Testing the equality of a large number of normal population means

It is challenging to consider the problem of testing the equality of normal population means when the number of populations is large compared to the sample sizes. In ANOVA with the assumption of homogeneous variance, the F-test is known as an exact test. When variances are heterogeneous, due to the complication, there are various tests with only approximate forms-either approximate chi-square or approximate F-test. Two types of tests are proposed with their asymptotic normality as the number of population increases. p-values from those tests are adjusted based on higher order asymptotics such as Edgeworth expansion so that the proposed tests can be considered even for moderate values of k. Numerical studies including simulations and real data examples are presented with comparison to existing tests.

[1]  D. Mehrotra Improving the brown-forsythe solution to the generalized behrens-fisher problem , 1997 .

[2]  D. Cox,et al.  Asymptotic techniques for use in statistics , 1989 .

[3]  Nabendu Pal,et al.  A Revisit to the Behrens–Fisher Problem: Comparison of Five Test Methods , 2008, Commun. Stat. Simul. Comput..

[4]  James A. Neal,et al.  A Selective Review of the Validity of Student Ratings of Teaching , 1982 .

[5]  O. E. Asiribo,et al.  Coping with variance heterogeneity , 1990 .

[6]  A. Rukhin,et al.  Estimation of a Common Mean and Weighted Means Statistics , 1998 .

[7]  Peter A. Cohen,et al.  Comment on a Selective Review of the Validity of Student Ratings of Teaching , 1983 .

[8]  Sam Weerahandi,et al.  Exact Statistical Methods for Data Analysis , 1998, Journal of the American Statistical Association.

[9]  Joachim Hartung,et al.  Small sample properties of tests on homogeneity in one—way Anova and Meta—analysis , 2001 .

[10]  B. L. Welch ON THE COMPARISON OF SEVERAL MEAN VALUES: AN ALTERNATIVE APPROACH , 1951 .

[11]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[12]  W. G. Cochran Problems arising in the analysis of a series of similar experiments , 1937 .

[13]  Bimal K. Sinha,et al.  Bootstrap Procedures for Testing Homogeneity Hypotheses , 2012 .

[14]  B. Sinha,et al.  Statistical Meta-Analysis with Applications , 2008 .

[15]  Lili Tian Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable , 2006, Comput. Stat. Data Anal..

[16]  Morton B. Brown,et al.  The Small Sample Behavior of Some Statistics Which Test the Equality of Several Means , 1974 .

[17]  Roger Bilisoly,et al.  Testing the homogeneity of the means of several groups of count data in the presence of unequal dispersions , 2009, Comput. Stat. Data Anal..