Eta Correlation Example Eta Correlation is used to determine if a relationship exists between an interval variable and a categorical variable. To run an Eta Correlation, an Analysis of Variance is first run to determine if there is a significant difference between the group’s averages. With significance determined through the F-ratio, an Eta correlation can be calculated to determine the percentage of variation in the dependent variable that can be explained through the independent variable. In this example, first the safety manager wanted to determine if there is a significant difference in the mean audit scores each month for three plants he manages over a seven-month period. The audit scores were set up on a scale as follows: Number of hazards corrected – Number of accidents reported For example if there were 3 hazards corrected during a month and 5 accidents reported, the plant would get a score of -2.00, 10 corrected and 4 accidents then a score of 6.00 and so on; thus creating an interval scale. First, an ANOVA procedure was performed yielding the following results table: ANOVA Summary Table Source of Sum of df Mean Squares F Ratio Variation Squares Between 34.67 2 17.33 5.15* Within 60.57 18 3.4 Total 95.24 20 *The F-ratio was determined to be significant at the .05 level since the critical F Score is 3.55 from the F Tables. The Eta Coefficient can be calculated using the information from the ANOVA as follows: Eta 2 = SS between – (p –1)MS within SS total + MS Within = 34.67 – (2)(3.4) = .28 95.24 + 3.4 P is the number of groups, in this case, 3 plants. The result from the Eta procedure is interpreted in the same manner as the squared correlation coefficient with .28 which indicates that 28% of the variability in the dependent variable can be attributed to the independent variable.