Taking serial correlation into account in tests of the mean

The comparison of means derived from samples of noisy data is a standard 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, data frequently are serially correlated in climatological applications with the result that the t-tests in its standard form is not applicable. The usual solution to this problem is to scale the t-statistic by a factor which depends upon the equivalent sample size n_e. We show, 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). We re-examine the difficulties inherent in difference of means tests when there is serial dependence. We provide guidelines for the application of the 'usual' t-test and propose two alternative tests which substantially improve upon the 'usual' t-test when samples are small. (orig.)Available from TIB Hannover: RR 1347(120) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A ten year climate simulation with a coupled ocean-atmosphere general circulation model

SIGLEAvailable from TIB Hannover: RR 1347(21) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Explaining extreme events of 2011 from a climate perspective

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