Improved testing for the binomial distribution using chi-squared components with data-dependent cells

A power study suggests that a good test of fit analysis for the binomial distribution is provided by a data-dependent Chernoff-Lehmann X² test with class expectations greater than unity, and its components. These data-dependent statistics involve arithmetically simple parameter estimation, convenient approximate distributions and provide a comprehensive assessment of how well the data agree with a binomial distribution. We suggest that a well-performed single test of fit statistic is the Anderson-Darling statistic.