Statistical Considerations for Climate Experiments. Part II: Multivariate Tests

Abstract

Several multivariate tests for differences of the mean which are based upon resampling schemes are examined in a series of Monte Carlo experiments. We examine the power of these tests under two sets of experimental situations: one in which the resolution of the simulated observing network increases, and one in which the simulated observing network expands geographically with a fixed resolution The behavior of these essentially nonparametric tests is compared with classical multivariate tests and it is argued that the sensitivity of one with respect to the other depends upon the spatial correlation structure of the observed fields. The question of whether or not to reduce the dimensionality of the observed fields prior to conducting a statistical test is studied, as is the effect of temporal correlation upon tests based on resampling schemes.