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5. Divide the sum by s ∗ s .
x
y
6. Divide the result by n – 1, where n is the number of (x, y) pairs. (It’s
the same as multiplying by 1 over n – 1.)
This gives you the correlation, r.
For example, suppose you have the data set (3, 2), (3, 3), and (6, 4). You
calculate the correlation coefficient r via the following steps. (Note for this
data the x-values are 3, 3, 6, and the y-values are 2, 3, 4.)
1.
is 12 ÷ 3 = 4, and is 9 ÷ 3 = 3.
2. The standard deviations are s = 1.73 and s = 1.00.
y
x
See Chapter 5 for step-by-step calculations.
3. The differences found in Step 3 multiplied together are: (3 – 4)(2 – 3) =
(– 1)( – 1) = +1; (3 – 4)(3 – 3) = (– 1)(0) = 0; (6 – 4)(4 – 3) = (2)(1) = +2.
Part V: Statistical Studies and the Hunt for a Meaningful Relationship
4. Adding the Step 3 results, you get 1 + 0 + 2 = 3.
5. Dividing by s ∗ s gives you 3 ÷ (1.73 ∗ 1.00) = 3 ÷ 1.73 = 1.73.
x y
6. Now divide the Step 5 result by 3 – 1 (which is 2), and you get the cor-
relation r = 0.87.
Interpreting the correlation
The correlation r is always between +1 and –1. To interpret various values of
r (no hard and fast rules here, just Rumsey’s rule of thumb), see which of the
following values your correlation is closest to:
✓ Exactly –1: A perfect downhill (negative) linear relationship
✓ –0.70: A strong downhill (negative) linear relationship
✓ –0.50: A moderate downhill (negative) relationship
✓ –0.30: A weak downhill (negative) linear relationship
✓ 0: No linear relationship
✓ +0.30: A weak uphill (positive) linear relationship
✓ +0.50: A moderate uphill (positive) relationship
✓ +0.70: A strong uphill (positive) linear relationship
✓ Exactly +1: A perfect uphill (positive) linear relationship

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