tests whether data is normally distributed using the Pearson test.

tests whether data is distributed according to dist using the Pearson test.

returns the value of "property".

Details and OptionsDetails 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 {x1,x2,} or multivariate {{x1,y1,},{x2,y2,},}.
  • 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 ^(th) 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 "property".
  • Properties related to the reporting of test results include:
  • "DegreesOfFreedom"the degrees of freedom used in a test
    "PValueTable"formatted version of "PValue"
    "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 "TestData"
    "TestStatistic"test statistic
    "TestStatisticTable"formatted "TestStatistic"
  • 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:
  • MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff 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 "TestConclusion" and "ShortTestConclusion" properties is controlled by the SignificanceLevel option. By default, is set to 0.05.
  • With the setting Method->"MonteCarlo", datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from PearsonChiSquareTest[si,dist,"TestStatistic"] is then used to estimate the -value.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Perform the Pearson test for normality:

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Click for copyable input

Test the fit of some data to a particular distribution:

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Compare the distributions of two datasets:

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Extract the test statistic from the Pearson test:

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Introduced in 2010