Contradictory test results My question is relatively simple, and has to do with reporting seemingly contradictory results from statistical tests. This is the problem.
There are two independent groups, and two research questions are important:

*

*Are the two (population) group means equal

*Do both (population) means differ significantly from zero?

An independent groups t-test leads to the conclusion (A) that both group means do NOT differ significantly from one another. Further, two “one sample t-tests”, lead to the conclusion (B) that group-mean 1 differs significantly from zero, whereas group-mean 2 does NOT.
These two test conclusions seem contradictory, because for the true means in the populations conclusion (A) and (B) could not both be valid. Sample tests, of course, can lead to such contradictory conclusions. Hence my question is: how to deal with such results, or how to report them? Simply reporting both conclusions (A) and (B) is not "wrong" but it feels inconsistent. Any thoughts about this?

Consider the simplified case of intersecting intervals (see below). It can be the case to have three intervals such that A and C both overlap with B, but A and C don't overlap with each other.

To translate this to hypothesis testing, think of the test as of looking if confidence intervals overlap.
