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ON TESTING AGAINST RESTRICTED ALTERNATIVES FOR THE VARIANCES OF GAUSSIAN MODELS
Author(s) -
Adegboye O. Sola,
Gupta A.K.
Publication year - 1989
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1989.tb00985.x
Subject(s) - mathematics , f test of equality of variances , homogeneity (statistics) , statistics , simple (philosophy) , combinatorics , levene's test , simple random sample , gaussian , statistical hypothesis testing , physics , population , medicine , test statistic , philosophy , environmental health , epistemology , quantum mechanics
Summary Let π 1 ,…,π p be p independent normal populations with means μ 1 …, μ p and variances σ 2 1 ,…, σ 2 p respectively. Let X(n i ) be a simple random sample of size n i from π i , i = 1,…, p. Given the simple random samples X(n 1 ),…, X(n p ) from π 1 ,…,π p respectively, a test has been proposed for testing the homogeneity of variances H 0 : σ 2 1 =…σ 2 p , against the restricted alternative, H 1 : σ 2 1 ≥…≥σ 2 p , with at least one strict inequality. Some properties of the test are discussed and critical values are tabulated.