A legal example

So the approach is not to use the data to accept the alternative hypothesis we are interested in proving, but instead to use the data to reject the null hypothesis that our peculiar sample of data might just have happened by chance. In other words, we try to falsify the pure chance hypothesis. To help understand why this somewhat perverse approach actually makes sense, consider the legal case of trying to prove whether a suspect is guilty of murder. Based on the available evidence, a decision must be made between the alternative hypothesis that ``the suspect is guilty'' and the null hypothesis that ``the suspect is innocent''. ^6.2If we assume the alternative ``guilty'' hypothesis, then to avoid conviction we must find evidence of innocence e.g. no sign of a murder weapon with the suspect's fingerprints. However, no sign of a murder weapon (or any other evidence of innocence) does not prove that the suspect is innocent since it could just be that the suspect is guilty but the murder weapon has not yet been found. A different sample of evidence a few years later may contain the murder weapon and invalidate the earlier evidence of innocence. Now consider what happens if we start by considering that the null ``innocent'' hypothesis is true, and then look for evidence inconsistent with this hypothesis (e.g. the murder weapon). If we find the murder weapon with the suspect's fingerprints, we can clearly reject the null hypothesis that the suspect is innocent, and thereby deduce that the suspect is guilty of murder. One bit of data inconsistent is enough to falsify a hypothesis, but no amount of consistent data can verify a non-trivial hypothesis! Look at what happened to Newton's laws of motion - the theory was consistent with all observed data over several centuries, until finally measurements of the speed of light in the 20th century showed that the whole theory was fundamentally wrong. Therefore, in statistical inference as in science, the correct approach is to use data to falsify rather than verify hypotheses.