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We have completed a study comparing control with vitamin D supplement and with bone building drug. The primary outcome is change in bone mineral density. My statistician states that because we are using ANOVA to compare control to vitamin D Control to Bone building drug and vitamin D to bone building we have to do a Bonferroni correction. But this is the primary end point of the study. Why would we need to do this correction?

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  • $\begingroup$ Primary endpoint and primary outcome is the same, so the second last sentence does not make much sense. How many null hypotheses are tested in total to answer the primary research question? I'd say more than one, thus supporting your statistician. $\endgroup$ – Michael M Sep 18 '15 at 16:00
  • $\begingroup$ maybe this can help you ? stats.stackexchange.com/questions/167289/… $\endgroup$ – user83346 Sep 18 '15 at 17:31
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As quoted in an answer on this Cross Validated page, "this is a subject on which reasonable people can differ." See that page for links to further discussion.

Presumably there is an overall significant ANOVA or this wouldn't be an issue. Thus I take it that you have found some difference in bone density among your 3 groups (control, vitamin D, bone-building drug) and the question is which pairwise differences are "significant."

I'd suggest that you think about the significance tests as protecting you from fooling yourself about those pairwise differences. That said, the Bonferroni correction might be more conservative than necessary. With only 3 groups and an overall significant ANOVA, the Fisher LSD test could provide adequate protection, and the Holm-Bonferroni method, as noted on this page, provides a less conservative and more powerful alternative to the simple Bonferroni correction.

Finally, don't lose a focus on the magnitudes of the treatment effects, which are probably more important for guiding future work. It's too easy to get hung up on statistically "significant" differences that aren't of practical importance. For example, say you found that the bone-building drug led to a "significantly" higher bone density that was only 2% more than that with vitamin D. If the drug costs 200 times as much as vitamin D, what would you recommend as a policy decision: drug, or vitamin D?

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