Monte Carlo Significance Testing as Applied to Statistical Tropical Cyclone Prediction Models

Abstract

Use of the F test in assessing the statistical significance of a regression equation developed from meteorological data and using the concept of stepwise screening of predictors presents problems in determining degrees of freedom. Some of these problems relate to characteristics of the data. The main problem, however, is the result of making a large number of predictors available to a screening program and retaining only a few. This adds an additional play of chance not ordinarily accounted for in the usual application of the F test. Unless proper compensation is made to degrees of freedom, the variance ratio is overestimated or underestimated, and a prediction equation can be judged significant when it is not, or not significant when it is. The derivation of a test-statistic to avoid this pitfall in the development of statistical models for the prediction of tropical cyclone motion is the subject of the present paper.