Hockenbury Discovering Psychology 5th txtbk

Descriptive StatisticsA-9simple example, let’s determine the correlation between height (we’ll call this thex variable) and weight (the y variable). We start by obtaining height and weightmeasurements for each individual in a group. The idea is to combine all these measurementsinto one number that expresses something about the relationship betweenthe two variables, height and weight. However, we are immediately confronted witha problem: The two variables are measured in different ways. Height is measuredin inches, and weight is measured in pounds. We need some way to place bothvariables on a single scale.Think back to our discussion of the normal curve and z scores. What do z scoresdo? They take data of any form and put them into a standard scale. Remember, too,that a high score in a distribution always has a positive z score, and a low score in adistribution always has a negative z score. To compute a correlation coefficient, thedata from both variables of interest can be converted to z scores. Therefore, eachindividual will have two z scores: one for height (the x variable) and one for weight(the y variable).Then, to compute the correlation coefficient, each person’s two z scores are multipliedtogether. All these “cross-products” are added up, and this sum is divided bythe number of individuals. In other words, a correlation coefficient is the average(or mean) of the z-score cross-products of the two variables being studied:correlationThe relationship between two variables.correlation coefficientA numerical indication of the magnitudeand direction of the relationship (the correlation)between two variables.positive correlationA finding that two factors vary systematicallyin the same direction, increasing ordecreasing in size together.negative correlationA finding that two factors vary systematicallyin opposite directions, one increasingin size as the other decreases.correlation coefficient a z xz yNA correlation coefficient can range from 1.00 to 1.00. The exact number providestwo pieces of information: It tells us about the magnitude of the relationshipbeing measured, and it tells us about its direction. The magnitude, or degree, ofrelationship is indicated by the size of the number. A number close to 1 (whetherpositive or negative) indicates a strong relationship, while a number close to 0 indicatesa weak relationship. The sign ( or ) of the correlation coefficient tells usabout the relationship’s direction.A positive correlation means that as one variable increases in size, the secondvariable also increases. For example, height and weight are positively correlated: Asheight increases, weight tends to increase also. In terms of z scores, a positive correlationmeans that high z scores on one variable tend to be multiplied by highz scores on the other variable and that low z scores on one variable tend to be multipliedby low z scores on the other. Remember that just as two positive numbersmultiplied together result in a positive number, so two negative numbers multipliedtogether also result in a positive number. When the cross-products are addedtogether, the sum in both cases is positive.A negative correlation, in contrast, means that two variables are inversely related.As one variable increases in size, the other variable decreases. For example, professorslike to believe that the more hours students study, the fewer errors they will make onexams. In z-score language, high z scores (which are positive) on one variable (more© The New Yorker Collection 1994 Leo Cullumfrom cartoonbank.com. All Rights Reserved.