Statistics, used in goodness-of-fit tests, that have the formwhere f_j is an observed frequency, e_j is the corresponding expected frequency, and λ is a constant. The case λ=1 gives the chi-squared test statistic, the limiting case as λ approaches 0 gives the likelihood-ratio goodness-of-fit statistic, and the case λ=−½ gives the Freeman–Tukey test statistic.