Chapter Introduction

What can be said about the emotional health of college freshmen? The Freshman Survey administered nationally by the Higher Education Research Institute (HERI) at UCLA’s Graduate School of Education & Information Studies sampled 201,818 college freshmen in 2010.¹ Only 51.9% of students surveyed reported that their emotional health was “above average,” the lowest value since the survey began in 1985. The 51.9% describes the sample but we use it to estimate the percentage of all freshman who would report their emotional health as “above average.” This is an example of statistical inference: we use information from a sample to infer something about a wider population.

Because the results of random samples and randomized comparative experiments include an element of chance, we can’t guarantee that our inferences are correct. What we can guarantee is that our methods usually give correct answers. The reasoning of statistical inference rests on asking, “How often would this method give a correct answer if we used it very many times?” If our data come from random sampling or randomized comparative experiments, the laws of probability answer the question “What would happen if we did this many times?” This chapter presents some facts about probability that help answer this question.