Exact inference for complex clustered data using within-cluster resampling

This paper introduces exact permutation methods for use when there are independent clusters of data with arbitrary within-cluster correlation. To eliminate the problem of clustering, we randomly select a data point from each cluster and for this now independent data, and calculate our test statistic and the associated support points for all possible permutations. While clearly valid, this is also inefficient. We repeat this process until all possible independent data sets have been created and use the support points averaged over the randomly created data sets as our reference distribution for the averaged test statistic. This approach uses all of the data and is a permutation extension of within-cluster resampling (WCR). We discuss both exact and Monte Carlo versions of the approach and apply it to several data sets. WCR permutation can be applied in quite general settings when within cluster correlation is a nuisance and exact inference is necessary.