A Study of Dispersion Effect Identification using Levene-Type Transformations in Replicated Factorial Designs




Cornelius, Haley

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University of Guelph


Interest in the analysis of dispersion effects has become increasingly popular and many methods for identifying such effects in factorial designs have been proposed; however, many methods for replicated designs typically result in a loss in degrees of freedom. Levene-type transformations were introduced as a means to transform the response variable such that each observation is now a measure of dispersion. In this thesis, six Levene-type transformations of the response variable in a 2^f factorial design will be performed and analyzed using an analysis of variance to identify dispersion effects. The use of these transformations, compared to a previous method, proves adequate with limitations. It is also of interest to determine how increasing the number of factors while holding the replication size and power level constant affects the detectable effect size. For a fixed power, the decrease in detectable effect size as the number of factors increases is quantified.



Replicated Factorial Designs, Levene's Test, Dispersion Effects, Levene Transformations, Absolute Deviation, Balanced Factorial Designs, Half-Normal Distribution, Folded-Normal Distribution