Multiple comparison tests of Dunnett, Tukey, Holm, and Bonferroni have been explored in Example 13.3.8. The confidence intervals are reported only for Tukey HSD. The reader should obtain the confidence intervals for the rest of the multiple comparison tests contrasts.

Data from in  Example 13.3.8

The R package  multcomp is useful for multiple testing. For more details about the package, refer to Bretz,  et al. (2011). R codes are in action now.

The glht function represents the General Linear Hypotheses according to the description in the multcomp package. In Dunnett, Bonferroni, and Holm’s multiple testing procedures, the treatment level 15 is taken as a base for the purposes of comparison. The difference between treatment levels is shown through the p-values. The interpretation of the results is along similar lines as earlier and obvious too.

The tensile strength experiment is an example of a balanced design. Fortunately, there is a slight change of ri, instead of the r, but all the results continue to hold. In R there are no changes in the structure of the commands and functionality. Thus, the user can easily solve the multiple testing problem for the Olson dataset, which is an example of an unbalanced design.

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> library (mult comp) > tensile.mc <- glht (tensile_aov, linfct = mcp (CWP="Dunnett"), + alternative="two.sided") > summary (tensile.mc) Simultaneous Tests for General Linear Hypotheses Multiple Comparisons of Means: Dunnett Contrasts Fit: aov (formula = Tensile_Strength CWP, data = tensile)