), Levene (1960), and Box (1953), among others. The tests developed by the above statisticians are either approximate tests or tests using numerical tabulation of the critical points, so the validity of the tests relies on sample sizes. We have developed a test, the so-called New-Test, for the equality of variances whose Type I error is well controlled and whose power is competitive to the optimal alternative tests. Extensive empirical experiments are conducted to compare the performance of the New-Test with three classical methods. An experiment with exponential data is also done by simulation. It seems that under exponential distribution situation, Type I error is not as controlled as in the case of normal distribution situation. With relatively higher power and precise control of Type I error, the New-Test can be recommended for future use by the practitioners when the underlying data are from normal distribution.

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

Pages (from-to) | 109-117 |

Number of pages | 9 |

Journal | Communications in Statistics: Simulation and Computation |

Volume | 38 |

Issue number | 1 |

DOIs | |

State | Published - Nov 21 2008 |

### Fingerprint

### Keywords

- Bartlett's test
- Hartley's F max-Test
- Homogeneity of variances
- Levene's test
- New-Test

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation

### Cite this

**An Alternative Test for the Equality of Variances for Several Populations When the Underlying Distributions are Normal.** / Bhandary, Madhusudan; Dai, Hongying.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An Alternative Test for the Equality of Variances for Several Populations When the Underlying Distributions are Normal

AU - Bhandary, Madhusudan

AU - Dai, Hongying

PY - 2008/11/21

Y1 - 2008/11/21

N2 - Homogeneity of variance test has been studied by Bartlett (1937), Hartley (1950), Levene (1960), and Box (1953), among others. The tests developed by the above statisticians are either approximate tests or tests using numerical tabulation of the critical points, so the validity of the tests relies on sample sizes. We have developed a test, the so-called New-Test, for the equality of variances whose Type I error is well controlled and whose power is competitive to the optimal alternative tests. Extensive empirical experiments are conducted to compare the performance of the New-Test with three classical methods. An experiment with exponential data is also done by simulation. It seems that under exponential distribution situation, Type I error is not as controlled as in the case of normal distribution situation. With relatively higher power and precise control of Type I error, the New-Test can be recommended for future use by the practitioners when the underlying data are from normal distribution.

AB - Homogeneity of variance test has been studied by Bartlett (1937), Hartley (1950), Levene (1960), and Box (1953), among others. The tests developed by the above statisticians are either approximate tests or tests using numerical tabulation of the critical points, so the validity of the tests relies on sample sizes. We have developed a test, the so-called New-Test, for the equality of variances whose Type I error is well controlled and whose power is competitive to the optimal alternative tests. Extensive empirical experiments are conducted to compare the performance of the New-Test with three classical methods. An experiment with exponential data is also done by simulation. It seems that under exponential distribution situation, Type I error is not as controlled as in the case of normal distribution situation. With relatively higher power and precise control of Type I error, the New-Test can be recommended for future use by the practitioners when the underlying data are from normal distribution.

KW - Bartlett's test

KW - Hartley's F max-Test

KW - Homogeneity of variances

KW - Levene's test

KW - New-Test

UR - http://www.scopus.com/inward/record.url?scp=55449130151&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55449130151&partnerID=8YFLogxK

U2 - 10.1080/03610910802431011

DO - 10.1080/03610910802431011

M3 - Article

AN - SCOPUS:55449130151

VL - 38

SP - 109

EP - 117

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 1

ER -