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Significance Tests in Climate Science
Maarten H. P. Ambaum
Department of Meteorology, University of Reading, United Kingdom
A large fraction of papers in the climate literature includes erroneous uses of significance tests.
A Bayesian analysis is presented to highlight the meaning of significance tests and why typical
misuse occurs. The significance statistic is not a quantitative measure of how confident we can be
of the `reality' of a given result. It is concluded that a significance test very rarely provides useful
In the climate literature one can regularly read state-
ments such as `this correlation is 95% significant' or `areas
of significant anomalies at the 90% significance level are
shaded' or `the significant values are printed in bold.' Un-
fortunately this is a misleading way of using significance
tests. The significance test does not quantify how likely
the hypothesis is, given the observation we just made; it
quantifies how likely the observation is, given that some
opposite hypothesis is true. These are two different things.