From observed data, statistical inference infers the properties of the underlying probability distribution. For hypothesis testing, the t-test and some non-parametric alternatives are covered. Ways to infer confidence intervals and estimate goodness of fit are followed by the F-test (for test of variances) and the Mann-Kendall trend test. Bootstrap sampling and field significance are also covered.

Field significance is concerned with testing a large number of hypothesis simultaneously. Previous chapters have discussed methods for testing one hypothesis, such as whether one variable is correlated with one other variable. Field significance is concerned with whether one variable is related to a random vector. In climate applications, a characteristic feature of field significance problems is that the variables in the random vector correspond to quantities at different geographic locations. As such, neighboring variables are correlated and therefore exhibit spatial dependence. This spatial dependence needs to be taken into account when testing hypotheses. This chapter introduces the concept of field significance and explains three hypothesis test procedures: a Monte Carlo method proposed by Livezey and Chen (1983) and an associated permutation test, a regression method proposed by DelSole and Yang (2011), and a procedure to control the false discovery rate, proposed in a general context by Benjamini and Hockberg (1995) and applied to field significance problems by Ventura et al. (2004) and Wilks (2006).