Standardized Scores

This chapter begins with a discussion of normal distributions, probability, and area under the curve in light of the Central Limit Theorem. We point out that, like all geometric shapes, specific areas within a distribution can be determined and we can use a table of probabilities (the Normal Curve Table) to tell us the likelihood of a sample falling in any position within a distribution. The chapter walks students, step-by-step, through calculating z-scores from raw scores, and includes illustrations of distributions comparing raw scores to their corresponding z-scores. We use z-scores to compare a student’s relative position in two dissimilar distributions (a Cognitive Psychology course and an Educational Psychology course), and we provide an equation for students to use to work in reverse to calculate the raw score when given the z-score. Two additional examples put all of the concepts from this chapter together, walking students through calculating z-scores, locating the z-scores on the distribution, and using the Normal Curve Table to determine the percentage of the population falling above or below the target score. As in the previous chapter, sidebar notes alert students to common misconceptions and errors. The chapter concludes with a chapter summary, an illustrated, step-by-step guide to computing z-scores using Excel’s Data Analysis Toolpak, and critical thinking questions and practice problems.