Since such tests are based on the calculated space-time autocorrelation function, the variance of these correlations must be known when, in fact, the underlying process is temporally independent. Previously, the variance of the sample space-time autocorrelation function was developed for the case when the observed process consists of 'T' independent observations of a vector random variable with mean zero and spherical variance covariance matrix 'a squared I.' This paper extends these results to the case of contemporaneously correlated variables. In this instance, 'G,' the error covariance matrix of the observations, is nonspherical. Formulas and six references are included. (Author abstract modified)