Final answer:
Tukey's honestly significant difference test is the most suitable post-hoc test to use after a significant multivariate analysis of variance to compare which drugs differ in pain measures following surgery.
Step-by-step explanation:
After conducting a multivariate analysis of variance (MANOVA) to compare three drugs on measures of pain following surgery, the next step is to determine which drugs significantly differ from each other. Among the listed options, the most appropriate method for post-hoc comparisons would be Tukey's honestly significant difference (Tukey's HSD). This test is specifically designed to compare all possible pairs of means while controlling for the Type I error rate when multiple comparisons are conducted.
Why Tukey's HSD is appropriate:
It directly compares mean differences between the levels of a factor (in this case, the different drugs).
Tukey's HSD controls the family-wise error rate effectively.
It is commonly used following ANOVA when we have a significant overall effect and need to pinpoint where the differences lie.