So, I have a database of more than 2000 individuals that belong to different centers. My variable is the service climate. The goal of conducting ANOVA is to justify that an organizational level aggregation is feasible as there are significant differences in means between centers. But, ANOVA doesn't conduct Levene's test when there are more than 50 groups (I have more than 200 centers). How can I test the homogeneity of variances for more than 50 groups?
I'm not sure ANOVA is quite the right approach. This looks like a clustered/nested design and I'd normally think in terms of a multilevel (linear mixed) model (or possibly a model that handles clustering some other way). In this kind of model you treat centre as a random effect with individuals nested within that. You can potentially model heterogeneity in the variation - but that is somewhat expected when centres have different numbers of individuals. This approach can also give you an ICC for the clustering from the level 2 variance as a proportion of total level 1 and 2 variance in the null model.
I suggest you conduct MANOVA instead as this test offers BOX's test which is rather robust than the Leven's for homogeneity of variances. You can estimate Mahalanobis distance for significant differences in means between centers, it also helps to normalize the data which again aid for homogeneity of variances within and between groups. Like ANOVA, you can have Post hoc tests e.g. Tuckey's, Duncan, Wallace, etc. And later Bonferroni Alpha may help you with converged significance.
I hope this help!
You might also compute the intraclass correlation or ICC(1) to show the proportion of total variance due to center differences. This is what people often use to justify using multilevel methods and aggregating individual employee responses to the higher level.
I'm not sure ANOVA is quite the right approach. This looks like a clustered/nested design and I'd normally think in terms of a multilevel (linear mixed) model (or possibly a model that handles clustering some other way). In this kind of model you treat centre as a random effect with individuals nested within that. You can potentially model heterogeneity in the variation - but that is somewhat expected when centres have different numbers of individuals. This approach can also give you an ICC for the clustering from the level 2 variance as a proportion of total level 1 and 2 variance in the null model.
Can you say why you would want to ignore variation below the organizational level? As Thom Baguley says, the multilevel approach (or variance components) would give you the level 1 variance and if his is small you could ignore, but that would pre-suppose you have no interesting variables at this level.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA