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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