 
Summary: Significance Tests in Climate Science
MAARTEN H. P. AMBAUM
Department of Meteorology, University of Reading, Reading, United Kingdom
(Manuscript received 23 March 2010, in final form 8 August 2010)
ABSTRACT
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 sig
nificance statistic is not a quantitative measure of how confident one can be of the ``reality'' of a given result. It
is concluded that a significance test very rarely provides useful quantitative information.
1. Introduction
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.'' Unfortunately, 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 dif
ferent things. In this note we will formalize this notion. We
