Model validation using equivalence tests

Model validation that is based on statistical inference seeks to construct a statistical comparison of model predictions against measurements of the target process. Previously, such validation has commonly used the hypothesis of no difference as the null hypothesis, that is, the null hypothesis is that the model is acceptable. This is unsatisfactory, because using this approach tests are more likely to validate a model if they have low power. Here we suggest the usage of tests of equivalence, which use the hypothesis of dissimilarity as the null hypothesis, that is, the null hypothesis is that the model is unacceptable. Thus, they flip the burden of proof back onto the model. We demonstrate the application of equivalence testing to model validation using an empirical forest growth model and an extensive database of field measurements. Finally we provide some simple power analyses to guide future model validation exercises.