The latter notion—statistical testing of hypotheses—is simple in principle. You make an assumption (often forbiddingly termed the null hypothesis), design and perform an experiment, then calculate to see if the results of the experiment are sufficiently probable, given the assumption. If they aren’t, you throw out the assumption, sometimes provisionally accepting an alternative hypothesis. In this sense, statistics is to probability as engineering is to physics—an applied science based on a more intellectually stimulating foundational discipline.
