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CHAPTER 11: Data Analysis and Interpretation: Part I. Describing Data, Confidence Intervals, Correlation 377indicated in the scatterplot in Figure 11.7, low scores on the worry measurestend to go with low scores on the concentration measure, and high scores withhigh scores. We may state that the two variables are positively related. Morespecifically, we can say that the more students worry, the more likely they are tohave difficulty concentrating during exams. But can we say that worrying causesstudents to have difficulty concentrating?Correlation and Causality As you may recall from our discussion of correlations inChapters 4 and 5, “correlation does not imply causation.” Knowing that two variablesare correlated does not allow us to infer that one causes the other (even if oneprecedes the other in time). It may be that worry about grades causes concentrationdifficulty during exams, or that the experience of difficulty while concentratingduring exams causes worry about grades. In addition, a spurious relationshipexists when a third variable can account for the positive correlation between worryabout grades and concentration difficulty during exams. For example, number ofhours employed might serve as a third variable that can account for this relationship.As number of hours employed increases, students might experience greaterconcern about grades and greater difficulty concentrating during exams.Conclusion A Pearson Product-Moment Correlation Coefficient may be used tosummarize the relationship between two variables. It is important, however,to inspect the scatterplot of the two variables prior to calculating a Pearson r tomake sure that the relationship is best summarized with a straight line, that is,that there is a linear trend. As the correlation coefficient approaches 1.00, therelationship between the two variables observed in the scatterplot approachesa straight line, and our ability to predict one variable based on knowledge ofanother increases.Stage 3: Constructing a Confidence Intervalfor a Correlation• We can obtain a confidence interval estimate of the population correlation,, just as we did for the population mean, .A Pearson r calculated from a sample is an estimate of the correlation inthe population just as a sample mean is an estimate of a population mean (). Thepopulation correlation is symbolized with the Greek letter rho (). Moreover,just as a sample mean is subject to sampling error or variation from sampleto sample, so, too, is a correlation coefficient. Thus, in some situations we maywish to obtain an interval estimate of the population value, , just as we didfor the population value, . In other words, we can calculate a confidence intervalfor . We will leave this topic, however, for books providing more comprehensivetreatment of statistical procedures (e.g., Zechmeister & Posavac, 2003).SUMMARYThere are three distinct, but related stages of data analysis: getting to knowthe data, summarizing the data, and confirming what the data reveal. In thefirst stage we want to become familiar with the data, inspecting them carefully,