The Behrens-Fisher Problem in General Factorial Designs with Covariates




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The Behrens-Fisher Problem exists in many disciplines. The original problem aims to make inferences about the difference between the means of two normally distributed populations without assuming the equal variances. When the covariates are present, the treatment effects can be obscured. Existing analysis of covariance (ANCOVA) methods are typically based on the assumptions of a normal distribution and equal variances across the groups. These methods do not tend to control the type I error rate satisfactorily when the assumptions are violated. In this dissertation, we tackle this problem and derive group-specific unbiased variance estimators. These estimators are used to develop the new test statistic and compute the degree of freedom by Box-type approximation for a Behrens-Fisher Problem with covariates. Additionally, we generalize the new method to a broad range of factorial designs with covariates. Extensive simulation studies demonstrate the robustness of the new approaches, even for very small samples, moderately skewed distributions, unbalanced designs and under variance heteroscedasticity. The proposed methods are motivated and demonstrated by the real data sets.



Heteroscedasticity, Analysis of covariance, Factorial experiment designs


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