Pairwise Comparisons of Means in ANOVA

This publication is a technical report that discusses the methodology of pairwise comparisons of means in the context of Analysis of Variance (ANOVA). It outlines the objective of comparing various treatments to identify significant differences in their means, specifically focusing on three methods: Fisher’s Least Significant Difference (LSD), Bonferroni, and Tukey methods. The report details how ANOVA can indicate whether differences exist among means, but additional pairwise comparisons are necessary to determine which specific means are different. It presents an example involving six stations producing molded containers, with statistical analysis performed using SPC for Excel software. The report includes ANOVA tables, calculations of means and standard deviations, and the implications of family error rates in multiple comparisons. The findings indicate which pairs of means are statistically significant, while also addressing the limitations of the Fisher LSD method due to the potential for false conclusions in multiple hypothesis tests.