%0 Journal Article
%T Proposal and Pilot Study: A Generalization of the W or W' Statistic for Multivariate Normality
%A Jos¨¦ Moral-De La Rubia
%J Open Journal of Statistics
%P 119-169
%@ 2161-7198
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojs.2023.131008
%X 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
%K Multivariate Normality
%K Statistical Power
%K Type II Error
%K Specificity
%K Efficiency
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=123465