Ignoring variance and how it relates to group size is a simple but common error. As Wainer notes, building on a discussion in Gelman and Nolan, counties with low cancer rates tend to be rural counties in the south, mid-west and west. Is it the clean country air or some other factor peculiar to rural counties which accounts for this fact? Probably not. The countries with the highest cancer rates also tend to be rural counties in the south, mid-west and west! Once again, small size and random variation appear to be the main culprit.
