Using confidence intervals instead of pairwise comparisons

Question

Is it possible to use confidence intervals in order to determine if there is a statistically significant difference in means between two (or more) groups instead of conducting pairwise comparisons? For example, if we have the following 95% confidence intervals for the mean of each group:

 Control   |   Group A   |   Group B
[0.1,0.2]     [0.3,0.6]     [0.5,0.7]

Can we say that both Group A and Group B have a significantly different mean than the control at 95% confidence level, and non-significantly different means from each other?

Answer 1

Confidence intervals and hypothesis tests are closely related, and intervals that could be used in the manner you desire can be constructed. However, your intervals are intervals for the means themselves rather than the differences between means.

If you wanted to invert the intervals into hypothesis tests with the null hypotheses that the true means were a fixed value (generally zero, but any number is possible) then your intervals would be what you need.

When you are comparing the groups you would be interested in the differences between means and so the interval that would be directly reflect that difference is the confidence interval of the difference.

You might find this question and Whuber's answer helpful: Relation between confidence interval and testing statistical hypothesis for t-test

Answer 2

In general, no. Instead, compute confidence intervals on the differences among means. It is possible for confidence intervals on means to overlap yet the difference still be significant. In computing these intervals, you should probably use the studentized range distribution rather than the t distribution to control the Type I error rate.