Analysis of Treatment Means KNNL – Chapter 17

Cell Means Model – Sampling Distributions and Graphs

Inference for Individual Treatment Means

Comparing Two Treatment Means

Contrasts among Treatment Means

Simultaneous Comparisons Confidence Coefficient (1-a) applies to only one estimate or comparison, not several comparisons simultaneously. Confidence Coefficient for a “family” of tests/intervals will be smaller than confidence coefficient for “individual” tests/intervals If we construct five independent confidence intervals, each with confidence level = 0.95, Pr{All Correct} = (0.95)5 = 0.774 Confidence Coefficient (1-a) applies to only pre-planned comparisons, not those suggested by observed samples (referred to as “data snooping”). If we wait until after observing the data, then decide to test whether most extreme means are different, actual a too high

Tukey’s Honest Significant Difference (HSD) - I

Tukey’s Honest Significant Difference (HSD) - II

Scheffe’s Method for Multiple Comparisons

Bonferroni’s Method for Multiple Comparisons

SNK Method for All Pairwise Comparisons Controls False Discovery Rate at e Uses Different Critical Values for different ranges of means

Duncan’s Method for All Pairwise Comparisons More powerful than SNK method, at cost of increasing e for longer stretches (does not control experimentwise error rate) Uses Different Critical Values for different ranges of means