The Significance of Evidence

Abstract

Imagine you believe the mean human body weight is 72kg. The mean human weight isn’t a random number, but it’s very hard to measure directly. You are forced to take a sample, and compute the sample mean. This sample mean is a random variable, and it will have different values for different samples. You need to know how to tell whether the difference between the observed value and 72kg is just an effect of variance caused by sampling, or is because the mean weight actually isn’t 72kg. One strategy is to construct an interval around the sample mean within which the true value will lie for (say) 99% of possible samples. If 72kg is outside that interval, then very few samples are consistent with the idea that 72kg is the mean human body weight. If you want to believe the mean human body weight is 72kg, you have to believe that you obtained a very odd sample.