TAKING SERIAL-CORRELATION INTO ACCOUNT IN TESTS OF THE MEAN

The comparison of means derived from samples of noisy data is a standa rd part of climatology. When the data are not serially correlated the appropriate statistical tool for this task is usually the conventional Student's t-test. However, frequently data are serially correlated in climatological applications with the result that the t test in its st andard form is not applicable. The usual solution to this problem is t o scale the t statistic by a factor that depends upon the equivalent s ample size n(e). It is shown, by means of simulations, that the revise d t test is often conservative (the actual significance level is small er than the specified significance level) when the equivalent sample s ize is known. However, in most practical cases the equivalent sample s ize is not known. Then the test becomes liberal (the actual significan ce level is greater than the specified significance level). This syste matic error becomes small when the true equivalent sample size is larg e (greater than approximately 30). The difficulties inherent in differ ence of means tests when there is serial dependence are reexamined. Gu idelines 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.