# What is Dunnett's method for multiple comparisons?

Dunnett's method for multiple comparisons is used in ANOVA to create confidence intervals for differences between the mean of each factor level and the mean of a control group.

If an interval contains zero, then there is no significant difference between the two means under comparison. You specify a family error rate for all comparisons, and Dunnett's method determines the confidence levels for each individual comparison accordingly.

## Example of Dunnett's method

You are studying three weight loss pills to determine whether they are significantly different from a placebo. In a double-blind experiment, fifty people receive Pill A, fifty people receive Pill B, fifty people receive Pill C, and fifty people receive a placebo. The placebo group is the control group. You record the average weight loss of each group and perform ANOVA with Dunnett's method to determine whether any of the three pills produce weight loss that is significantly different than the placebo. Dunnett's method produces three confidence intervals: one for the difference in mean weight loss between group A and the placebo group, one for the difference in mean weight loss between group B and the placebo group, and one for the difference in mean weight loss between group C and the placebo group. You set the family error rate for all three comparisons at 0.10, so the confidence level for all the comparisons is 90%.

The confidence interval for the difference between Pill A and the placebo contains zero; therefore, you conclude that there is no difference between the weight loss in group A and the placebo group. The confidence interval for the difference between Pill B and the placebo contains only negative numbers; therefore, you conclude that subjects in group B lost less weight than subjects in the placebo group. In other words, Pill B prevents weight loss. Finally, the confidence interval for the difference between Pill C and the placebo contains only positive numbers; therefore, you conclude that Pill C produces significantly greater weight loss than a placebo. As a result of this study, you recommend Pill C.