The Modified t Test

Determining measures of association between two processes on the space is not a simple task. Clifford and Richardson (1985) and Clifford et al. (1989), (see also Dutilleul 1993) introduced a modified t statistic based on a correction of both, the sample covariance and the degrees of freedom of the distribution under the null hypothesis. This procedure also allows the introduction of an estimate for the effective sample size, which corresponds to the number of equivalent independent observations due to the spatial covariance structure underlying each process. In this chapter, a parametric approach is described to evaluate the correlation between two processes. Its simplicity has captured the attention of many researchers who have applied this technique in several different applied fields such as environmental sciences and sociology. The discussion of the modified t-testt-test is accompanied by computational experiments and applied considerations. An alternative proposal for the same problem studied by Viladomat et al. (2014), and based on resample procedures is described, which allows this type of test to be carried out by relaxing the distributional assumptions. Finally, we describe an extension of the modified t-testModified t-test that can be used to determine the spatial association between one process and several others.