Section 35 Significance of a Pearson r

Question 1

Pearson r and Statistical Significance

Answer 1

Once you’ve determined your Pearson r, (Correlation Coefficient (between -1 and +1) you want to know whether it is statistically significant. To see how to do this, let’s follow an example.

• Ex: 20 students were drawn at random from a population and their GPAs were correlated with their heights. A Pearson r of .23 was obtained, indicating that those with higher GPAs are taller.
  
  • To test the Pearson r, you use a special version of the t -Test. Fortunately, the value of t does not need to be computed. Instead:
  1. Refer to Table 10 near the end of this book.
  2. To use Table 10, first compute the degrees of freedom, using this formula: df = n - 2 Where n is the number of subjects.
     
     • Because there are 20 subjects in the example, df = 20 - 2 = 18.
     • Looking up 18 degrees of freedom in Table 10 indicates that a _minimum value of *r* for significance at the .05 level is .444_.
• DECISION RULE: If the observed value of r (Ex: .23) is GREATER than the minimum value in Table 10, THEN REJECT the NULL HYPOTHESIS and DECLARE the Pearson r STATISTICALLY SIGNIFICANT. Otherwise, do not reject it.
  
  • Because the observed value of .23 is NOT GREATER than the minimum value of .444, do NOT REJECT the NULL HYPOTHESIS and conclude that the difference is NOT STATISTICALLY SIGNIFICANT at the .05 level.
  • The researcher has failed to demonstrate a significant correlation between GPA and height.