This study applies a Bayesian latent variable analysis to the task of determining rankings of universities in the UK and US, on the basis of a set of quality-related measures. It estimates the degree of uncertainty in the rankings and permits the assessment of statistically significant differences across universities. It also provides a methodology for determining the weighting of various measures that is based on the patterns embedded in the data and compares the latent variable rankings with traditional weight-and-sum rankings. Overall, the methodology contributes to a better understanding of ranking efforts and illustrates the need for caution in interpreting distinctions published in traditional ranking systems.