BUILT-IN MATHEMATICA SYMBOL

PearsonChiSquareTest

PearsonChiSquareTest[data]
tests whether data is normally distributed using the Pearson test.

PearsonChiSquareTest[data, dist]
tests whether data is distributed according to dist using the Pearson test.

PearsonChiSquareTest[data, dist, "property"]
returns the value of .

Details and Options Details and Options

PearsonChiSquareTest performs the Pearson 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 Pearson test effectively compares a histogram of data to a theoretical histogram based on dist. The bins are chosen to have equal probability in dist. »
For univariate data the test statistic is given by , where and are the observed and expected counts for the histogram bin, respectively.
For multivariate tests, the sum of the univariate marginal -values is used and is assumed to follow a UniformSumDistribution under .
PearsonChiSquareTest[data, dist, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
PearsonChiSquareTest[data, dist, "property"] can be used to directly give the value of .
Properties related to the reporting of test results include:

	"DegreesOfFreedom"	the degrees of freedom used in a test
	"PValue"	-value
	"PValueTable"	formatted version of
	"ShortTestConclusion"	a short description of the conclusion of a test
	"TestConclusion"	a description of the conclusion of a test
	"TestData"	test statistic and -value
	"TestDataTable"	formatted version of
	"TestStatistic"	test statistic
	"TestStatisticTable"	formatted

The following properties are independent of which test is being performed.
Properties related to the data distribution include:
"FittedDistribution" fitted distribution of data

"FittedDistributionParameters" distribution parameters of data
The following options can be given:
Method Automatic the method to use for computing -values

SignificanceLevel 0.05 cutoff for diagnostics and reporting
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->"MonteCarlo", datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from PearsonChiSquareTest[s_i, dist, "TestStatistic"] is then used to estimate the -value.