science

Modifiable areal unit problem

Modifiable areal unit problem is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Modifiable areal unit problem rather than just read about it. In short: The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. The MAUP affects results when point-based measures of spatial phenomena are aggregated into spatial partitions or areal units (such as regions or districts) as in, for example, population density or illness rates.

Key takeaways

Modifiable areal unit problem belongs to science; place it in that map before memorising details.
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Reproduce the core statement of Modifiable areal unit problem from memory before moving on to harder problems.

Reference excerpt

The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. The MAUP affects results when point-based measures of spatial phenomena are aggregated into spatial partitions or areal units (such as regions or districts) as in, for example, population density or illness rates. The resulting summary values (e.g., totals, rates, proportions, densities) are influenced by both the shape and scale of the aggregation unit. For example, census data may be aggregated into county districts, census tracts, postcode areas, police precincts, or any other arbitrary spatial partition. Thus, the results of data aggregation are dependent on the mapmaker's choice of which "modifiable areal unit" to use in their analysis. A census choropleth map calculating population density using state boundaries will yield radically different results from a map that calculates density based on county boundaries. Furthermore, census district boundaries are also subject to change over time, meaning the MAUP must be considered when comparing past to current data.

Background This issue was first recognized by Gehlke and Biehl in 1934, and later described in detail in an entry in the Concepts and Techniques in Modern Geography (CATMOG) series by Stan Openshaw (1984) as well as in the book by Giuseppe Arbia (1988). In particular, Openshaw (1984) observed that "the areal units (zonal objects) used in many geographical studies are arbitrary, modifiable, and subject to the whims and fancies of whoever is doing, or did, the aggregating." The problem is especially apparent when the aggregate data are used for cluster analysis for spatial epidemiology, spatial statistics or choropleth mapping, in which misinterpretations can easily be made without realizing it. Many fields of science, especially human geography, are prone to disregard the MAUP when drawing inferences from statistics based on aggregated data. MAUP is closely related to the topic of ecological fallacy and ecological bias (Arbia, 1988). Stan Openshaw's work on this topic has led to Michael F. Goodchild suggesting it be referred to as the "Openshaw effect." Ecological bias caused by MAUP has been documented as two separate effects that usually occur simultaneously during the analysis of aggregated data. First, the scale effect causes variation in statistical results between different levels of aggregation (radial distance). Therefore, the association between variables depends on the size of areal units for which data are reported. Generally, correlation increases as areal unit size increases. The zoning effect describes variation in correlation statistics caused by the regrouping of data into different configurations at the same scale (areal shape). Since the 1930s, research has found extra variation in statistical results because of the MAUP. The standard methods of calculating within-group and between-group variance do not account for the extra variance seen in MAUP studies as the groupings change. The MAUP can be used as a methodology to calculate upper and lower limits as well as average regression parameters for multiple sets of spatial groupings. The MAUP is a critical source of error in spatial studies, whether observational or experimental. As such, unit consistency, particularly in a time-series cross-sectional (TSCS) context, is essential. Furthermore, robustness checks of unit sensitivity to alternative spatial aggregation should be routinely performed to mitigate associated biases on resulting statistical estimates.

Suggested solutions Several suggestions have been made in the literature to reduce aggregation bias during regression analysis. A researcher might correct the variance-covariance matrix using samples from individual-level data. Alternatively, one might focus on local spatial regression rather than global regression. A researcher might also attempt to design areal units to maximize a particular statistical result. Others have argued that it may be difficult to construct a single set of optimal aggregation units for multiple variables, each of which may exhibit non-stationarity and spatial autocorrelation across space in different ways. Others have suggested developing statistics that change across scales in a predictable way, perhaps using fractal dimension as a scale-independent measure of spatial relationships. Others have suggested Bayesian hierarchical models as a general methodology for combining aggregated and individual-level data for ecological inference. Studies of the MAUP based on empirical data can only provide limited insight due to an inability to control relationships between multiple spatial variables. Data simulation is necessary to have control over various properties of individual-level data. Simulation studies have demonstrated that the spatial support of variables can affect the magnitude of ecological bias caused by spatial data aggregation.

MAUP sensitivity analysis

… excerpt ends here. Continue reading the full article.

Illustrations

Modifiable areal unit problem: A hand map with different spatial patterns. Note: p is the probability of q-statistic; * denotes statistical significant at level 0.05, ** for 0.001, *** for smaller than 10−3;(D) subscripts 1, 2, 3 of q and p denotes the strata Z1+Z2 with Z3, Z1 with Z2+Z3, and Z1 and Z2 and Z3 individually, respectively; (E) subscripts 1 and 2 of q and p denotes the strata Z1+Z2 with Z3+Z4, and Z1+Z3 with Z2+Z4, respectively. — A hand map with different spatial patterns. Note: p is the probability of q-statistic; * denotes statistical significant at level 0.05, ** for 0.001, *** for smaller than 10−3;(D) subscripts 1, 2, 3 of q and p denotes the strata Z1+Z2 with Z3, Z1 with Z2+Z3, and Z1 and Z2 and Z3 individually, respectively; (E) subscripts 1 and 2 of q and p denotes the strata Z1+Z2 with Z3+Z4, and Z1+Z3 with Z2+Z4, respectively.

Worked examples

Example 1 — a first encounter with Modifiable areal unit problem

Start with the simplest possible case. Write down what Modifiable areal unit problem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Modifiable areal unit problem before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Modifiable areal unit problem ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Modifiable areal unit problem

In research: Modifiable areal unit problem appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Modifiable areal unit problem in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Modifiable areal unit problem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Bias, Geographic information systems, Problems in spatial analysis, so understanding it makes those chapters shorter.
In everyday life: Look for Modifiable areal unit problem outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Modifiable areal unit problem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Modifiable areal unit problem means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Modifiable areal unit problem in simple terms?

Why does Modifiable areal unit problem matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Modifiable areal unit problem?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Modifiable areal unit problem.