Why don't you need to use multiple comparison adjustments when you choose to look at one out of many possible comparisons? I was explaining multiple comparison adjustments to a colleague and explained how, if you test one hypothesis alone (call it hypothesis A), it's appropriate to use a certain alpha (say .05) but if you test that same hypothesis A among many (say B-K), it's appropriate to use a stricter alpha (e.g. .005 with Bonferroni). Their question was, "why does looking at hypotheses B-K change the amount of evidence I need to reject the null for hypothesis A? If any of these 10 possible hypotheses could be spurious, shouldn't we adjust the alpha for hypothesis A to .005 even if it's the only one we look at?"
I understand this intuitively but found myself at a loss for a helpful explanation. Does anybody want to give this a shot? I'm looking for something intuitive and not very technical.
Thanks!
 A: You're in luck, I was just grappling with a similar problem.
The key concept here is the Familywise Error Rate (FWER), which is the probability that at least one of a "family" of tests incorrectly rejects the null hypothesis.  The Bonferroni Correction controls this rate.
What is a "family"? I'll quote Wikipedia which is in turn quoting Hochberg: "any collection of inferences for which it is meaningful to take into account some combined measure of error".
But you asked for intuitive, so here's an analogy.  You are playing Russian Rolette with a revolver with 1000 chambers.  You fire the gun ten times, you want to control the chance you get shot even once (FWER).  So based on the number of times you pull the trigger (# of hypotheses tested), you set the probability that a given chamber is loaded correspondingly lower (Bonferroni Correction to alpha).
But I think your colleague is on to something.  We find a similar objection in the widely cited "What's Wrong with Bonferroni", Pernegger 1998, under the section "Inference Defies Common Sense".

Bonferroni adjustments imply that a given comparison will be interpreted differently according to how many other tests were performed. For example, the difference in remission rates between two chemotherapeutic treatments could be interpreted as statistically significant or not depending on whether or not survival rates, quality of life scores, and complication rates were also tested. In a clinical setting, a patient’s packed cell volume might be abnormally low, except if the doctor also ordered a platelet count, in which case it could be deemed normal. Surely this is absurd, at least within the current scientific paradigm. Evidence in data is what the data say—other considerations, such as how many other tests were performed, are irrelevant.

I'd recommend looking into controlling the False Discovery Rate (FDR) as an alternative to controlling the FWER.  See various work by Hochberg, Benjamini, and others.
Back to the Russian Rolette analogy, the FDR is measuring the probability that you get shot any time that you pull the trigger.  Some folks think this is the more sensible thing to control.  Of course, it depends on the circumstance.  I'd go with the FWER if I were dealing with real guns, or equally dangerous hypotheses.
