SpatialRandomnessTest

SpatialRandomnessTest[pdata]

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

SpatialRandomnessTest[pdata,"property"]

returns the value of "property".

Details and Options

  • 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:
  • {p1,p2,}points pi
    GeoPosition[],GeoPositionXYZ[],geographic points
    SpatialPointData[]spatial point collection
    {pts,reg}point collection pts and observation region reg
  • 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 multinomial 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:
  • "AllTests"list of all applicable tests
    "AutomaticTest"test chosen if Automatic is used
    "PValue"list of -values
    "PValueTable"formatted table of -values
    "ShortTestConclusion"a short description of the conclusion of a test
    "TestConclusion"a description of the conclusion of a test
    "TestData"list of pairs of test statistics and -values
    "TestDataTable"formatted table of -values and test statistics
    "TestStatistic"list of test statistics
    "TestStatisticTable"formatted table of test statistics
  • The following options can be used:
  • SignificanceLevel0.05cutoff for diagnostics and reporting

Examples

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Basic Examples  (2)

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:

Scope  (10)

Testing  (7)

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:

Reporting  (3)

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":

Options  (1)

SignificanceLevel  (1)

Specify the significance level:

The test conclusions may differ:

Full test conclusions:

Neat Examples  (1)

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

Wolfram Research (2020), SpatialRandomnessTest, Wolfram Language function, https://reference.wolfram.com/language/ref/SpatialRandomnessTest.html.

Text

Wolfram Research (2020), SpatialRandomnessTest, Wolfram Language function, https://reference.wolfram.com/language/ref/SpatialRandomnessTest.html.

BibTeX

@misc{reference.wolfram_2020_spatialrandomnesstest, author="Wolfram Research", title="{SpatialRandomnessTest}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/SpatialRandomnessTest.html}", note=[Accessed: 20-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_spatialrandomnesstest, organization={Wolfram Research}, title={SpatialRandomnessTest}, year={2020}, url={https://reference.wolfram.com/language/ref/SpatialRandomnessTest.html}, note=[Accessed: 20-January-2021 ]}

CMS

Wolfram Language. 2020. "SpatialRandomnessTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SpatialRandomnessTest.html.

APA

Wolfram Language. (2020). SpatialRandomnessTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpatialRandomnessTest.html