When is absence of evidence = evidence of absence?

You often hear the old mantra "absence of evidence is not evidence of absence," but I think that this is an oversimplification. The truth is, sometimes it is, and sometimes it isn't. It depends on the experiment, and also how well you understand the implication of the results.

There are times when you can make an excellent case that something is absent because there is no evidence of it. If you are is small, well-lit room, you probably don't need to look under many things to convince any reasonable person that there is no tiger there. In general, you need two things:

1. You need a solid argument for what sort of evidence you would expect if what you are looking for is there, and how that would be different from the null hypothesis (not there). 
2. A set of data that tends to falsify the hypothesis, thus advancing the null hypothesis.

We're not talking about "proof" here. I would just as soon we not talk about proof much at all, unless the topic is logic or mathematics. Rather, simply raising or lowering the odds of the null hypothesis, i.e. that the claim in question is not true.

What Skepticism Isn't

A woman came up to me and said,
"I'd like to poison your mind,
With wrong ideas that appeal to you,
Though I am not unkind."
  - - - They Might Be Giants, "Whistling in the Dark"

I have recently written a post advocating what I would call skepticism.  In my view, skepticism comprises some fairly basic value judgments, some fundamental skills, and a process or approach to all testable claims.  Skepticism is a necessary component for navigating the minefield of delusion, deception and cognitive dissonance we all must pass through, whether we are scientists or not.  A necessary component yes, but we are learning the hard way it is not sufficient - we also need a set of emotional tools to stay calm, be kind, and to keep from getting lost.  I would like to address how we recognize skepticism and tell it apart from its imitators.