For each of the 42 combinations, we test the combination of treatment parameters on each of seven subjects to yield a single real number as a result. Per the professor's specification, it is the ratio of the alternative treatment result to the standard treatment result. We separately compute the mean for each of these 42 treatments and test the hypothesis that each of the 42 mean values is equal to one, i.e. standard treatment is equivalent to alternative treatment. Is the Bonferroni adjustment required here even though each of the 42 t-tests is considered independent of the others? (The trials are still each being done on the same seven subjects at different times.)

In addition, the professor says we must also stratify according to the five levels of A to perform pairwise t-tests between those levels. (He did not specify how to handle levels of B and C.) The null hypothesis is that the means are equal. Statistics professors have rightly cautioned against "data dredging" and performing too many statistical tests on the same set of data to try to find something significant. If it were the pairwise t-tests only, perhaps the Bonferroni adjustment would help, but performing one-sample t-tests then performing pairwise t-tests on the same data is troubling.

Just 2 questions:

1. Is some other test better than pairwise t-test here?

2. Is some appropriate correction possible for these different kinds of test on the same data?

The search for answers gave these leads, none viable so far:

This post applies to part of the problem mentioned above, but no-one has answered the post so far:

http://www.talkstats.com/showthread.php/5707-One-sample-t-tests-and-bonferroni

This other post may apply, but no-one gave a definitive answer so far:

http://www.talkstats.com/showthread...ts?highlight=familywise+error+multiple+t-test

This similar one went unanswered as well:

http://www.talkstats.com/showthread...sures-with-Bonferroni-and-t-tests-(no-t-value)

Thank you for your advice!