This paper investigates the logarithmic least squares (LLSM) approach to Saaty's (Journal of Mathematical Psychology, 1977, 5, 234-281) scaling method for priorities in hierarchical structures. It is argued that statistical criteria are important in deciding the scaling method controversy. It is shown that LLSM is statistically optimal under a number of realistic and practical models. Variances and covariances of parameter estimates are derived. The covariance matrix associated with overall priority differences is also developed. These results allow for a significance analysis of apparent priority differences.