Statistical considerations for climate experiments. Part I: scalar tests

Abstract

Statistical tests used in model intercomparisons or model/climate comparisons may be either 'scalar' or 'multivariate' tests. The former are employed when testing a hypothesis about a single variable observed at a single location, or through a single derived coefficient. The latter are employed when testing a hypothesis about an entire field, or a set of derived coefficients. In this paper, we examine several scalar tests for differences of mean and variance. Models are developed which relate the true significance level of these tests to sample size and the stochastic properties of the data, and these models are used to make recommendations for the design of experiments for the design of experiments using time-series-based tests. -from Authors