Watson's test

A test of a specified circular distribution, adapted from the Crame´r–von Mises test, and introduced by Geoffrey Watson in 1961. Denote the n observations by θ₁, θ₂,..., θ_n and write

where F(θ) is the probability of a value in the interval (0, θ) according to the null hypothesis. The test statistic is U², given by


A large value of U² leads to rejection of the null hypothesis. A transformed version of U² is provided by U^*, given by


The distribution of U^* is approximately independent of n. The upper 10%, 5%, 2.5%, and 1% points of U^* are 0.152, 0.187, 0.222, and 0.268, respectively.

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A test which measures urobilinogen and urobilin in urine using ferrous hydroxide to reduce the urobilin to urobilinogen.