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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 at-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. [ABSTRACT FROM AUTHOR]

In epidemiology, an infection lasting n weeks may be monitored by taking weekly serum samples. If tests on samples are independent Bernoulli trials with probability q of correctly testing positive, the apparent duration of infection ( from the first positive test to the last positive test inclusive) may be less than n weeks. This distribution of apparent length also arises when plants in a row of n each have a probability q of germinating, for example. This distribution is shown to be related to that of the number of tails obtained when tossing a coin until two heads are obtained, in a maximum of n tosses. The properties of the 'apparent length' distribution are described, and some compounded (mixed) distributions that can be derived from it are also discussed. The distribution was used to estimate the underlying distribution of the duration of infection, in a longitudinal study of infections of children. The methodology was also used to estimate the proportion of infectious episodes that were not detected. It can be similarly used to correct episode durations and rates in longitudinal studies in which episodes of any kind are detected by regular sampling. [ABSTRACT FROM AUTHOR]