I Remember You: Independence and the Binomial Model.

We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how this dependence alters the probability of a successful match of dog to owner, and thus alters the expected number of successful matches and the variance of this expected quantity. Finally, we show that a false assumption of independence that results in incorrect probability calculations changes the probability of incorrectly rejecting the null hypothesis (i.e. the Type I error).