WatsonUSquareTest performs the Watson goodness-of-fit test with null hypothesis that data was drawn from a population with distribution dist and alternative hypothesis that it was not.

By default a probability value or -value is returned.

A small -value suggests that it is unlikely that the data came from dist.

The dist can be any symbolic distribution with numeric and symbolic parameters or a dataset.

The data can be univariate or multivariate .

The Watson test assumes that the data came from a continuous distribution.

The Watson test effectively uses a test statistic based on where and , is the empirical CDF of data, and is the CDF of dist.

For multivariate tests, the mean of the univariate marginal test statistics is used. -values are computed via Monte Carlo simulation.

WatsonUSquareTest returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].

For a test for goodness of fit, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. By default is set to .

With the setting Method, datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from WatsonUSquareTest is then used to estimate the -value.

Estimate the power of the Watson test when the underlying distribution is a UniformDistribution, the test size is 0.05, and the sample size is 12:

A statistics class decides to test a board game spinner for bias. Each of the 50 students in the class spins the spinner once. A device was used to record the angle of rotation in radians for each spin:

Convert each measure to a measure on :

A test for uniformity on the circle shows the spinner to be unbiased: