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.

Where

Cov(y,x) = the covariance of y and x

Var(x)= the variance of x

Var(y)= the variance of y

Where

and

(Z_xi= is the standard score for Xi. It tells you how many standard deviation units (SD_x) 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.