Analysing Deviation-From-Target Data: Applying the Correct Force in Sellick's Maneuver

The problem of comparing the deviation from a target of two or more treatments or procedures arises now and again in medicine. Practitioners usually carry out a t-test on a loss function such as absolute error. We have adapted and developed statistical methods to give a normative methodology for deviation-from-target problems and exemplify them by evaluating the performance of a tactile feedback device. Parametric and nonparametric analyses are compared and contrasted. We recommend nonparametric methods for inference about loss functions such as absolute error, with a permutation test for testing the hypothesis that the two methods perform identically, and the nonparametric bootstrap for deriving standard errors and confidence intervals on loss function ratios. We develop a new permutation test that can be used when the practitioner is unwilling to decide which loss function should be used. We recommend parametric analysis when more insight into how one method is superior is desired, or there are covariates, and discuss the complications. The results for our example are that the tactile sensing device reduces an upward bias in applied force, and more importantly reduces the spread (variance) of the applied force. It performs significantly better than manual force application.