Contents

CHAPTER 11: Data Analysis and Interpretation: Part I. Describing Data, Confidence Intervals, Correlation 375FIGURE 11.6 Two examples of nonlinear relationships between two variables: X and Y.Scores on YHighLowxxxxLowxx xxx xx x xxxx x xxxxxx x xScores on XHighHighLowx xxx xxxxxxxxx xxLowScores on Xx xxxxxxx xx xHighFigure 11.7 shows a scatterplot describing the relationship between scoreson the worry (X) and concentration difficulty (Y) measures from our hypotheticalsurvey. Since we really don’t know in this case which factor “comes first,”we have arbitrarily put the measure of worry on the x-axis and the measureof con centration difficulty on the y-axis in the scatterplot found in Figure 11.7.That is, we are using the measure of worry to predict the measure of concentration.Can you see a trend in the scatterplot? If so, is it generally linear?Calculating a Correlation Coefficient The direction and strength of a correlationare determined by computing a correlation coefficient. The correlation coefficientis a quantitative index of how well we are able to predict one set of scores(e.g., concentration ratings) using another set of scores (e.g., worry ratings). AFIGURE 11.7Scatterplot showing relationship between scores on self-report measure of degree of worry aboutgrades (X) and self-report measure of difficulty concentrating during an exam (Y). Each point inthe graph is the intersection of the two measures for each respondent.1098Concentration Difficulty (Y)76543211 2 3 4 5 6 7 8 9 10Worry (X)