The effect of error non-normality on the power of parametric and non-parametric ANOV tests.

Abstract

The purpose of this thesis is to determine the power relationship, through computer simulation, between the parametric ANOV and non-parametric Wilson tests under controlled conditions of error non-normality. Data is simulated using the 12 cell factorial ANOV model with three levels of factor A, four levels of factor B, and six observations per cell. Interaction is characterized such that its effect is proportional to the effect of factor A with the constant of proportionality related to factor B. Non-normality of the error term is characterized in three distribution types: skewed, leptokurtic (peaked), and platykurtic (flat). Four degrees of the three error distribution types are utilized, each related to the Pearson family of frequency curves. Three thousand-seven hundred sets of data are generated for each degree of error type. Power is then estimated directly for both the ANOV F tests and Wilson Chi-square tests for main effects and interaction. Comparison is then made between corresponding tests showing the effect of error non-normality on the power of each.