### Abstract

In the last 50 years, eight major modifications and extensions of Levene's test and Bartlett's test had been developed for Randomized Complete Block Design (RCBD). The improvement from these works can be divided mostly into three categories as follows: (i)adjust fixed block effects and degrees of freedom in F test, (ii)improve the power of variance homogeneity tests, and (iii)develop a robust test that can be applied to non-normal distributions. Surprisingly, very little attention has been paid to the homogeneity of within treatment variance when the number of treatment groups is large and the number of blocks is relatively small. Even under normality assumption, all tests either suffer from severe inflation of TypeI error rate or lose statistical power to detect heterogeneity of variances.In this paper, we consider the problem of homogeneity of variance in Randomized Complete Block Design (RCBD) and develop a new F _{max}-test for the equality of variances in RCBD. The TypeI error of this new test is well controlled and the power is higher than eight other tests when the number of treatment groups is larger than the number of blocks. Under normality assumption, none of the eight other tests are consistent top-performer. Our new F _{max}-test either outperforms or is comparable to the top-performer of the other eight tests. The new F _{max}-test can be recommended for future use by practitioners in cases such as sensory monadic testing with more than 10 products and blood glucose variability testing.

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

Pages (from-to) | 22-35 |

Number of pages | 14 |

Journal | Statistical Methodology |

Volume | 11 |

DOIs | |

State | Published - Mar 1 2013 |

### Fingerprint

### Keywords

- And O'Neill's test
- Han's test
- Homogeneity of variances
- Levene's test
- New -test
- Shukla's test
- Yitnosumarto's test

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**An alternative test for the equality of variances for several populations in randomised complete block design.** / Bhandary, Madhusudan; Dai, Hongying.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An alternative test for the equality of variances for several populations in randomised complete block design

AU - Bhandary, Madhusudan

AU - Dai, Hongying

PY - 2013/3/1

Y1 - 2013/3/1

N2 - In the last 50 years, eight major modifications and extensions of Levene's test and Bartlett's test had been developed for Randomized Complete Block Design (RCBD). The improvement from these works can be divided mostly into three categories as follows: (i)adjust fixed block effects and degrees of freedom in F test, (ii)improve the power of variance homogeneity tests, and (iii)develop a robust test that can be applied to non-normal distributions. Surprisingly, very little attention has been paid to the homogeneity of within treatment variance when the number of treatment groups is large and the number of blocks is relatively small. Even under normality assumption, all tests either suffer from severe inflation of TypeI error rate or lose statistical power to detect heterogeneity of variances.In this paper, we consider the problem of homogeneity of variance in Randomized Complete Block Design (RCBD) and develop a new F max-test for the equality of variances in RCBD. The TypeI error of this new test is well controlled and the power is higher than eight other tests when the number of treatment groups is larger than the number of blocks. Under normality assumption, none of the eight other tests are consistent top-performer. Our new F max-test either outperforms or is comparable to the top-performer of the other eight tests. The new F max-test can be recommended for future use by practitioners in cases such as sensory monadic testing with more than 10 products and blood glucose variability testing.

AB - In the last 50 years, eight major modifications and extensions of Levene's test and Bartlett's test had been developed for Randomized Complete Block Design (RCBD). The improvement from these works can be divided mostly into three categories as follows: (i)adjust fixed block effects and degrees of freedom in F test, (ii)improve the power of variance homogeneity tests, and (iii)develop a robust test that can be applied to non-normal distributions. Surprisingly, very little attention has been paid to the homogeneity of within treatment variance when the number of treatment groups is large and the number of blocks is relatively small. Even under normality assumption, all tests either suffer from severe inflation of TypeI error rate or lose statistical power to detect heterogeneity of variances.In this paper, we consider the problem of homogeneity of variance in Randomized Complete Block Design (RCBD) and develop a new F max-test for the equality of variances in RCBD. The TypeI error of this new test is well controlled and the power is higher than eight other tests when the number of treatment groups is larger than the number of blocks. Under normality assumption, none of the eight other tests are consistent top-performer. Our new F max-test either outperforms or is comparable to the top-performer of the other eight tests. The new F max-test can be recommended for future use by practitioners in cases such as sensory monadic testing with more than 10 products and blood glucose variability testing.

KW - And O'Neill's test

KW - Han's test

KW - Homogeneity of variances

KW - Levene's test

KW - New -test

KW - Shukla's test

KW - Yitnosumarto's test

UR - http://www.scopus.com/inward/record.url?scp=84867824108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867824108&partnerID=8YFLogxK

U2 - 10.1016/j.stamet.2012.08.002

DO - 10.1016/j.stamet.2012.08.002

M3 - Article

AN - SCOPUS:84867824108

VL - 11

SP - 22

EP - 35

JO - Statistical Methodology

JF - Statistical Methodology

SN - 1572-3127

ER -