Does the use of "robust standard errors" in cluster randomized trials suggest heterskadistic data, implying there is high between-cluster variability?

Question

Please bear with me. I am only recently familiar with some of these concepts. Please correct any poor assumptions.

I am analysing a cluster randomized trial with crossover between intervention and control. The authors say they will divide the difference between the groups by the 'robust standard error based on the Huber-White Sandwich Estimator'.

From the mention of robust standard error, I am inferring that they are predicting a heteroskedastic presentation of their data i.e., the between-cluster variability is greater than the within-cluster variability (or at least the between-cluster variability is high).

I am then using this assumption to estimate that the ICC (p) for this study will be relatively high and thus their effective sample size will be lower than their actual sample size. This has implications for whether or not their study was adequately powered.

Am I on the right lines? If you could explain in fairly simple terms, I don't have any formal statistics education and have gleened this interpretation from some independent reading. Thank you in advance.

Answer 1

I don't think you can make that assumption. In my experience, using robust standard errors is one standard way of dealing with clustering, regardless of whether there is heteroscedasticity.

Whether people should do this automatically is another matter, but certainly some do.