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SpatialRandomnessTest—Wolfram Language Documentation

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• See Also
  • PoissonPointProcess
  • BinomialPointProcess
  • PointProcessFitTest
  • RandomPoint
  • RandomPointConfiguration
• Related Guides
  • Spatial Point Collections
  • Spatial Statistics
  • Probability & Statistics

SpatialRandomnessTest[pdata]

tests whether the point collection pdata is distributed uniformly over the observation region.

• SpatialRandomnessTest performs a goodness-of-fit hypothesis test with null hypothesis that pdata was drawn from a PoissonPointProcess 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 pdata comes from a PoissonPointProcess.
• The point data pdata can have the following forms:
• If the observation region reg is not given, a region is automatically computed using RipleyRassonRegion.
• SpatialRandomnessTest[pdata,"test"] will report the -value according to "test".
• SpatialRandomnessTest[pdata,All] will choose all tests.
• Under the null hypothesis , the points in pdata were drawn from a PoissonPointProcess[λ]. This means they should be uniformly distributed over the given observation region reg. By binning the points, the standard bin count residual , where and are the count and expected count in bin i, respectively, should be approximately chi-square distributed, and the count should be multinomially distributed.
• The following tests can be used:
• "BesagL" based on BesagL, which is expected to be a straight line as a function of radius, slower and higher statistical power "ChiSquare" based on binning, where standard bin count residuals are expected to be chi-square distributed, fast and approximate "ModifiedChiSquare" based on binning, where counts are expected to be multinomially distributed, exact for small samples, using "ChiSquare" for large data
• SpatialRandomnessTest[pdata,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• SpatialRandomnessTest[pdata,"property"] can be used to directly give the value of "property".
• Properties related to the reporting of test results include:
• The following options can be used:

Uniform point distribution on a disk:

The data came from a point process with homogeneous intensity:

Points distributed over a geographical region:

The data came from a point process with homogeneous intensity:

Test spatial randomness:

The -values are typically large when points are uniformly distributed:

The -values are typically small when there is spatial heterogeneity:

Perform a particular test for spatial randomness:

Extract a property for a specific test:

Using Automatic applies the "AutomaticTest" option:

The property "AutomaticTest" can be used to determine which test was chosen:

Perform all tests appropriate to the data simultaneously:

Use the property "AllTests" to identify which tests were used:

Create a HypothesisTestData object for repeated property extraction:

The properties available for extraction:

Extract some properties from the HypothesisTestData object:

The -value and test statistic from the "ChiSquare" test:

Extract any number of properties simultaneously:

The -value and test statistic from a "ChiSquare" test:

Tabulate the results from a selection of tests:

A full table of all appropriate test results:

A table of selected test results:

Retrieve the entries from a test table for customized reporting:

The -values are above 0.05, so there is not enough evidence to reject at that level:

The significance level is used for "TestConclusion" and "ShortTestConclusion":

Specify the significance level:

The test conclusions may differ:

Full test conclusions:

Distribution of the "ModifiedChiSquare" test statistic under a null hypothesis:

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