MSc Stats Defence: A study on the performance of the aligned rank transform procedure for testing interaction in split-plot designs, using count data generated from Neyman Type A distributions

CANDIDATE:   WENJUN YANG

ABSTRACT:

Rank transformations are commonly employed in nonparametric alternatives to parametric procedures, including Analysis of Variance (ANOVA) tests, when sampling violates key underlying assumptions. The Aligned Rank Transform (ART) procedure was developed to alleviate deficiencies in simpler rank transform techniques when testing for interaction in factorial design ANOVAs. Most investigations to date have focussed on continuous data and/or regular factorial designs. This simulation study focusses on the performance of the ART procedure in comparison to simpler ANOVA analyses on raw (untransformed) and square root transformed data from 3×3 CRD split-plot designs, where the data is drawn from a range of Neyman Type A distributions. Neyman Type A distributions were derived to model clustered count data, such as is commonly encountered where the response variable involves counts of insects. A range of parameter values was selected to include a distribution with a high proportion of zeroes and a diversity of clustering patterns for a fixed mean. The three methods showed similar robustness and power. At least for the range of parameters employed for the Neyman Type A distributions, the ART procedure did not demonstrate any advantage over using simpler ANOVA procedures.