The Joint Distribution of the Standardized Row Sums of Squares from a Balanced Two-Way Layout
- 1 June 1977
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 72 (358) , 407
- https://doi.org/10.2307/2286808
Abstract
A balanced two-way layout with no interaction is considered with the observations y ij being arranged in r rows and c columns (i = 1, …, r, j = 1, …, c). The error sum of squares for each row is defined as , and the total error sum of squares is defined as S = Σ r i = 1 S i. The joint distribution of S 1, …, S k (k ≤ r) and the joint distribution of S 1/S, …, S k/S (k < r) are derived. The distributional results are of the form conjectured by N.L. Johnson (1962). Finally, a procedure is considered for testing equality of the variances in the different rows which assumes the column variances are equal.Keywords
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