Spatial Dependence: Why It Matters, When It Matters and What to Do about It.

Many conventional statistical analyses are based on the assumption of statistical independence.  For example, in an analysis of variance we assume that the residuals from the class means in our data set are independent random variables.  In this talk I shall examine why this assumption matters, the conditions under which it is justified and the problems that occur when independence is inappropriately assumed.  I shall also discuss the statistical methods that can be used when the assumption of  independence is not justified.

It is sometimes stated that soil data can never be treated as independent because of the scale-dependence of the processes that determine soil properties.  In fact independence is not an intrinsic property of the variables that we study, but is primarily justified by an appropriate sampling strategy.  If we assume independence when this is not justified then our statistical inferences are unsafe.  I shall show how model-based statistics can be used to analyse data when independence cannot be assumed, and illustrate this with examples from the analysis of data on soil.