Methods for estimating peak physiological performance and correlating performance measures

Estimates of animal performance often use the maximum of a small number of laboratory trials, a method which has several statistical disadvantages. Sample maxima always underestimate the true maximum performance, and the degree of the bias depends on sample size. Here, we suggest an alternative approach that involves estimating a specific performance quantile (e.g., the 0.90 quantile). We use the information on within-individual variation in performance to obtain a sampling distribution for the residual performance measures; we use this distribution to estimate a desired performance quantile for each individual. We illustrate our approach using simulations and with data on sprint speed in lizards. The quantile method has several advantages over the sample maximum: it reduces or eliminates bias, it uses all of the data from each individual, and its accuracy is independent of sample size. Additionally, we address the estimation of correlations between two different performance measures, such as sample maxima, quantiles, or means. In particular, because of sampling variability, we propose that the correlation of sample means does a better job estimating the correlation of population maxima than the estimator which is the correlation of sample maxima.