# Accession Number:

## AD0684428

# Title:

## CORRELATION BETWEEN TWO VECTOR VARIABLES

# Descriptive Note:

## Technical rept.

# Corporate Author:

## SOUTHERN METHODIST UNIV DALLAS TX DEPTOF STATISTICAL SCIENCE

# Personal Author(s):

# Report Date:

## 1969-03-04

# Pagination or Media Count:

## 19.0

# Abstract:

H. Ruben 1966 has suggested a simple approximate normalization for the correlation coefficient in normal samples, by representing it as the ratio of a linear combination of a standard normal variable and a chi variable to an independent chi variable and then using Fishers approximation to a chi variable. This result is extended in this paper to a matrix, which in a sense is the correlation coefficient between two vector variables x and y. The result is then used to obtain large sample null and non-null but in the linear case distributions of the Hotelling-Lawley criterion and the Pillai criterion in multivariate analysis. Williams 1955 and Bartlett 1951 have derived some exact tests for the goodness of fit of a single hypothetical function to bring out adequately the entire relationship between two vectors x and y, by factorizing Wilks lambda suitably. These factors are known as direction and collinearity factors, as they refer to the direction and collinearity aspects of the null hypothesis. In this paper, the other two criteria viz. the Hotelling-Lawley and Pillai criteria are partitioned into direction and collinearity parts and large sample tests corresponding to them are derived for testing the goodness of fit of an assigned function.

# Descriptors:

# Subject Categories:

- Statistics and Probability