This paper explores parameter-based hypothesis tests for selecting between candidate models that predict an unknown variable from observations. This is the form of many time series models, classifiers, and data-fitting models. The basis for this paper is that if a model contains redundant terms the associated parameters can be set to zero without penalty. Hypothesis tests are proposed for assessing the statistical evidence for parameters taking non-zero values. These compare closely with standard criteria such as Akaike's and the Bayesian Information Criterion. A numerical simulation is presented to illustrate the criteria. The link between selection criteria based on parameter distributions and those based on data distributions is relevant to techniques such as change-point methods. Resampling and other similar techniques may be applied using this framework.