Outline

Pearson Product-Moment Correlation Coefficient ( r )

Demonstrate how r is computed

Discuss the impact of extreme scores (outliers) on r

How is the r interpreted

PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT (r)

              degree to which X and Y vary together            (covariability)

            r = -------------------------------------------------------

                        degree to which X and Y vary separately

When a perfect linear relationship exists, covariability is identical to the variability of X and Y separately, and

r = 1

• The Pearson Product - Moment correlation is the most widely used measure of correlation.

• The value of r can range from +1 through 0 to - 1.

• The magnitude of r expresses the degree of LINEAR relationship between variables.

• The sign of r expresses the direction (positive or negative) of the relationship.

• The presence of extreme scores (outliers) affects the sign and magnitude of r.

• It is typically used when scores are normally distributed.

INTERPRETING THE PEARSON CORRELATION

1.         The correlation coefficient DESCRIBES a relation.  It does not explain WHY the relation exists.  It does not provide proof of a cause-effect relation.

2.         The range of scores affects r (restricted range problem).

3.         OUTLIERS can have a dramatic effect on r.

4.         A correlation SHOULD NOT be interpreted as a proportion.

5.         The amount of variability that can be predicted, on the basis of a relationship between variables, is determined by r² .