designs may not produce representative samples. Random samples are not necessarily representative samples because of the way processes can vary in time and space. For spatially referenced data there is no consistent relationship between the number of observations and their representativeness. Quite commonly, other information is available that permits the differential weighting of sample observations. Such Bayesian weighting schemes, for example, are becoming especially important in interpreting the geographic patterns of disease distributions. The "samples" of observed diseases are hypothesized to be drawn from known processes, and the interest is in observing differences between observed and expected patterns of disease given the geographic distribution of conditions known to affect the likelihood of the disease being present in a population (Langford, 1994). Generating samples from known processes, computing the reference distribution and finding the relationship of an observed sample estimate to it, is often accomplished using Monte Carlo simulation methods (Openshaw et al., 1987, 1988).
Many samples of geographic data are taken from datasets designed for other purposes (e.g., from the census). This resampling of samples confounds classical statistical probability assessments and hypothesis testing. A number of geographers have begun to move away from classical statistical approaches toward more flexible approaches that incorporate geographic understanding. The move from "direct" to "indirect" estimation techniques that rely on knowledge from related observations to estimate the conditions of small areas illustrates this change. In qualitative approaches in human geography, formal sampling designs are often questioned, since space is not conceived of as an empty space whose content is to be captured through systematic samples—but, rather, as a differentiated space with meanings attached to areas that change across space in noncontinuous ways. In qualitative analyses a contrast is made between time, which is seen as one-dimensional and unidirectional, and space, which is seen as multidimensional and ordered in many different ways. For the qualitative geographer, who is often cultivating the middle ground between the universality of science and the particularity of history, interpreting the meaning of change in space becomes the goal and purposive sampling the tool for this end.
An example of a new approach to sampling design and evaluation is the ongoing effort to assess global climate and climatic change from weather station measurements. Rain gauge networks provide spatial samples of the continually varying global precipitation field. Their spatial distributions are neither random by design nor demonstrably random in effect (see Figure 4.3); nevertheless, the nodes of these sampling networks (the rain gauge locations) are arguably the best representations of historical precipitation variability. Standard statistical approaches are inadequate for assessing precipitation variability from such samples for the reasons mentioned above. In their place, computer-intensive, nonparametric methods of evaluating the rain gauge networks and, in turn, the precipita-