Introduction

When we give a test, we generally want to use the scores to describe the abilities of the test takers. It's pretty easy, just by looking at the scores, to know who got the top score and who got the lowest, and we may have some sense of how the group did as a whole. However, if we want to use these scores appropriately to make inferences and decisions, we need to be able to describe them more precisely than this.

This chapter discusses procedures for calculating descriptive statistics and using these to better understand how test takers performed. These descriptive statistics also provide the basis for all of the other statistical procedures discussed in this book. In this chapter I will discuss the following:

• score distributions;

• some ways of graphically representing information about test scores;

• step-by-step procedures for calculating descriptive statistics, the appropriate uses of each, and ways in which these can be interpreted.

Score distributions

Whenever we give a test, not all the students will get the same score; some students will get high scores, some will get low scores, and others will get scores in between. In other words, the test takers’ scores will vary, and will be distributed along a range, from the highest to the lowest, forming a score distribution. This score distribution is a distribution for a variable, with each score constituting a value for that variable. For some tests, such as those designed for norm-referenced interpretation, the scores may be distributed widely, with a great deal of variation, so that the differences among scores may be considerable.