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Bivariate Equations

Module by: Adan Galvan

Summary: Equations for Bivariate Data

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Formulas for Bivariate Data

Pearson's Correlation

r=∑XYXY−∑XX∑YYN∑XX2−∑XX2N∑YY2−∑YY2N 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 (1)
A simpler looking formula can be used if the numbers are converted into zz scores:
r=∑XY z x z y N r X Y z x z y N (2)

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 XX becomes a rank of 1, the second smallest becomes a value on XX becomes a rank of 2, etc. The same ranking procedure is done with the values of YY. Spearman's rho can be computed with the formula for Pearson's rr using the ranked data.

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