PROPERTIES OF CORRELATION

1.  Correlation requires that both variables be quantitative (numerical).

            You can’t calculate a correlation between “income” and “city of residence”   because “city of residence” is a qualitative (non-numerical) variable.

2.  Positive r indicates positive association between the variables, and negative r

     indicates negative association.

            A positive r indicates that above average values of x tend to be matched with     above average values of y and below average values of x tend to be matched   with below average values of y.

                        POSITIVE  r               high with high, low with low

            A negative r indicates that above average values of x tend to be matched with    below average values of y and below average values of x tend to be matched with        above average values of y.

                        NEGATIVE  r             high with low, low with high

3.  The correlation coefficient (r) is always a number between -1 and +1.

            Values of r near 0 indicate a very weak linear relationship.  The extreme values of          -1 and +1 indicate the points in a scatterplot lie exactly along a straight line.

4.  The correlation coefficient (r) is a pure number without units.

            r is not affected by:

            --interchanging the two variables

            (it makes no difference which variable is called x and which is called y)

            --adding the same number to all the values of one variable

            --multiplying all the values of one variable by the same positive number

            Because r uses the standardized values of the observations, r does not change    when we change units of measurement (inches vs. centimeters, pounds vs.           kilograms, miles vs. meters).   r is “scale invariant”.

5.  The correlation coefficient measures clustering about a line, but only relative to

      the SD’s.

            Pictures can be misleading.

6.  The correlation can be misleading in the presence of outliers or nonlinear

     association.

            r does not describe curved relationships.  r is affected by outliers.  When possible,         check the scatterplot.

7.  Ecological correlations based on rates or averages tend to overstate the strength

     of associations.

            (See demo problem on worksheet #6)

8.  Correlation measures association.  But association does not necessarily show

     causation.

            Both variables may be influenced simultaneously by some third variable.

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