Why is geography important? Issues such as

• the modifiable areal unit problem (MAUP),
• the scale, grain and extent of a study,
• the nature of the boundaries of a study area, and
• spatial dependence / heterogeneity

are all geographic in nature, and are all issues that must be explicitly considered in any study that uses geographic data. As such, landscape ecologists, epidemiologists, health geographers, and crime analysts all must carefully consider the 'geography' of their problem, and what effects that geography alone may have on their analyses (e.g., do more crimes occur in area A than area B simply because more people live in area A, or are there more crimes because there are higher levels of drug use in the area?).

A discussion of scale, grain and extent from a landscape ecology perspective can be found here. For a detailed discussion on the impact of backgrounds, borders and boundaries, read over the FragStats Help File on User Guidelines / Overview / Backgrounds, borders and boundaries. Notes on spatial autocorrelation can be found here. A 'game' that asks you to create patterns with different spatial autocorrelation can be found here. In a recent article D. Griffith (Annals of the AAG 95(4): 740-760) observed that the effective sample size can be reduced from (e.g.) 900 to 25 once the effects of spatial autocorrelation are taken into account, so for anyone considering conducting a statistical analysis involving geospatial data learning about spatial autocorrelation is important. Some interesting thoughts on spatial associations / patterns (e.g., why positive spatial autocorrelation might arise when analyzing crime patterns).

The modifiable areal unit problem is endemic to all spatially aggregated data. It consists of two interrelated parts: First, there is uncertainty about what constitutes the objects of spatial study--identified as the scale and aggregation problem. The scale effect: different statistical results can be obtained from the same set of data when the information is grouped at different levels of spatial resolution(e.g., enumeration areas, census tracts, cities, regions). The aggregation or zoning effect: variability in statistical results is observed as a function of the various ways these units can be grouped at a given scale, and not as a result of the variation in the size of those areas. A figure showing the two effects can be found here. Note how the statistical parameters change when the groups are oriented vertically rather than horizontally (and also how neither of the grouped statistics agrees with the ungrouped data's statistics). Another example of the MAU effect.

The second part follows from the uncertainty in choosing zonal units: different areal arrangements of the same data produce different results, so we cannot claim that the results of spatial studies are independent of the units being used and the task of obtaining valid generalizations or of comparable results becomes extraordinarily difficult. MAUP therefore consists of two problems-one statistical and the other geographical, and it is difficult to isolate the effects of one from the other. An interesting paper that discusses the difficulty in establishing the appropriate scale at which to study species-habitat relations. A paper that looks at the differences in behaviour of commuters and marauders in Australia. Emergent processes in nature (wiki).

We should recall that two distinct types of spatial units are commonly used in geographic analysis--artificial and natural units. Census data collected for individuals, but aggregated and represented as artificial areas, present a major problem in interpretation to social geographers, and cannot be treated in the same way as 'natural' areal data, such as soil type, that is collected and represented as areal data. One could say that physical geographers are therefore somewhat immune to the MAUP, but the classification of a landscape into elements, such as the toe of a slope, a ridge, etc., is not without ambiguity in definition, and therefore physical geographers also need to be aware of the MAUP.

The MAUP has been known of since the early 30's, when a study of the scale effect in census data the authors noted that "a relatively high correlation might conceivably occur by census tracts when the traits so studied were completely dissociated [in the ultimate possessors of those traits]... individuals or families" (Gehlke and Biehl 1934). This particular effect of MAUP is more formally known as ecological fallacy, and is one of the serious problems which follow from the MAUP. (The converse effect is known as the individualistic fallacy.)

However, there are other elements which may impact any study using aggregated data--Simpson's Paradox, for example. If the value of one variable varies in correlation with another (e.g., high areas of unemployment are often found in areas with a high number of a particular social-economic characteristic), then it may be impossible to obtain a reliable estimate of the true correlation between the two variables (Table). The paradox in the example arises because we assume that race is the independent variable while unemployment is the dependent variable. In fact, location is the independent variable (and unavailable for examination when we only examine the totals) and unemployment (and race) the dependent variables. (An example of a common response relation.)

As discussed in the notes, developing an understanding of the role that geography alone can play in an analysis is vital--before one can search for meaningful biological, environmental or sociological explanations for an observation, one should first eliminate the geographic explanation. (A discussion of the minimum mapping unit.)

References:

Armhein C. 1995. Searching for the elusive aggregation effect: Evidence from statistical simulations. Environment & Planning A, Jan95, Vol. 27 Issue 1, p105.

FragStats Help Manual (Available from the Fragstats 3.3 Menu)

Gehlke, C. and Biehl, K., 1934. Certain Effects of Grouping Upon the Size of the Correlation Coefficient in Census Tract Material, Journal of American Statistical Association, 29:169-170.

Green, M. and Flowerdew, R. 1996. New evidence on the modifiable areal unit problem. Page 41-54 in P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment. Cambridge: GeoInformation International.

Jone, K. and Duncan, C. 1996. People and places: The multilevel model as a general framework for the quantitative analysis of geographical data. Pages 79-104 in Longely and Batty.

Martin, D. 1991. Geographic Information Systems and their socioeconomic applications. London: Routledge.

Openshaw, S. 1996. Developing GIS-relevant zone-based spatial analysis methods. Page 55-73 in P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment. Cambridge: GeoInformation International.

Wrigley, N., Holt, T., Steel, D., and Tranmer, M. 1996. Analysing, modelling, and resolving the ecological fallacy. Pages 25-40 in P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment. Cambridge: GeoInformation International.