Title

Controlling the Proportion of Falsely Rejected Hypotheses when Conducting Multiple Tests with Climatological Data

Date of Original Version

11-2004

Type

Article

Rights Management

© Copyright 2003 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (http://www.ametsoc.org/) or from the AMS at 617-227-2425 or copyright@ametsoc.org.

Abstract or Description

The analysis of climatological data often involves statistical significance testing at many locations. While the field significance approach determines if a field as a whole is significant, a multiple testing procedure determines which particular tests are significant. Many such procedures are available, most of which control, for every test, the probability of detecting significance that does not really exist. The aim of this paper is to introduce the novel “false discovery rate” approach, which controls the false rejections in a more meaningful way. Specifically, it controls a priori the expected proportion of falsely rejected tests out of all rejected tests; additionally, the test results are more easily interpretable. The paper also investigates the best way to apply a false discovery rate (FDR) approach to spatially correlated data, which are common in climatology. The most straightforward method for controlling the FDR makes an assumption of independence between tests, while other FDR-controlling methods make less stringent assumptions. In a simulation study involving data with correlation structure similar to that of a real climatological dataset, the simple FDR method does control the proportion of falsely rejected hypotheses despite the violation of assumptions, while a more complicated method involves more computation with little gain in detecting alternative hypotheses. A very general method that makes no assumptions controls the proportion of falsely rejected hypotheses but at the cost of detecting few alternative hypotheses. Despite its unrealistic assumption, based on the simulation results, the authors suggest the use of the straightforward FDR-controlling method and provide a simple modification that increases the power to detect alternative hypotheses.

DOI

10.1175/3199.1