Computing Pearson's r


David M. Lane


Summation Notation, Introduction to Bivariate Data

Learning Objectives
  1. Define X and x
  2. State why Σxy = 0 when there is no relationship
  3. Calculate r

There are several formulas that can be used to compute Pearson's correlation. Some formulas make more conceptual sense whereas others are easier to actually compute. We are going to begin with a formula that makes more conceptual sense.

To compute the correlation between the variables X and Y, begin by computing the mean for X and subtracting this mean from all values of X. The new variable is called "x." The variable "y" is computed similarly. The correlation is then computed using the following formula:



An alternative computational formula that avoids the step of computing deviation sores is:

Please answer the questions:
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