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376 PART V: Analyzing and Reporting ResearchKey ConceptKey Conceptcorrelation coefficient expresses the relationship between two variables in termsof both the direction and the magnitude of that relationship. The most commonlyused correlation coefficient is the Pearson Product-Moment CorrelationCoefficient, designated as r. It is easily calculated with an electronic calculatoror computer software program. (An Internet search will identify web sites thatprovide methods for computing a correlation.)The direction of a correlation coefficient can be either positive or negative. Apositive correlation indicates that, as the values for one measure increase, the valuesfor the other measure also increase [see panel (a) in Figure 11.5]. As we’veseen, measures of smoking and lung disease are positively correlated (moresmoking, more lung disease). Another predictive relationship concerns ScholasticAptitude Test (SAT) scores: SAT scores and college students’ first- semesterGPAs are positively correlated. Thus, we can predict that students with higherSAT scores should have higher first-semester GPAs, and students with lowerSAT scores should have lower first-semester GPAs. With correlations, the“reverse” prediction can be made too. If we know only the first- semester GPAs ofstudents, we can “predict” what their SAT scores were prior to entering college.Students with higher GPAs would be more likely to have higher SAT scores,and students with lower GPAs would be likely to have lower SAT scores.In a negative correlation, as the value of one measure increases, the valueof the other measure decreases [see panel (c) in Figure 11.5]. A national survey ofhigh school seniors showed a negative correlation between the amount of timespent watching TV and the number of correct answers on an academic achievementtest (Keith, Reimers, Fehrmann, Pottebaum, & Aubrey, 1986). Studentswho spent more time watching TV answered fewer questions correctly on anachievement test. What about the reverse prediction? Based on this finding, ifyou knew that a student scored very high on the achievement test, would youpredict that the student had spent “a lot” of time or “a little” time watching TV?Is the relationship between measures of worry and concentration difficultyseen in Figure 11.7 positive or negative?The magnitude (degree) of a correlation coefficient can range in absolute valuesfrom 0.0 to 1.00. A value of 0.0 indicates there is no correlation and there is no basisfor making predictions. The relationship between intelligence and mental illness,for example, exhibits a zero correlation; we cannot predict the likelihood that aperson will become mentally ill by knowing the person’s IQ (nor can we predict aperson’s IQ based on his or her mental health). A value of 1.00 indicates a perfectpositive correlation, and a value of 1.00 indicates a perfect negative correlation.When a correlation coefficient is either 1.00 or 1.00, all the points in thescatterplot fall on a straight line and we can make predictions with absolute confidence.Values between 0 and 1.00 indicate predictive relationships of intermediatestrength and, therefore, we have less ability to predict confidently. Remember,the sign of the correlation signifies only its direction; a correlation coefficient of.46 indicates a stronger (more predictive) relationship than one of .20. (Note: Inpractice, only the sign of negative correlation coefficients is indicated; a coefficientwithout a plus or minus sign is treated as positive, that is, .20 .20.)The correlation coefficient for the relationship between worry and concentrationdifficulty based on the 20 students in our hypothetical study is .62. As