The Correlation Coefficient (Pearson's r)
CORRELATION COEFFICIENT (Pearson's r)
What it does:
It measures the linear relationship between two interval/ratio level variables.
Cov(y,x) = the covariance of y and x
Var(x)= the variance of x
Var(y)= the variance of y
(Zxi= is the standard score for Xi. It tells you how many standard deviation units (SDx) the score Xi is from its mean. )
Pearson's r is always between -1 and +1, where -1 means a perfect negative, +1 a perfect positive relationship and 0 means the perfect absence of a relationship.
Pearson's r is symmetric. The correlation between x and y is the same as the correlation between y and x.
Pearson's r is also referred to as the "bivariate correlation coefficient" or the "zero-order correlation coefficient."
Word of caution:
The correlation coefficient assumes that the relationship is linear.