A Note on the Likelihood Ratio Test for Equality of k Normal Populations |
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| Authors: | Lingyun Zhang Dong Q Wang Min Chen |
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| Institution: | 1. School of Engineering and Advanced Technology, College of Sciences , Massey University , Wellington , New Zealand;2. School of Mathematics, Statistics and Operations Research , Victoria University of Wellington , New Zealand;3. Academy of Mathematics and Systems Sciences, Academia Sinica , Beijing , P. R. China |
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| Abstract: | The authors derive the analytic expressions for the mean and variance of the log-likelihood ratio for testing equality of k (k ≥ 2) normal populations, and suggest a chi-square approximation and a gamma approximation to the exact null distribution. Numerical comparisons show that the two approximations and the original beta approximation of Neyman and Pearson (1931
Neyman , J. ,
Pearson , E. S. ( 1931 ). On the problem of k samples . In:
Neyman , J. ,
Pearson , E. S. , eds. Joint Statistical Papers . Cambridge : Cambridge University Press , pp. 116 – 131 . Google Scholar]) are all accurate, and the gamma approximation is the most accurate. |
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| Keywords: | Beta approximation Chi-square approximation Gamma approximation Likelihood ratio test |
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