Equations for Bivariate Data 2.4 2001/06/20 2002/11/07 Adan Galvan jago@rice.edu Adan Galvan jago@rice.edu bivariate statistics Equations for Bivariate Data

Formulas for Bivariate Data

Pearson's Correlation r X Y X Y X X Y Y N X X 2 X X 2 N Y Y 2 Y Y 2 N 2 A simpler looking formula can be used if the numbers are converted into z scores: r X Y z x z y N

Spearmans's Rho Spearman's rho is a measure of the linear relationship between two variables. It differs from Pearson's correlation only in that the computations are done after the numbers are converted to ranks. When converting to ranks, the smallest value on X becomes a rank of 1, the second smallest becomes a value on X becomes a rank of 2, etc. The same ranking procedure is done with the values of Y. Spearman's rho can be computed with the formula for Pearson's r using the ranked data.