Discussion: Should Accumulation Analysis and Related Methods Be Used for Industrial Experiments?
Michael S. Hamada, C. F. Jeff Wu · Technometrics · 1986
When we were first introduced to accumulation analysis (AA), it appeared to be somewhat mysterious. We congratulate Nair for providing a definitive explanation of it and its relation to Pearson's chisquared test in the single-factor setting. Nair has given the conceptual framework for the analysis of ordered categorical data from industrial experiments. He points out that dispersion effects in addition to location effects should be and can be studied in this setting. We are thankful for his work in the single factor setting that provided the foundation for our work in the multifactor setting. We also recognize independent work by George Box on the decomposition of the AA statistic (Box 1985). Our main reservation is with the author's exclusive treatment of the single-factor setting, a setting not often used in industrial experiments. It will be shown that in the multifactor setting inference for a factor effect based on accumulation analysis depends on the other factor effects. This is in sharp contrast with the usual ANOVA for continuous data, where the orthogonality of the design allows each factor to be analyzed separately and independently of the other factors. Examples will be given that demonstrate the serious and misleading consequences of using accumulation analysis. Therefore, we seriously question the use of accumulation analysis to analyze ordered categorical data. Our findings provide a compelling reason to search for alternatives. We will show that the second component of the AA statistic and its simpler alternative proposed by the author are not often applicable in the multifactor setting. Even in the singlefactor setting, they can detect something other than a dispersion effect. The first component of the AA statistic and the Kruskal-Wallis test can be useful in certain situations, however. Finally, we will comment on some aspects of the analysis of the contact window forming data and will make some concluding remarks.