The answer to this question has to do with something you may recall from Chapter 2—namely, that psychology is a science. To make sense of human nature, psychologists do not rely on intuition; they go into the natural world to gather data and test hypotheses. But they do not make their observations haphazardly; rather, they operationally define their variables so that others can verify their findings. Let’s start with an example to illustrate the need for the scientific approach, and then we’ll spell out the role of statistics within this framework.

Imagine you are a developmental psychologist who wants to find out whether adolescent boys and girls differ in their self-esteem. You approach teens at a nearby high school and ask them, “So, how’s your self-esteem?” and write down their answers. At the end of the day, you have two columns of data: one for boys and one for girls. Within these two columns, you might find responses like “great” and “okay” and “just fine, thank you.” How far would you get in finding out whether there are differences in self-esteem between boys and girls?

Careful readers will have already picked up on the idea that you could have gathered much more useful information by assigning numbers to the variable of self-esteem. This would enable you to succinctly summarize the data by calculating averages for boys and girls. In doing so, you would be using statistics to describe self-esteem.

Statistics refers simultaneously to three things. First, statistics is a field of study; statisticians are mathematicians who focus on analyzing large sets of numbers to extract meaning from them. Second, a statistic is a number that describes some aspect of a larger set of numbers. For instance, the statistic that describes the average of a sample of numbers is the mean, whereas the statistic that tells us the middlemost score in a set of scores is the median (as in “median family income”). Third, statistics is a mathematical tool for helping scientists describe and make inferences about data. The purpose of this appendix is to introduce you to some of the statistical methods researchers use to describe data and draw inferences based on them. The first section will focus on descriptive statistics, or mathematical techniques geared toward helping scientists summarize their data. Then you will be introduced to inferential statistics, or mathematical techniques that enable scientists to make inferences about populations based on data collected from samples.