Correlation Measure of the relationship between two variables
Correlation
Measure of the relationship between two variables n 2 variables are taken into consideration simultaneously n n n Warning, it is never a cause and effect n n -> Experimental manipulations The relationship is described by the coefficient of correlation (r) n n Ex. Scores in English and in Mathematics. Smoking and cancer It varies between -1 and 1: 1 (or -1) = perfect relationship 0 = absence of relationship There is thus three possible cases: n n n Positive relationship : x increases; y increases Negative relationship : x decreases; y increases Absence of relationship: x increases (or decreases); y does not change
Examples of correlation
Examples of correlation
Example Subject
Example Subject Measure the direction of the relationship
Note
Example Because we cannot compared covariance measures, we need to standardize it. Subjec t
Coefficient of determination Shared variance = 0 % x y Shared variance = 25 % x y Shared variance = 80 % x y
Example 1 77% of the variability in y can be explained by the variability in x Example 2 (SAT) 36% of the variability of sucess at the university can be explained by the variability of the score of the SAT.
Bias in coefficients of correlation Restriction of the range: decreases the correlation
Bias in coefficients of correlation Extreme groups: increases the correlation L L L L L r = 0. 75 H H H H H
Bias in coefficients of correlation Extreme groups: increases the correlation r = 0. 50 x L x x x L LL L L x x x L L x xx x x L x x x H H x x H HH H x x x H H x x H
Bias in coefficients of correlation Combining two groups: increases or decreases the correlation r 2 = 0 r 1 = 0 > 0 r 2 > r 2 0 r 1 > 0
Bias in coefficients of correlation Outliers: increases or decreases the correlation x xxx xx xx x x x
Bias in coefficients of correlation Nonlinear relationship: decreases the correlation
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