Artificial joints consist of a ceramic ball mounted on a taper. The article "Friction in Orthopaedic Zirconia Taper Assemblies" (W. Macdonald, A. Aspenberg, et al., Proceedings of the Institution of Mechanical Engineers, 2000: 685-692) presents data on the coefficient of friction for a push-on load of 2 kN for taper assemblies made from two zirconium alloys and employing three different neck lengths. Five measurements were made for each combination of material and neck length. The results presented in the following table are consistent with the cell means and standard deviations presented in the article.

a. Compute the main effects and interactions.
b. Construct an ANOVA table. You may give ranges for the P-values.
c. Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.
d. Can the effect of material on the coefficient of friction be described by interpreting the main effects of material?
If so, interpret the main effects. If not, explain why not.
e. Can the effect of neck length on the coefficient of friction be described by interpreting the main effects of neck length? If so, interpret the main effects, using multiple comparisons at the 5% level if necessary. If not, explain why not.

Transcribed Image Text:

Taper Material Coefficient of Friction CPTi-ZnO2 CPTi-ZrO2 CPT-ZrO2 TiAlloy-Zr02 TiAlloy-Zr02 TiAlloy-ZrO Neck Length Short Medium Long Short Medium Long 0.254 0.195 0.281 0.289 0.220 0.196 0.220 0.185 0.259 0.197 0.329 0.481 0.320 0.296 0.178 0.150 0.118 0.158 0.175 0.131 0.180 0.184 0.154 0.156 0.177 0.178 0.198 0.201 0.199 0.210