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January, 1975 Testing Hypotheses in Unbalanced Variance Components Models for Two-Way Layouts
Ib Thomsen
Ann. Statist. 3(1): 257-265 (January, 1975). DOI: 10.1214/aos/1176343017


Consider the model equation $y_{ijk} = \mu + \alpha_i + \beta_j + \gamma_{ij} + e_{ijk} (i = 1,2,\cdots, r; j = 1,2,\cdots, s; k = 1,2,\cdots, n_{ij})$, where $\mu$ is a constant and $\alpha_i, \beta_j, \gamma_{ij}, e_{ijk}$ are distributed independently and normally with zero means and variances $\sigma_A^2, \sigma_B^2, \sigma^2_{AB}, \sigma^2$, re spectively. In this paper procedures for testing hypotheses on $\sigma_A^2/\sigma_B^2, \sigma^2/\sigma^2$, and $\sigma^2_{AB}/\sigma^2$ are given. The test procedure for $\sigma^2_{AB}/\sigma^2$ is compared with the corresponding test procedures when $\alpha_i, \beta_j$, and $\gamma_{ij}$ are fixed effects instead of being random.


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Ib Thomsen. "Testing Hypotheses in Unbalanced Variance Components Models for Two-Way Layouts." Ann. Statist. 3 (1) 257 - 265, January, 1975.


Published: January, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0302.62034
MathSciNet: MR362745
Digital Object Identifier: 10.1214/aos/1176343017

Keywords: testing hypotheses , two-way layouts , unbalanced variance components model

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 1 • January, 1975
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