a hypothesis test in a a milne’s 1922 “the red house mystery”

I am doing some summer reading and just came across a nice literary example of one of the key methodological approaches in science: hypothesis testing.

What do we do when we perform a hypothesis test? We form a theory and call it our null hypothesis.  We then look at data and ask ourselves how probable it is that we would see this data (or something like it) if the null hypothesis were true. This probability is called the p-value. If this probability is very low, we then abandon our null hypothesis in favor of its opposite.

Detective stories are generally a good potential source for examples of this approach, as detectives constantly entertain theories or hypotheses that have to be revised or rejected as new evidence is found. The present example is special in that the author really gives us all the steps of such a test in a specific setting, including the calculation of the p-value, that is the probability of seeing such data as was observed under the assumption that the null hypothesis is true. Continue reading