Eta Squared Notes

Eta Squared: A Measure of Effect Size

Definition

• Eta squared ($\eta^2$) is a measure of effect size, similar to r-squared ($r^2$).
• It indicates the proportion of variance in the outcome variable that is explained by the effect.

Calculation

• The formula for eta squared is:
  $\eta^2 = \frac{\text{Sums of Squares for the Effect}}{\text{Sums of Squares Total}}$

Application

• Eta squared can be calculated for:
  • Omnibus tests
  • Individual planned comparisons
• Reporting a measure of effect size is recommended whenever a significance test is conducted.

Omnibus Test Example

• Scenario: Examining the effects of diet on happiness.
• Values from SPSS output:
  • Sums of Squares Total = 73.661
  • Between-Groups Sums of Squares = 11.2
• Calculation:
  $\eta^2 = \frac{11.2}{73.661} = 0.152$
• Interpretation:
  • The model (overall effect of diet) accounts for 15.2% of the variance in happiness.
  • The differences between the fruit, veggie, and donut groups explain 15.2% of the variability in the outcome variable.

Comparison Example

• Scenario: Complex comparison comparing the average of fruit and veggie groups to the donut group.
• Sums of Squares for the effect = 10.8
• Sum of Squares Total = 73.661 (same as omnibus test)
• Calculation:
  $\eta^2 = \frac{10.8}{73.661} = 0.147$
• Interpretation:
  • This specific comparison (fruit/veggie vs. donut) accounts for 14.7% of the variance in the outcome.
  • The difference between the donut group and the other conditions appears to drive most of the overall effect.

Significance

• Eta squared provides a simple and intuitive measure of effect size.
• It is easily derived from standard SPSS output.
• Eta squared values map onto other statistical concepts, making it a useful tool for understanding effect sizes.