This thesis addresses the statistical analysis of zirconia bioceramic strength data. Strength of brittle materials is known to follow the Weibull distribution. When linear models are used, the assumption of normality is not met. Rank transformation and permutation tests can be used instead.
We perform a simulation study concerning the type I error and power on normal and Weibull distributed data. We show that notable differences only emerge in extremely asymmetric Weibull distributions not relevant for real data. For linear models, we detect a reduction in the type I error and power. With the type I error preserved, the power loss of permutation tests and the power increase of rank transformation is evident. Additionally, we consider different treatments of categorical variables and show that inappropriate treatment results in an inflated type I error and overestimated power.
We also present a real data set and conclude that linear models are a reliable method to analyze the strength data.