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MardiaCombinedTest

MardiaCombinedTest[data]
tests whether data follows a MultinormalDistribution using the Mardia combined test.
MardiaCombinedTest
returns the value of .
  • By default a probability value or -value is returned.
  • A small -value suggests that it is unlikely that the data came from dist.
  • The data can be univariate or multivariate .
  • 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:
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 and properties is controlled by the SignificanceLevel option. By default is set to .
Perform a test for multivariate normality:
Extract the test statistic from the Mardia combined test:
Obtain a formatted test table:
Perform a test for multivariate normality:
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Extract the test statistic from the Mardia combined test:
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Obtain a formatted test table:
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Perform a Mardia test for multivariate normality:
The -value for the normal data is large compared to the -value for the non-normal data:
Create a HypothesisTestData object for repeated property extraction:
The properties available for extraction:
Tabulate the results of the Mardia combined test:
The full test table:
A -value table:
The test statistic:
Retrieve the entries from a Mardia combined 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:
Set the significance level used for and :
By default is used:
A power curve for the Mardia combined test:
Visualize the approximate power curve:
Estimate the power of the Mardia combined test when the underlying distribution is a MultivariateTDistribution, the test size is 0.05, and the sample size is 12:
Five morphological measures were recorded for two separate varieties of a crab species. A researcher hopes to simultaneously compare all the measures across the species using multivariate analysis of variance, which requires that the data is multivariate normal:
Use MardiaCombinedTest to determine if both sets of data are multivariate normal:
Univariate density estimates of the five measures for each species:
The deviation from normality appears to be in the skewness:
The multivariate test statistic:
Under the test statistic asymptotically follows a ChiSquareDistribution:
For univariate data the test is equivalent to the JarqueBeraALMTest:
If the covariance matrix of the data is not positive definite the test will fail:
The number of data points must be greater than the dimension of the data:
The distribution of the Mardia combined test statistic:
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