Statistical model selection using the Akaike Information Criterion (AIC) and similar criteria is a useful tool for comparing multiple and non-nested models without the specification of a null model, which has made it increasingly popular in the natural and social sciences. De- spite their common usage, model selection methods are not driven by a notion of statistical confidence, so their results entail an unknown de- gree of uncertainty. This paper introduces a general framework which extends notions of Type-I and Type-II error to model selection. A theo- retical method for controlling Type-I error using Difference of Goodness of Fit (DGOF) distributions is given, along with a bootstrap approach that approximates the procedure. Results are presented for simulated experiments using normal distributions, random walk models, nested linear regression, and nonnested regression including nonlinear mod- els. Tests are performed using an R package developed by the author which will be made publicly available on journal publication of research results.

Salivary cortisol is the least invasive way in measuring hormonal response during exercise without interruption. In nationally ranked fencers (n=21), changes in cortisol were monitored by measurement of salivary cortisol sampled throughout different rounds of three North American Cup tournaments during the 2017-2018 United States fencing season. The changes were also compared when looking at if a bout ended in a victory or defeat; the difference in rank between opponents; and the difference in score at the end of the bout. Immediately before the tournament cortisol levels were sampled, changes were in comparison to the initial sample as well as change from one bout to the next. The primary purpose of this study was to (a) compare how cortisol levels fluctuate during a tournament and (b) analyze cortisol levels to see if there is an optimal rage for performance. Eustress, “good stress” was considered optimal when the athletes were at peak performance. Here, peak performance means accomplishing the task, with the task being the bout ending in a victory. It was hypothesized that (a) cortisol levels would peak after a loss or stressful bout and (b) there would be an optimal range of cortisol for peak performance. This study supports the findings that cortisol peaks after a loss, and could point to optimal cortisol levels being more of an individualized range for each athlete. If these athletes can explicitly see just how their hormones rise and fall, then perhaps being more aware of these levels and being able to embrace them could lead to peak performance.