ABSTRACT

A great many statistical techniques are directed towards inferring the nature of a population when only a sample is available. Somewhat paradoxically, it turns out that statisticians can best approach this problem from the opposite direction. The probability that a randomly selected unit of a population lies in a given category is simply the proportion of the population that belongs to that category, that is to say the relative frequency of the category. The definition of probability based on relative frequency requires a little clarification when applied to infinite populations; the top and bottom lines of the relative frequency are now infinite. Hypothesis testing has achieved its prominence in statistical analysis partly because many people are unhappy if they cannot conclude with a yes/no answer, partly because such a relatively easy-to-apply recipe is seen as a welcome substitute for some original thought, and partly because examination questions in the topic are easy to produce.