1. An Alternative to Satterthwaite's's Test Involving Positive Linear Combinations of Variance Components.
- Author
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Howe, Richard B. and Myers, Raymond H.
- Subjects
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APPROXIMATION theory , *REGRESSION analysis , *ANALYSIS of variance , *LINEAR statistical models , *DEGREES of freedom , *STATISTICS , *MATHEMATICS , *STATISTICAL hypothesis testing , *MATHEMATICAL analysis , *ALGEBRA - Abstract
This article proposes a refinement of the usual approximation due to Satterthwaite for making a significance test when the test statistic involves a single mean square in the numerator and a linear combination of mean squares in the denominator, that linear combination involving known positive constants. The test procedure is outlined in detail, and its derivation given in a separate section. The development of the technique essentially involves determining, by successive approximations, a function which serves as the test criterion. This function is given through terms in the cubes of the reciprocals of the degrees of freedom involved in the problem, thereby giving a deviation from the advertised significance level which is smaller (in magnitude) than the deviation provided by the Satterthwaite procedure. An expression approximating the power of the test is also developed. [ABSTRACT FROM AUTHOR]
- Published
- 1970
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