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374 PART V: Analyzing and Reporting ResearchKey ConceptThe direction of a correlation can be seen in the scatterplot by noting how thepoints are arranged. When the pattern of points seems to move from the lowerleft corner to the upper right [panel (a)], the correlation is positive (low scoreson the x-axis go with low scores on the y-axis and high scores on the x-axis gowith high scores on the y-axis). When the pattern of points is from the upperleft to the lower right [panel (c)], the correlation is negative (low scores on thex-axis go with high scores on the y-axis and high scores on the x-axis go withlow scores on the y-axis).Assume that 20 college students provided responses to the two questionswe described above. Assume further that the data were carefully inspected forerrors and any anomalies and that the data were judged to be clean.We wish to find out whether scores on one measure are related to (i.e.,“go with”) scores on the second measure. Is reported worry about gradesrelated to self-reported difficulty concentrating on exams? To find out wecan construct a scatterplot showing the relationship between the scores. Ascatterplot is constructed by drawing a graph showing the intersection of thetwo measures from each respondent. The axes on the graph represent the twomeasures of interest. By convention, the measure of the behavior that “comesfirst” or that is used to predict the second behavior is placed on the horizontalor x-axis. The second behavior or that which is predicted by the first is placedon the vertical or y-axis. In many situations such a decision is easy. If youwere correlating volunteers’ blood alcohol levels and a measure of their performanceon a driving simulator, we would easily see that alcohol was firstconsumed and then simulated driving performance was measured. Bloodalcohol levels would be used to predict performance on a driving simulator.In other situations the decision is not as easy. Does worry about grades comebefore difficulty concentrating on exams? Or does difficulty concentratingon exams lead to worry about grades? We believe a case could be made foreither.We want to examine the scatterplot for possible trends. More specifically,we look to see if there is evidence of a linear trend in the scatterplot. Simply,a linear trend is one that may be summarized by a straight line. As you haveseen, scatterplots (a) and (c) in Figure 11.5 show evidence of a linear trend. Itis also possible to see no trend in the scatterplot. In this case, scores on onemeasure are just as likely to go with low, middle, or high scores on the secondmeasure. If there is no discernible trend in the graph, as in the middle panel ofFigure 11.5, then we can conclude there is no relationship between the setsof scores. Note that in this case we are not able to use our knowledge of scoreson one measure to make predictions about scores on the second measure.Finally, it is also possible to see a relationship in the scatterplot, but onethat is not linear. Figure 11.6 provides two examples of nonlinear relationshipsbetween variables. We may judge these relationships to be interesting and evenworthy of further investigation; however, a nonlinear relationship poses seriousproblems of interpretation for a correlation coefficient. Consequently, ifthe trend in the scatterplot is nonlinear, a correlation coefficient should not becalculated. Outliers in a scatterplot also pose problems when interpreting acorrelation coefficient.