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In an experiment,the impact of self-control on intoxication is tested. An experiment randomly assigned 11 males to each of four groups. Each group was given a treatment, with one of the four given a placebo. Their performances on a written test were recorded after the treatment.

The null hypothesis being tested is that the means of all groups are equal, versus the alternative hypothesis that the means are unequal. Following the test, it is concluded that the resulting p value is very small, indicating that the null hypothesis be rejected. There is statistical evidence to prove that the means of all groups are different.

My question

Once such a conclusion is reached, how can I investigate further by identifying the group(s) responsible for the test outcome? Are there any recommended methods that I can apply? One suggestion I got was to calculate pairwise confidence intervals for all 4 groups. However when the number of groups increases, this process would be very time consuming.

Thank you in advance for your inputs.

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1 Answer 1

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There are a couple of options available at this point, depending on what you are really interested in. Also in your approach, since you are doing multiple testing, you would need to acccount for it by adjusting the p-values. A common option is to use a post-hoc Tukey HSD test. The Tukey test will compare the means of all the possible pairs, saving you the trouble of doing all this by hand, also the test has a better theory behind it.

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