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This article used to be written to aid the reader gather a base of data approximately classical psychometrics and to combine new principles into that framework of information.
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Ton and later mathematically derived by Pearson. When the X and Y observations are expressed as z-scores, the formula for the product moment correla tion is l:zXZy Pxy = ----,;- (2. 1 2) where N is the number of persons. It is important to note that in computing the total cross product of the z-scores, ZXZy, must be comp1Jted for each individual prior to summing. 3 presents z-scores on aptitude test score and grade-point average for 10 individuals and illustrates the computation of the correlation coefficient.
Two other cautions should be noted in the interpretation of correlation coeffi cients . The discovery of a strong relationship between X and Y does not imply a cause-and-effect relationship between these variables . For example, an examination of the records of teachers ' salaries and rates of violent crime for metropolitan areas across the United States would probably indicate a positive correlation between these variables . Yet this does not imply that raising teachers' salaries will lead to escalation of community crime rates .
In these situations, Equations 2. 5 (for the standard deviation) are unusable. An equivalent formula to Equa tion 2. 8) where XI: is the kth possible value of X, and Pk is the probability of occurrence of that value of X. Note that if we applied this formula to a finite population of scores (such as those in Table 2. 1 ) , it would equal the value obtained from Equation 2. 1 . 5. It may be of interest to note that statisticians sometimes refer to the properties of a frequency distribution as moments.