## Mardia test for N equal circular distributions

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A non-parametric statistical test of whether N circular distributions are equal (homogenous)

Updated 16 Aug 2017

Usage: [bH, fPEst, fWTest, strPMethod] = mardiatestn_circ_equal(cvfX , fAlpha)
'cvfX' is a cell array, each cell containing samples from a distribution to test. The Mardia test is a non-parametric rank test whether the distributions in 'cvfX' are identical (H0: homogeneous) [1, 2].
'bH' is a boolean value indicating whether we must reject H0: if true, then the distributions in 'cvfX' are not all homogeneous. No further indication is made as to which distributions are different, or which samples are different. The optional argument 'fAlpha' can be used to set the significance threshold for the test (default: 5%).

This statistical test compares 2 or more distributions on a periodic domain [-pi pi]. It is a rank test, and is insensitive to centre of mass location on the circular domain. For small sample sizes, p-value estimates are computed using Monte-Carlo resampling of the distributions. For larger sample sizes the test statistic adopts a Chi^2 distribution and a p-value estimation is made accordingly.

'fPEst' is an estimate for the p-value of the W test statistic, which is returned in 'fWTest'. 'strPMethod' indicates which method was used to estimate the p-value: 'monte-carlo' or 'chi^2', accordingly.

This test is suitable for 2 to N distributions. For comparing two distributions, the Kuiper test may be more sensitive.

References:
 N.I. Fisher 1993. "Statistical analysis of circular data." Cambridge University Press.
 K.V. Mardia 1972. "A multi-sample uniform scores test on a circle and its parametric competitor." J Royal Statistical Society B (Methodological) 34, 102-113.

### Cite As

Dylan Muir (2022). Mardia test for N equal circular distributions (https://www.mathworks.com/matlabcentral/fileexchange/40439-mardia-test-for-n-equal-circular-distributions), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
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