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# EXAM REVIEW CORRELATION COEFFICIENT.doc

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Department
Psychology
Course
PSYB07H3
Professor
Douglas Bors
Semester
Fall

Description
AFTER MIDTERM EXAM NOTES PEARSON-PRODUCT MOMENT CORRELATION COEFFICIENT (r) -tells us the strength of the relationship between x and y -the average product of z-scores  same thing as z scores -correlation coefficients are the covariance when there are standard variables  standardize x but leave y and its use  get a measure in y units COV xya measure of the relation between x and y  the covariance standardized by the standard deviation of x and y -o standardize , we divide the covariance by the size of the standard deviations. -g iven 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 +1.0 or – 1.0 -the correlation coefficient is not an unbiased esimator C O V r = x y sxy If the regression coefficient is computed the slopes can be he same but the correlation is different i.e. the second scatterplot has more noise. Example: x- y- 3 4 9 4 4 1 10 1 5 0 12 1 6 1 11 0 7 4 13 4 xy=1 1 sy=1.5 8 x =5 x s =1.5 8 x 1. C x = yO.2 5 V 2. C x y O V r = sxsy 2.2 5 r = (1.5 ) 1.) ( 8 r = 0.9 3. 2 r = 1− (1− r ) N ( 1) a d j (N − 2) (1−.8 ) −11) 5 ra= d− j ( − 25) = .75 -expected value of r is not ρ (rho --> Greek letter), then we correct for it -correlation cannot = 1 because there will be many variables that affect (influence) relationship of behaviour you’re trying to predict r = that proportion of the variance is y that is shared (accounted for) by x. Sometimes called “coefficient of determination” 2 -therefore, r = 0.9 and r = 0.81 or x account for 81% of the variance in y
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