Taking serial correlation into account in tests of the mean

Abstract

The comparison of means derived from samples of noisy data is a standard part of climatology. It is shown, by means of simulations, that the revised t test is often conservative (the actual significance level is smaller than the specified significance level) when the equivalent sample size is known. However, in most practical cases the equivalent sample size is not known. Then the test becomes liberal (the actual significance level is greater than the specified significance level). This systematic error becomes small when the true equivalent sample size is large (greater than approximately 30). The difficulties inherent in difference of means test when there is serial dependence are reexamined. Guidelines for the application of the "usual' t test are provided and two alternative tests are proposed that substantially improve upon the "usual' t test when samples are small. -from Authors