The aim of this paper is to present a generalization of the Shapiro-Wilk
W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of
calculating all the unweighted linear combinations of the variables and their
W- or W'-statistics with the Royston’s log-transformation and standardization, zln(1-W) or zln(1-W'). Because the calculation of the probability of zln(1-W) or zln(1-W') is to the right tail, negative values are truncated to 0 before doing
their sum of squares. Independence in the sequence of these half-normally
distributed values is required for the test statistic to follow a chi-square
distribution. This assumption is checked using the robust Ljung-Box test. One
degree of freedom is lost for each cancelled value. Defined the new
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