Eta squared (η²) is a measure of effect size in the analysis of variance (ANOVA) that evaluates the proportion of total variance in the dependent variable that is explained by the independent variable. In other words, eta squared provides an indication of the strength and importance of a relationship between variables. This article will guide you through the steps on how to calculate eta squared for your ANOVA results.

Step 1: Obtain your ANOVA summary table

To calculate eta squared, you need access to your ANOVA summary table which should include the following information:

– Between-groups sum of squares (SS_between)

– Within-groups sum of squares (SS_within)

– Total sum of squares (SS_total)

These values can typically be obtained from statistical software output or calculated manually from raw data using appropriate formulas.

Step 2: Compute partial eta squared

Partial eta squared is used when there are multiple independent variables or factors. If this is your case, you need to calculate the partial eta squared as follows:

Partial η² = SS_effect/ (SS_effect + SS_error)

Where:

– SS_effect refers to the sum of squares for a specific effect or independent variable

– SS_error refers to the residual or error sum of squares

Step 3: Calculate eta squared for each independent variable

Now, if you have only one independent variable, you can calculate eta squared directly using this formula:

η² = SS_between / SS_total

If you have multiple independent variables, add up all the partial eta squared values and divide by the number of independent variables to arrive at an average eta squared value.

Step 4: Interpret eta squared value

The resulting eta squared value ranges between 0 and 1; with higher values indicating a greater strength in the relationship or effect. Eta squared can be interpreted as follows:

– η² < 0.01: Small effect

– 0.01 ≤ η² < 0.06: Medium effect

– η² ≥ 0.14: Large effect

Conclusion

Understanding how to calculate eta squared is crucial for analyzing and interpreting the results of your ANOVA test. Not only does it provide a measure of effect size, but it also helps determine the importance of the relationship between variables. By following these steps, you will be able to confidently compute and assess eta squared values in your research or analysis projects.