Ambiguities inherent in sums-of-squares-based error statistics |
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| Authors: | Cort J Willmott Kenji Matsuura Scott M Robeson |
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| Institution: | 1. Center for Climatic Research, Department of Geography, University of Delaware, Newark, DE 19716, USA;2. Department of Geography, Indiana University, Bloomington, IN 47405, USA;1. Division of Hepato-Biliary-Pancreatic and Transplant Surgery, Graduate School of Medicine, Kyoto University, Kyoto, Japan;2. Department of Hepato-Biliary-Pancreatic and Transplant Surgery, Graduate School of Medicine, Ehime University, Ehime, Japan;1. Graduate School of Life and Environmental Sciences, University of Tsukuba, 305-8572 Ibaraki, Japan;2. Graduate School of Science, Kyoto University, 606-8502 Kyoto, Japan;3. School of Life Sciences, Arizona State University, Tempe, AZ 85287-4501, USA;1. Laboratory of Insect Ecology, Graduate School of Agriculture, Kyoto University, Kyoto, Japan;2. Laboratory of Evolutionary Genomics, National Institute for Basic Biology, Okazaki, Japan;1. Industrial Technology Center of Fukui Prefecture, Kawaiwashizuka, Fukui 910-0102, Japan;2. Hamburg University of Technology, Institute of Polymer and Composites, Denickestraße 15, 21073 Hamburg, Germany;3. Department of Mechanical Engineering and Science, Kyoto University, C3, Kyoto Daigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan;1. Department of Zoology, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan;2. Division of Ecology and Evolutionary Biology, Graduate School of Life Sciences, Tohoku University, Aoba, Sendai 980-8578, Japan |
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| Abstract: | Commonly used sums-of-squares-based error or deviation statistics—like the standard deviation, the standard error, the coefficient of variation, and the root-mean-square error—often are misleading indicators of average error or variability. Sums-of-squares-based statistics are functions of at least two dissimilar patterns that occur within data. Both the mean of a set of error or deviation magnitudes (the average of their absolute values) and their variability influence the value of a sum-of-squares-based error measure, which confounds clear assessment of its meaning. Interpretation problems arise, according to Paul Mielke, because sums-of-squares-based statistics do not satisfy the triangle inequality. We illustrate the difficulties in interpreting and comparing these statistics using hypothetical data, and recommend the use of alternate statistics that are based on sums of error or deviation magnitudes. |
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