Nº DE ESTUDIANTES 25 HOMBRES: 8 MUJERES: 17 DOCENTE

The conclusions of the critique of Robinson’s areal weighting lead to the recognition that spatial autocorrelation is important in any statistical understanding of the MAUP. Goodchild (1986) presents a general review of spatial autocorrelation, where he introduces the subject as being concerned with the “degree with which objects or activities in some place on the earth’s surface are similar to objects that are located nearby” (p.3). Indeed, Goodchild (1986) recognises the link between spatial autocorrelation and MAUP, albeit indirectly, by stating that the “concept of scale is implicit in any measure of spatial autocorrelation, and that spatial patterns may possess quite different forms of autocorrelation at different scales”. Spatial autocorrelation is closely related to Tobler’s “First Law of Geography”, (1970, p.236), whereby similarity is related to distance. Spatial autocorrelation itself appears to have multiple definitions. One was presented by Upton and Fingleton (1985), where they described it as an organized spatial pattern. This reinforced the definition from Cliff and Ord (1981, p.105), who refer to spatial autocorrelation as “systematic spatial variation”. Furthermore, they extend their definition in relation to the MAUP, and note that the size of the cells in the areal unit system are important in the strength of the spatial autocorrelation, or in their terms, spatial dependence. In essence, “the larger the areas, the weaker the dependence will be”. This suggests that there are interactions and dependencies that occur at certain levels, and if the areal units are at a different level than those interactions then the level of dependence will fall.

Arbia (1989) builds on the work by Cliff and Ord (1981) by providing a more formal framework within which the discussion can take place. Arbia presents an example using Cliff and Ord’s discussion considering settlement patterns first presented by Matui (1932). Here data relating to the location of the homes of a population were

divided on a lattice of 32 by 32 cells. These were aggregated further into combinations of 16 by 16, 8 by 8, 4 by 4 and 2 by 2 (Arbia 1989). The results of the investigation demonstrate that with aggregation there is increase in the level of variance, and that as the level of aggregation increases the estimates of the variance of the data become more unreliable as the number of observations diminishes with fewer degrees of freedom. There is clearly, therefore, evidence of the MAUP, and it is possible to conclude that areal units are likely to contain a level of homogeneity, as people with similar characteristics tend to group together. Arbia termed this ‘systematic spatial variation’. Fotheringham and Wong (1991) in their work presented above concluded of spatial autocorrelation that it has a “role determining the rate at which the variances of X and Y decrease as the level of aggregation increases”.

Amrhein and Flowerdew (1989) investigate the effects of MAUP in relation to Poisson regression, and conclude that the choice of model with which MAUP effects are measured or presented is just as critical as the aggregation process itself. They are able to conclude this because their results show that within their Poisson model there is little aggregation effect to be found, not because it doesn’t exist, but as a result of the data and techniques used in the analysis. A paper that develops from this research is that of Amrhein (1995), in which he presents a set of conclusions that suggest that the world of the spatial analyst dealing with spatial data is not as bleak as previously presented by, among others, Fotheringham and Wong (1991, see page 21 above). He summarises this in six points, which suggest that certain statistics and results (for instance the standard deviation of coefficients, or the Pearson correlation coefficient) exhibit greater changes due to MAUP (scale) than other statistical methods (for instance, mean or the variance). However, this does not mean that the MAUP is close to being understood, or that aggregation effects can be “easily purged from the data” (Amrhein, 1995).

The importance of spatial autocorrelation has been further developed by a number of authors such as Green and Flowerdew (1996). They note that “correlations between variables tended to increase when zones were grouped together”, an effect that is clearly related to spatial autocorrelation. Their study provided statistical evidence that correlation coefficients will always suffer from MAUP in the presence of spatial autocorrelation. Green and Flowerdew employed simulated data to assess the impact

of the MAUP as they could build in a known pattern of spatial autocorrelation into a variable. The basic grid of raw simulated data was aggregated (a) randomly, (b) systematically based on the value of one of the simulated variables, and (c) spatially into contiguous blocks.

In conclusion Green and Flowerdew (1996) argue that the effects of spatial autocorrelation may “result from contiguous processes affecting the distribution of one or more of the variables being analysed, or the spatial distribution of other variables which have effects on these”. This is a very important conclusion, as it explicitly expresses the realisation that the variables of areal units may display linked characteristics. To explain this phenomenon Green and Flowerdew present three possible causes of spatial clusters:

1. “A tendency for people with similar attributes to choose to live near each other;

2. Effects of other characteristics of the area (which may or may not be available for analysis);

3. A tendency for people living nearby to interact and as a result to develop common characteristics”.

Of these, the first and last are relatively straightforward, while the second point is the one that will present more difficulty due to its nature and the fact it is largely unquantifiable. In the future it is likely to be these types of unknown or unmeasurable variables that prevent or hinder fuller ‘explanation’ of MAUP.

2.4.2.2 Conclusion

It is considered here that the purging of MAUP from the data would not be beneficial to areal data analysis as the effects that different aggregations can have on data could provide additional information about the structure of the data and the processes that occur within groupings, which are of inherent interest to geographers as well ass social scientists as a while. Furthermore, spatial autocorrelation has been important in the understanding of the MAUP and it is a link that is explored in more detail in the following sections.