Intra-cluster correlation in the normal model

A common difficulty when using binomial or Poisson models is that the variance estimates based on the mean/variance structures of these models are often untrustworthy due to overdispersion. One way in which this overdispersion may appear is through unobserved intra-cluster correlation. The normal distribution, as well as many other distributions that allow separate estimation of their mean and variance, are usually regarded as not being affected by overdispersion. This paper shows that the effect of unobserved intra-cluster correlation in the standard normal model is exactly the same as in the binomial or Poisson models. Approaches to detect this type of correlation are also given.