Covariance 7 - Covariance and Correlation 1 The Concept of...

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1 Covariance and Correlation
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2 The Concept of Bivariate Association Question: How can we quantify the association between two variables?
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3 x y [A] 9.75 9.56 [B] 7.72 7.81 [C] 10.84 10.30 [D] 9.37 8.57 [E] 10.04 10.22 [F] 10.94 11.15 How do people’s scores on one variable vary as a function of another variable?
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4 x y [A] 9.75 9.56 [B] 7.72 7.81 [C] 10.84 10.30 [D] 9.37 8.57 [E] 10.04 10.22 [F] 10.94 11.15 People with high scores on x seem to have high scores on y Can we define what we mean by “high scores” more precisely?
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5 xd yd [A] -0.03 -0.04 [B] -2.06 -1.79 [C] 1.07 0.70 [D] -0.40 -1.03 [E] 0.26 0.62 [F] 1.16 1.55 yes. we can study deviations from the mean (X – M x ) and (Y – M y ) now we can ask whether people who are above the mean (i.e., “high” on x ) are above the mean on y 60 . 9 78 . 9 = = y x M M
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6 xd yd [A] -0.03 -0.04 both below [B] -2.06 -1.79 both below [C] 1.07 0.70 both above [D] -0.40 -1.03 both below [E] 0.26 0.62 both above [F] 1.16 1.55 both above One way to do this is to tally the matches. People who are above the mean on X should be above the mean on Y. People who are below the mean on X should be below the mean on Y. 100% match
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7 Now E, C, B, & D show the same pattern on the two variables, but persons A & F do not. 4/6 (66%) show the matching pattern.
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8 xd yd (xd*yd) [A] -0.03 -0.04 0.00 [B] -2.06 -1.79 3.69 [C] 1.07 0.70 0.75 [D] -0.40 -1.03 0.41 [E] 0.26 0.62 0.16 [E] 1.16 1.55 1.80 Multiply each person’s deviations together. Advantage: when there is a match (both + or both -), the product will be +. When there is a mismatch (one + and other -), the product will be -.
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9 xd yd (xd*yd) [A] -0.03 -0.04 0.00
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Covariance 7 - Covariance and Correlation 1 The Concept of...

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