Hockenbury Discovering Psychology 5th txtbk

Descriptive StatisticsA-11perceptions. In addition, following the high-fiber, low-fat traditional diet was associatedwith a higher level of coping and high vitamin intake.The study also found some negative correlations. Figure A.7 illustrates a negativecorrelation between compliance with the meditation part of the alternative programand cigarette smoking. This correlation coefficient is .77. Note that the datapoints fall in the opposite direction from those in Figure A.6, indicating that as thefrequency of meditation increased, cigarette smoking decreased. The pattern ofpoints in Figure A.7 is closer to a straight line than is the pattern of points in FigureA.6. A correlation of .77 shows a relationship of greater magnitude than doesa correlation of .59. But though .77 is a relatively high correlation, it is not aperfect relationship. A perfect negative relationship would be illustrated by a straightdiagonal line starting in the upper left-hand corner of the graph and ending at thelower right-hand corner.Finally, Figure A.8 shows two variables that are not related to each other. The hypotheticalcorrelation coefficient between compliance with the aerobic exercise part ofthe traditional program and a person’s level of coping is .03, barely above 0. In thescatter diagram, data points fall randomly, with no general direction to them. From az-score point of view, when two variables are not related, the cross-products aremixed—that is, some are positive and some are negative. Sometimes high z scores onone variable go with high z scores on the other, and low z scores on one variable gowith low z scores on the other. In both cases, positive cross-products result. In otherpairs of scores, high z scores on one variable go with low z scores on the other variable(and vice versa), producing negative cross-products. When the cross-productsfor the two variables are summed, the positive and negative numbers cancel eachother out, resulting in a 0 (or close to 0) correlation.In addition to describing the relationship between two variables, correlationcoefficients are useful for another purpose: prediction. If we know a person’sscore on one of two related variables, we can predict how he or she will performon the other variable. For example, in a recent issue of a magazine, I found a quizto rate my risk of heart disease. I assigned myself points depending on my age,HDL (“good”) and total cholesterol levels, systolic blood pressure, and other riskfactors, such as cigarette smoking and diabetes. My total points (2) indicatedthat I had less than a 1 percent risk of developing heart disease in the next fiveyears. How could such a quiz be developed? Each of the factors I rated is correlatedto some degree with heart disease. The older you are and the higher yourcholesterol and blood pressure, the greater your chance of developing heart disease.Statistical techniques are used to determine the relative importance of eachof these factors and to calculate the points that should be assigned to each levelof a factor. Combining these factors provides a better prediction than any singlefactor because none of the individual risk factors correlate perfectly with the developmentof heart disease.One thing you cannot conclude from a correlation coefficient is causality. Inother words, the fact that two variables are highly correlated does not necessarilymean that one variable directly causes the other. Take the meditation and cigarettesmokingcorrelation. This negative correlation tells us that people in the study whodiligently practiced meditation tended to smoke less than those who seldom meditated.Regular meditation may have had a direct effect on the desire to smoke cigarettes,but it is also possible that one or more other variables affected both meditationand smoking. For example, perhaps participation in the study convincedsome people that they needed to change their lifestyles completely. Both compliancewith the meditation routine and a decreased level of cigarette smoking may havebeen “caused” by this change in lifestyle. As discussed in Chapter 1, the experimentalmethod is the only method that can provide compelling scientific evidence of acause-and-effect relationship between two or more variables. Can you think of a wayto test the hypothesis that regularly practicing meditation causes a reduction in thedesire to smoke cigarettes?