Learning Objectives

After completing your study of this chapter, you should be able to do the following:

• Describe and identify the different levels of measurement.
• Summarize test scores using class intervals and frequency distributions.
• Describe the characteristics of the normal curve as well as skewed, peaked, and bimodal distributions.
• Describe the purpose and calculate measures of central tendency, measures of variability, and measures of relationship.
• Convert raw test scores into more meaningful units.
• Describe norm-based interpretation and the different types of norms.

Chapter Summary

Most psychological tests produce raw scores. The claims we can make using these scores depend on the scores’ level of measurement. Four common levels of measurement are nominal, ordinal, interval, and ratio. As we move from one level of measurement to the next, we are able to perform more mathematical operations (addition, subtraction, multiplication, and division) that allow us to make more and different claims regarding test results.

To make sense of raw scores, we rely on a number of techniques. For example, we plot frequency distributions and calculate measures of central tendency, variability, and relationship. Each technique we use has a different purpose. Frequency distributions provide us with a picture of a distribution of scores. Measures of central tendency (mean, mode, and median) help us identify the center of a distribution of scores. Measures of variability (range, variance, and standard deviation) help us understand the spread of scores in a distribution. Measures of relationship (correlation coefficients) help us determine the rela­tionship between distributions of test scores.

We also convert raw scores into standard units of measurement (e.g., percentage, standard deviation unit, z score, T score, percentile) to provide more meaning to individual scores and so that we can com­pare individual scores with those of a previously tested group or norm group. Norms provide us with a standard against which we can compare individual test scores and make accurate inferences. There are a number of different types of norms, and test users must select and use the norm group that is most similar to the test takers. Test users should also be careful to use up-to-date norms and be sure that the norm group is representative of the target population. Those who interpret test scores using norm-based interpretation should have a good rationale for using a specific norm group.