Resolving a Multi-Million Dollar Contract Dispute with a Latin Square

The City of New York negotiated a dispute over the performance of new garbage trucks purchased from a vehicle manufacturer. The dispute concerned the fulfillment of a specification in the purchase contract that the trucks load a minimum full-load of 12.5 tons of household refuse. On behalf of the City, but in cooperation with the manufacturer, the City's Department of Sanitation and consulting statisticians tested fulfillment of the contract specification, employing a Latin Square design for routing trucks. We present the classical analysis using a linear model and analysis of variance. We also show how fixed, mixed, and random effect models are useful in analyzing the results of the test. Finally, we take a Bayesian perspective to demonstrate how the information from the data overcomes the difference between the prior densities of the city and the manufacturer for the load capacities of the trucks to result in much closer posterior densities. This procedure might prove useful in similar negotiations. Supplementary material including the data and R code for computations in the article are available online.