Basic applications of the chi-square statistic using counting data.

The chi-square statistic has many scientific applications, including the evaluation of variance in counting data and the proper functioning of a radiation counting system. This paper provides a discussion of the fundamental aspects of the chi-square test using counting data. Practical applications of the chi-square statistic are discussed, including the estimation of extra-Poisson variance and dead time for a counting system. The consequences of passing or failing the chi-square test are discussed regarding the proper estimator for the population variance of the counting data. Example scenarios are used to provide insight into the applications of the chi-square statistic and the interpretation of values obtained in hypothesis testing.