Abstract

In one of the recent studies of this author he presented that if the multitest vector of n-components is normal in distribution, the Mahalanobls' squared distance from the mean vector to an observed multitest vector furnishes a good measure for the evaluation of clinical significance of the latter. As the squared distance is a variable which follows chi-squared distribution with n degrees of freedom, in the evaluation one must refer to the quantile table of chi-squared distribution. It gives, however, much inconvenience because the quantiles are dependent on degrees of freedom and the available tables are not detailed enough. One of the ways to exclude this inconvenience is to express the sqaured distance in the equivalent deviate of standard normal distribution. The author investigated the availability in such case of the Wilson-Hilferty transformation of the quantiles of chi-squarrd distribution into normal deviates, and found that as far as the clinical evaluation of the Mahalanbis' squared distance is concerned, the transformation is quite satisfactory even for the small degrees of freedom of chi-squared distribution which are between 2 and 10. The author, therefore, made this report to emphasize the fact that the Wilson-Hilferty's approximation formula are available irrespective of the size of degrees of freedom of chi-squared distribution in the evaluation of clinical significance of Mahalanobis' distance by transforming it into normal deviate.