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Pearson-Product Moment Correlation Coefficient (r)

Pearson-Product Moment Correlation Coefficient (r). A measure of the relation between x and y, but is not standardized. To standardize , we divide the covariance by the size of the standard deviations. Given that the maximum value of the covariance is plus or minus the product

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Pearson-Product Moment Correlation Coefficient (r)

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  1. Pearson-Product Moment Correlation Coefficient (r) A measure of the relation between x and y, but is not standardized To standardize , we divide the covariance by the size of the standard deviations. Given that the maximum value of the covariance is plus or minus the product of the variance of x and the variance of y, it follows that the limits on the correlation coefficient are + or – 1.0

  2. Example: X Y

  3. Compute the regression coefficient, but using standardized scores. X’ Y’ Why? b=

  4. Adjusted r From our example: = .75

  5. = that proportion of the variance in y that is shared (accounted for) by x. Sometimes called the “coefficient of determination.” Thus, r = .9 and = .81 Or x accounts for 81% of the variance in y. R = .2, thus = .04 or 4% R = .4, thus = .016 or 16% If on r is g times as large as a second r, then the proportion of the variance associated with the first r will be g(squared) times as great as that associated with the second. can also be misleading

  6. Factors Affecting r Range Restrictions Outliers Heterogeneous Subsamples

  7. Whole-Part correlations. This is were the score for variable x contributes to the score of variable y. Produces a + bias in r. Again, Correlation does not imply causality. Variables may be accidentally related, or both may be related to a third variable, or the may influence each other. Which is more informative, the slope of the regression line or the correlation coefficient?

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