A TECHNIQUE OF NONPARAMETRIC MULTIVARIATE ANALYSIS

Journal/Book: THE BIOMETBIC SOCIETY Vol. 26 No. 3 September 1970. 1970;

Abstract: NATHAN MANTEL Biometry Branch National Cancer Institute Bethesda Maryland 20014 U.S.A. AND RANCHHODBHAI S. VALAND Department of Biometrics Temple University Medical School SUMMARY On each of n individuals p + q variables are observed. A nonnegative distance or closeness measure between any two individuals an any one variable can be based on ranks or tied ranks for orderable variables (continuous discrete or categorical); for nonorderable categorical variables the distance measure reflects whether the two individuals belong to the same category. Let X ij and Yij represent weighted sums over the p and the q variables respectively of the distance measures between individuals i and j; there will be 1/2n(n ± 1) such pairs of weighted sums. A test statistic for judging whether closeness in the set of p variables is related to closeness in the set of q variables is given by = ij ij. The permutational distribution of the statistic is defined by the random pairing of p-variable and q-variable observation vectors. Being a U statistic this measure is asymptotically normally distributed. A computing procedure is given for obtaining permutational expectations and variances so that departure from the permutational distribution can be judged. schö

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