= Mardia's Test = '''Mardia's test''' is a statistical test for [[Analysis/NormalDistribution|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 [[Analysis/NormalDistribution|multivariate normal distribution]]. Suppose that there are ''n'' observations and ''k'' variables. 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. Furthermore, it follows that the following statistic based on sample kurtosis is normally distributed: {{attachment:stat.svg}} If either [[Statistics/TestStatistic|test statistic]] is less than the critical level, the null hypothesis is rejected. ---- CategoryRicottone