# Eta Coefficient

```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.
```