Boundary Conditions of Several Variables Relative to the Robustness of Analysis of Variance Under Violation of the Assumption of Homogeneity of Variances

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The purpose of this study is to determine boundary conditions associated with the number of treatment groups (K), the common treatment group sample size (n), and an index of the extent to which the assumption of equality of treatment population variances is violated (Q) with regard to user confidence in application of the one-way analysis of variance F-test for determining equality of treatment population means. The study concludes that the analysis of variance F-test is robust when the number of treatment groups is less than seven and when the extreme ratio of variances is less than 1:5, but when the ... continued below

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vi, 100 leaves : ill.

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Grizzle, Grady M. December 1977.

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  • Grizzle, Grady M.

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The purpose of this study is to determine boundary conditions associated with the number of treatment groups (K), the common treatment group sample size (n), and an index of the extent to which the assumption of equality of treatment population variances is violated (Q) with regard to user confidence in application of the one-way analysis of variance F-test for determining equality of treatment population means. The study concludes that the analysis of variance F-test is robust when the number of treatment groups is less than seven and when the extreme ratio of variances is less than 1:5, but when the violation of the assumption is more severe or the number of treatment groups is seven or more, serious discrepancies between actual and nominal significance levels occur. It was also concluded that for seven treatment groups confidence in the application of the analysis of variance should be limited to the values of Q and n so that n is greater than or equal to 10 In (1/2)Q. For nine treatment groups, it was concluded that confidence be limited to those values of Q and n so that n is greater than or equal to (-2/3) + 12 ln (1/2)Q. No definitive boundary could be developed for analyses with five treatment groups.

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vi, 100 leaves : ill.

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  • December 1977

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  • Aug. 22, 2014, 6 p.m.

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  • Nov. 15, 2018, 1:40 p.m.

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Grizzle, Grady M. Boundary Conditions of Several Variables Relative to the Robustness of Analysis of Variance Under Violation of the Assumption of Homogeneity of Variances, dissertation, December 1977; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc332297/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .