Random Sampling of Beef Cattle for Genetic Testing: Optimal Sample Size Determination

Sample size is often dictated by budget and acceptable error bounds. However, there are many economic problems where sample size directly affects a benefit or loss function, and in these cases, sample size is an endogenous variable. We introduce an economic approach to sample size determination utilizing a Bayesian decision theoretic framework that balances the expected costs and benefits of sampling using a Bayesian prior distribution for the unknown parameters. To demonstrate the method for a relevant applied economics problem, we turn to randomly sampling beef cattle for genetic testing. A theoretical model is developed, and several simplifying assumptions are made to solve the problem analytically. Data from 101 pens (2,796 animals) of commercially-fed cattle are then used to evaluate this solution empirically. Results indicate that at the baseline parameter values an optimal sample size of n^*=10 out of 100 animals generate returns from sampling of nearly $10/head, or a return-on-investment of 250%. Therefore, a large portion of the additional value for higher-quality cattle can be captured by testing a relatively small percentage of the lot. These results vary depending on the actual quality (or profitability) of a particular pen of cattle, the homogeneity within the pen, the variance of the buyer’s subjective prior distribution of expected profit, and the per-head cost of genetic testing. Nonetheless, results suggest that random sampling has the potential to provide a context in which the benefits of genetic testing outweigh the costs, which has not generally been the case in previous research.