Survey Statistics: ANOVA

Andrew recently answered “Why did ANOVA fall out of fashion?”:

Anova is still important; it’s just been subsumed by hierarchical models. The link is to my 2005 paper, Analysis of variance: Why it is more important than ever

Folks discussed whether ANalysis Of VAriance refers to 1) testing the null hypothesis that group means are equal, 2) fitting a regression model with categorical predictors, or 3) “an add-on to regression analysis, in which the predictors are structured and we estimate the variances of batches of coefficients.”

How does ANOVA relate to Survey Statistics ?

Andrew’s 2005 ANOVA paper‘s example in Section 7.2 is the Multilevel Regression (MR) of MRP. They made a new graphical display of the standard deviations of each batch of effects to replace the classical ANOVA table:

This is useful to assess the relative importance of different sources of variation, which can guide which interactions to add into the model.

In his discussion of Andrew’s paper, Alan Zaslavsky (the inspiration for this series) gave another example: a survey of members of Medicare managed care health plans. They modeled the data with variance components for geographical units (region, state, Metropolitan Statistical Area or MSA) and for the health plans. They found that for ratings of doctors, the majority of the variance was explained by geography, not the health plans. This suggested that improving quality of care might need to be directed towards low-performing areas rather than low-performing health plans.