LEARNING OBJECTIVES

CHAPTER OVERVIEW

This chapter covers standard scores, normal curves, and probability. Most people know a little about bell-shaped curves, what statisticians call normal curves. This chapter explains why normal curves are called normal, what their characteristics are, and how they are used in statistics.

Standard scores, also called z scores, are new territory for most students. Standard scores are useful in statistics because raw scores can be transformed into standard scores (and vice versa). Standard scores allow different kinds of measurements to be compared on a common scale—such as the juiciness of an orange vs. the crispiness of an apple. Standard scores are also useful for measuring distance on the normal curve, which shows how big the pieces of the bell curve are in terms of what percentage of cases fall in different sections of it. This allows scores to be expressed as percentile ranks, which tell what percentage of cases fall at or below a given score. Breaking the normal curve into chunks allows researchers to talk about how common or rare different scores should be, how probable they are. This excursion into probability opens the way to understanding how statistical tests work in upcoming chapters.