PearsonChiSquareTest

Perform a Pearson test for normality:

The -value for the normal data is large compared to the -value for the non-normal data:

Test the goodness of fit to a particular distribution:

Compare the distributions of two datasets:

The two datasets do not have the same distribution:

Test for multivariate normality:

Test for goodness of fit to any multivariate distribution:

Create a HypothesisTestData object for repeated property extraction:

The properties available for extraction:

Tabulate the results of the Pearson test:

The full test table:

A -value table:

The test statistic:

Retrieve the entries from a Pearson test table for custom reporting:

Report test conclusions using and :

The conclusion may differ at a different significance level:

Use Monte Carlo-based methods or a computation formula:

Set the number of samples to use for Monte Carlo-based methods:

The Monte Carlo estimate converges to the true -value with increasing samples:

Set the random seed used in Monte Carlo-based methods:

The seed affects the state of the generator and has some effect on the resulting -value:

A power curve for the Pearson test:

Visualize the approximate power curve:

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

The number of auto accidents was recorded for a city over the course of 30 days. The city council is planning on lowering speed limits in the city and wants a model of the accident rate as a baseline for later comparison:

Count data is often modeled well by PoissonDistribution:

Suppose the city collected data over another 30-day period after reducing the speed limit. Compare the distributions before and after the reduction:

The distributions are significantly different:

By default, univariate data is compared to NormalDistribution:

The parameters have been estimated from the data:

Multivariate data is compared to MultinormalDistribution by default:

The parameters of the test distribution are estimated from the data if not specified:

Specified parameters are not estimated:

Maximum likelihood estimates are used for unspecified parameters of the test distribution:

PearsonChiSquareTest effectively compares the observed and expected histograms:

The data is binned into approximately bins that are equiprobable under :

Under , each bin will contain an equal number of points:

Observed histograms for when is true and false, respectively:

The degrees of freedom are equal to the number of non-empty bins minus one:

One degree of freedom is removed for each parameter that is estimated from the data:

If the parameters are unknown, PearsonChiSquareTest corrects the degrees of freedom:

No correction is applied when the parameters are specified:

The fitted distribution is equivalent but the degrees of freedom and -value are corrected:

The Pearson statistic asymptotically follows ChiSquareDistribution under :

Independent marginal densities are assumed in tests for multivariate goodness of fit:

The test statistic is identical when independence is assumed:

The distribution of the Pearson test statistic: