The Use of Permutation Techniques in Evaluating the Outcome of a Randomized Storm Seeding Experiment

Abstract

The inappropriateness of standard parametric inference procedures for the analysis of weather modification experiments has been well documented and has led to permutation tests being strongly recommended by, among others, Tukey et al. and Gabriel. The result is that these nonparametric tests have become the standard technique for assessing the outcome of weather modification experiments. First, an efficient method to obtain confidence intervals for the difference between two means is introduced. Instead of using the common method of general displacement 100(1 ? α)% confidence intervals for the difference between the means are constructed using the fact that the end points of the confidence interval are the kth smallest and the kth largest in an ordering of a single set of numbers. With specific reference to the National Precipitation Research Programme currently being conducted in South Africa under the auspices of the Weather Bureau and the Water Research Commission, the need for treating the data as coming from two strata was identified. A stratified permutation test for the difference between the means is consequently explained. This method is the equivalent of the parametric two-way analysis of variance with no interactions, where the data are classified in a two-way table. Lastly, the need for a permutation test for the difference between the third quartiles, instead of the means, is briefly outlined.