S7. Covariance and Pearson's r

correlation

a relationship between two variables
correlated variables are non independent
causality cannot be inferred from correlation

what graph would you use when presenting correlational data

scatter graph

covariance

a measure of how much two variables vary together
- high covariance = if scores for one variable change, the the scores for the other variable also change in a predictable manner
- low covariance = change in one variable are no accompanied by a predictable change in the other variable

total covariance

TC(xy) = SUM ( (xI - mX) x (yI - mY) )

sample covariance

C(x,y) = SUM ( (xI - mX) x (yI - mY) ) / N-1

positive covariance

indicates that higher than average values of one variable tend to be paired with higher-than-average values of the other variable.

negative covariance

indicates that higher than average values of one variable tend to be paired with lower-than average values of the other variable

zero covariance

if two random variables are independent, the covariance will be zero

Pearson's r

r(x,y) = C(x,y)/√var(x) x var(y)

Pearson's r intuition

1 = a perfect +ve score
-1 = a perfect -ve score
0 = no correlation
0 < r < 1 = imperfect +ve correlation
-1 < r < 0 = imperfect -ve correlation