An Approximation to the Distribution of the Likelihood Ratio Statistic for Testing Complete Independence

A normal approximation to the distribution of the likelihood ratio statistic for testing the hypothesis of complete independence in a p-variate normal distribution is developed. This approximation is compared with approximations due to Box (1949) and Bartlett (1954). It is observed that the latter two approximations deteriorate as p increases. Moreover, they both give inaccurate results when the number of degrees of freedom for error is small. The normal approximation fares better than the other two and can also be used to compute percentiles.