I am analysing data from over 200 students from my school. In this process I've used a cluster analysis to make 5 different clusters of students using variables such as age, sex, and field of study.
I've made a one way ANOVA to determine whether or not there is a statistically significant difference in self-rated health (a score of 1-5) between the 5 clusters from my cluster analysis. The test came out significant. Because of this, I want to make an effect size test to see how big the difference is. I've made an eta-squared test but I'm unsure how to interpret the result.
The Eta-squared came back with 0.12 or 12%, does this mean that i can explain 12% of the students variability in self-rated health from their cluster? Does it even make sense to test effect size in this scenario where it might not be clear which is the dependent and independent variable?
