Geog 516† 2001
Openshaw and Alvanides (1999) warn that GIS users need to seriously consider
how the zones of analysis effect results.† If relations between variables change
with the selection of different areal units, the reliability of results is called
into question. The effect of the selection of areal units on analysis, is termed
the modifiable areal unit problem (MAUP), it is formally defined as:
ďa problem arising from the imposition of artificial units of spatial reporting on continuous geographical phenomenon resulting in the generation of artificial spatial patterns (1998 Heywood).Ē
The MAUP had been most prominent in the analysis of socio-economic and epidemiological
data (see 1999 Wong, Lasus, Falk; 2000 Nakaya; 1999 Openshaw and Alvandies).†
Such areal data cannot be measured at a single point, but must be contained
within a boundary to be meaningful.† For example, it is not possible to measure
the percent of low birth-weight babies at a single point, this percentage must
be calculated within a defined area.† It is the selection of these artificial
boundaries and their use in analysis that produces the MAUP.
The effects of the MAUP can be divided into two components: the scale effect
and the zonation effect (1995 Armhein).† The scale effect is the
variation in numerical results that occurs due to the number of zones used in
an analysis. For example, the difference in numerical results between mortality
rates by municipality and health area in British Columbia is a scale effect.
The zonation effect is the variation in numerical results arising from
the grouping of small areas into larger units.† For example, using Canada census
data, numerical differences in employment rates between a census tract data
and its enumeration area would be a zonation effect.†
It is necessary to understand the ways in which the MAUP effects the results of statistical analysis.† Caution, however, is required, as there is a random aspect to the effects of the MAUP.† It may be difficult to generalise how different data sets with different spatial units are effected by the MAUP.† This caution aside, the use of small areal units has a tendency to provide unreliable rates because the population used to calculate the rate is smaller. On the other hand, using larger areal units will provide more stable rates but may mask meaningful geographic variation evident with smaller areal units (Nakaya 2000).† Choosing between the scale of zones depends upon the particular use and requirements of the data.††††
Armheim (1995) in his study of a region, aggregated data into three scales of analysis and calculated mean, variance, regression and correlation coefficients.† This study found that regression correlation coefficients increase as data is aggregated into larger spatial units.† Intuitively, this makes sense because unstable rates tend to be averaged when aggregated into larger units, thereby increasing correlation coefficients. According to Armheim (1995) mean and variance are more stable as areal units of analysis change. Example 1 shows the change in means that occurs when smaller units are aggregated into larger units. Given the susceptibility of statistical results to change at different scales of analysis ecological fallacy needs to be considered.† For example, it is unlikely that an increase in correlation with larger areal units reflects stronger correlation at the individual level.
Modifiable Areal Unit Problem:† Scale Effects (a,b) and Zoning Effects (c,d)
x†† =† mean
These few paragraphs have discussed the MAUP and its effects on analysis.† It has, however, avoided discussing solutions to the problem.† There are two reasons for this omission: (1) researchers have only begun to unpack the effects of the MAUP on analysis and; (2) few generic and practical solutions exist.† The weighing areal units by population, as well as complex statistical procedures are currently being researched to address the MAUP. A simple strategy to deal with the problem, is to undertaking analysis at multiple scales or zones. Despite the lack of solutions, being cognisant of the fact that analysis results may be dependent on the zones used to aggregate data is an important step.
Armhein C 1995 Searching for the elusive aggregation effect: Evidence from statistical simulations. Environment & Planning A, Jan95, Vol. 27 Issue 1, p105
Heywood 1998 Introduction to Geographical Information Systems. New York: Addison Wesley Longman.
Nakaya, T 2000 An information statistical approach to the modifiable areal unit problem in incidence rate maps. Environment & Planning A, Vol. 32 Issue 1
Openshaw S, Alvandies S 1999 Applying geocomputation to the analysis of spatial distributions.† In Longley P, Goodchild M, Maguire D, Rhind, D (eds) Geograhpic Information Systems: Principles and Technical Issues. Vol 1, 2nd ed. New York: John Wiley and Sons Inc.†
Song D, Lasus W 1999 Exploring the variability of segregation index D with scale and zonal systems: an analysis of... H.; Environment & Planning A, Vol. 31 Issue 3, p507†
- A scale dependent analysis
of gentrification in Vancouverís Downtown Eastside.† Myself and four others
attempted to find evidence of gentrification using City neighbourhoods, census
tracts, enumeration areas, and individual properties. BC Assessment data and
census data was used.
-lecture notes on the MAUP
-on-line paper that addresses the modifiable areal unit problem
Goodchild M, Proctor J 1997 Scale in a digital world. Geographical and Environmental Modelling vol 1, no 1