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Modifiable areal unit problem

Andresen, M.A. (2021). Modifiable areal unit problem. In J.C. Barnes & D.R. Forde (Eds.), Encyclopedia of research methods and statistical techniques in criminology and criminal justice (pp. 854 – 855). Hoboken, NJ: Wiley Blackwell.

Published onJan 01, 2021
Modifiable areal unit problem

What it the modifiable areal unit problem?

The modifiable areal unit problem (MAUP) is an issue with spatial data and spatial analysis. Though first identified by Gehlke and Biehl (1934), the starting point of serious scholarship on the MAUP begins with Openshaw (1984). The MAUP emerges because individual level data are aggregated into other spatial units that are arbitrarily defined with results changing depending on the type of spatial unit under analysis. The most common form of such aggregations are with individuals aggregated into census tracts, or other census-defined units of analysis. The trouble is that the boundaries of these units of analysis are arbitrary in the sense that they do not define “natural” areas such as a neighborhood.

There are two ways in which the MAUP can emerge in an analysis. The first, and most common, is the scale problem: conducting your analyses with spatial units that are of different geographic sizes, census tracts and block groups for example. The second is the zoning problem in which the researcher uses the same units of analysis but they are placed on a different place on the map; a prime example could be dragging a set of square grids to a slightly different location on the map. In both cases, when the individual-level data are aggregated into the varying geographic units of analysis the aggregations are different (different counts of crime, for example) and may lead to different results.

At this point, it could be argued that the MAUP is not really a problem at all. If crimes, for example, are aggregated differently because the units of analysis change, so will the underlying socio-economic and socio-demographic characteristics to represent that areas being analyzed. Though this does, at times, occur such that the MAUP does not appear to be problematic, this is not always the case.

Is it really a problem?

The short answer here is: yes. Gehlke and Biehl (1934) found that the magnitude of correlation coefficients increased as the data were aggregated into ever larger geographic units. This has been reproduced, so it can occur, but no systematic pattern has emerged with subsequent research in this area. Moreover, Openshaw was able to show that he could generate correlation coefficients that ranged from -0.99 to 0.99 by invoking the zoning problem alone. As such, not only can the magnitude of the correlation coefficient be wrong in magnitude, but in sign. Fotheringham and Wong (1991) extended the research of Openshaw (1984) into a multivariate context, much more common in the social sciences. They found that the statistical results were not reliable because of the MAUP. Depending on the geographic size of the units of analysis, Fotheringham and Wong (1991) could alter the magnitude of a statistical estimate by nine times. They also showed that within a multivariate regression context, the results were even more unpredictable than those found by Openshaw (1984) because of the MAUP. This led to Fotheringham and Wong (1991) calling their results “depressing” because a researcher would most often not know which set of results would be correct, or only have one set of results with nothing to compare.

Such results do not bode well for the (spatial) analysis of data. However, though any results are possible because of the MAUP, some research has investigated this issue in a criminological context with some more promising results—there is very little of such work because multiple units of analysis are not always available. Wooldredge (2002) analyzed crime patterns considering individuals, census tracts, and official neighborhoods. Though he did find different results depending upon the unit of analysis, the statistical results varied very little for the different aggregations of data. This is some good news, but does not mean we can ignore the MAUP.

What can we do about it?

Fundamentally, there is little that can be done about the MAUP. The primary thing we can do is be aware of the issue and pay attention to its impact. Openshaw (1984) stated the importance of “natural units of analysis” that made sense for the relationship being studied. The arbitrary drawing of a boundary because it is convenient is not natural but, perhaps, a boundary at a river or some other physical attribute is. Hipp (2007) added to this consideration by noting that researchers need to consider their theory when choosing units of analysis: do not use an individual level theory for neighborhood level data, for example.

Thought in our analyses is the best way to address the MAUP, but sensitivity analyses are also important. Not all research has different units of analysis available, but if two or more units of analysis are available to the researcher then both should be used. If the results are essentially the same, then report one and refer to the other analysis in a footnote making it available to the interested reader; if not, the researchers have important decisions to make.


Andresen, M. A., & Malleson, N. (2013). Spatial heterogeneity in crime analysis. In

M. Leitner (ed), Crime modeling and mapping using geospatial technologies

(pp. 3 – 23). New York, NY: Springer.

Fotheringham, A. S., & Wong, D. W. S. (1991). The modifiable areal unit problem in

multivariate statistical analysis. Environment and Planning A, 23(7), 1025 – 1044.

Gehlke, C. E., & Biehl, H. (1934). Certain effects of grouping upon the size of the

correlation coefficient in census tract material. Journal of the American

Statistical Association, Supplement, 29(185), 169 – 170.

Hipp, J. R. (2007). Block, tract, and levels of aggregation: Neighborhood structure

and crime and disorder as a case in point. American Sociological Review,

72(5), 659 – 680.

Openshaw, S. (1984). The modifiable areal unit problem. CATMOG (Concepts and

Techniques in Modern Geography) 38. Norwich: Geo Books.

Wooldredge, J. (2002). Examining the (ir)relevance of aggregation bias for

multilevel studies of neighborhoods and crime with an example of comparing

census tracts to official neighborhoods in Cincinnati. Criminology, 40(3), 681 – 709.

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