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Tests of Bivariate Symmetry with a One‐sided Alternative in the Analysis of Variance
Author(s) -
Bhattacharya Bhaskar
Publication year - 1996
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710380705
Subject(s) - bivariate analysis , mathematics , variance (accounting) , symmetry (geometry) , statistics , econometrics , statistical physics , physics , geometry , economics , accounting
We consider a two‐factor experiment in which the factors have the same number of levels with a natural ordering among levels. We test the hypothesis that the effects of the two treatments are symmetric against a one‐sided alternative using the likelihood ratio criteria. Test of the one‐sided alternative as a null hypothesis against no restriction has also been studied. Exact distribution theory under the null hypothesis is derived and is shown to be a weighted mixture of chi‐square distributions. An example is used to illustrate the procedure.