Just as professional journals and newspapers are more interested in printing pieces that support hypotheses rather than papers with negative findings, so we all tend to spend more time discussing the risks of action rather than the risks of inaction.
That seems to be human nature, but it ain't rational and, fortunately, people vary across a spectrum of activity/passivity.
Passive people worry about the risks of action. Active people worry about the risks of inaction. I am more-or-less in the middle.
To discuss that half-intelligently, though, I first need to review the notion of Type 1 and Type 2 errors, now that we have taken a look at the null hypothesis a couple of days ago.
A Type 1 error, also known as False Positive, is the error of erroneously rejecting the null hypothesis. In other words, it supports a connection which does not really exist.
A Type 2 error, or False Negative, is the error of wrongly accepting the null hypothesis. In other words, it says nothing is there, when it is, in fact, there.
For example, a blood test which has a 10% False Positive rate will wrongly tell you that there is an abnormality 10% of the time. A blood test with a 10% False Negative rate will miss an abnormality 10% of the time.
For another example, convicting an innocent person is a Type 1 error; letting a guilty person go free is a Type 2.
Depending on the matter at hand, either sort of error could have worse consequences. A Type 1 error in a death penalty case is a grievous error. But sometimes you need Type 1 errors.
My favorite example of a good Type 1 error is in the emergency treatment of appendicitis. Since medical diagnosis contains both art and luck as well as science, some error rate is inevitable unless you have the diseased organ in hand. But since a False Negative diagnosis would have dire consequences (ruptured appendix), it is necessary to do some unnecessary appendectomies on patients who might have appendicitis, but do not turn out to. In the case of emergency appendectomies: one study indicates that the Type 1 error rate is around 10%, with 18% False negatives. I would have guessed that the False Positives would be higher, and you could argue that there is room for them to go higher. The point is that, with appendicitis, you want to minimize your False Negatives by having more False Positive diagnoses - by being deliberately biased against the Null Hypothesis that there is nothing there, but without cutting open everyone with a bad stomach ache.
Thus that is the opposite of what you want in a justice system, where the null hypothesis of innocence is presumed in order to minimize False Positives.
