Pearson Product-moment coefficient (r) - hand calculation

  1. List the paired scores.
  2. Calculate the product for each XY pair (3rd column below)
  3. Square each individual X and Y score (columns 4 and 5)
  4. Sum and label the columns (see bottom row)

raw scores

5. Use the following formula to calulate r.

  Pearson formula
  N = number of pairs
  X times Y = product of XY (multiply)
  sum of X times Y = multiply each X times each Y, then sum the products

hand calculation

6. Find the probability value (p) associated with the obtained r = .667
a. Calculate degrees of freedom (df)
  df = N (Number of pairs) - 2
df = 12 - 2 = 10
b. Use the abbreviated table of Critical Values for r to find the p value.
For this example, r = .667, df = 10. The obtained value of .667 exceeds the cutoff of .576 (df = 10) shown on the table at the .05 level. Therefore, p <.05. In a report the result is shown as r(10) = .667, p <.05.

If no sign is shown, r is assumed to be + (positive). If r is negative, the minus sign must be shown, e.g., r(20) = -.812, p <.01