Statistical analysis of the number of correct answers of a test consisting of n items will be considered in this article. A beta-binomial distribution is assumed to the model of the distribution of test scores in this article. For such test scores, the situation of extra zeros sometimes arises in practical applications. This can happen in WEB testing, for example, when examinees miss-operate their PC that may make their test scores zero. To model such extra zeros we consider zero-inflated beta-binomial (ZIBB) distribution, which is a mixture of a beta-binomial distribution and a distribution that has mass at zero. For the estimation of the ZIBB model parameters we adopt the method of moments that is easily implemented in PC. As an extension of the ZIBB model it is also considered a mixture model of a beta-binomial distribution and a binomial distribution with parameters known, abbreviated as BB+B. This model can be used for a particular test procedure. An estimation procedure of the parameters of BB+B model is provided. It will be shown that such models fit well to datasets from practical applications.
