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| '''Mardia's test''' is a statistical test for [[Statistics/NormalDistribution|multivariate normality]]. | '''Mardia's test''' is a statistical test for [[Analysis/NormalDistribution|multivariate normality]]. |
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| The null hypothesis is that a sample has a [[Statistics/NormalDistribution|multivariate normal distribution]]. Suppose that there are ''n'' observations and ''k'' variables. | The null hypothesis is that a sample has a [[Analysis/NormalDistribution|multivariate normal distribution]]. Suppose that there are ''n'' observations and ''k'' variables. |
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| It follows that the sample skewness, scaled by ''n/6'', has a [[Statistics/ChiSquaredDistribution|chi-squared distribution]] with ''k(k + 1)(k + 2)/6'' degrees of freedom. | It follows that the sample skewness, scaled by ''n/6'', has a [[Analysis/ChiSquaredDistribution|chi-squared distribution]] with ''k(k + 1)(k + 2)/6'' degrees of freedom. |
Mardia's Test
Mardia's test is a statistical test for multivariate normality.
Description
Mardia's test is derived from the calculations of multivariate skewness and kurtosis.
Usage
Test for Multivariate Normality
The null hypothesis is that a sample has a multivariate normal distribution. Suppose that there are n observations and k variables.
It follows that the sample skewness, scaled by n/6, has a chi-squared distribution with k(k + 1)(k + 2)/6 degrees of freedom.
Furthermore, it follows that the following statistic based on sample kurtosis is normally distributed:
If either test statistic is less than the critical level, the null hypothesis is rejected.