science

Indicators of spatial association

Indicators of spatial association 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 Indicators of spatial association rather than just read about it. In short: Indicators of spatial association are statistics that evaluate the existence of clusters in the spatial arrangement of a given variable. For instance, if we are studying cancer rates among census tracts in a given city local clusters in the rates mean that there are areas that have higher or lower rates than is to be expected by chance alone; that is, the values occurring are above or below those of a random distrib…

Key takeaways

Indicators of spatial association belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Indicators of spatial association to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Indicators of spatial association from memory before moving on to harder problems.

Reference excerpt

Indicators of spatial association are statistics that evaluate the existence of clusters in the spatial arrangement of a given variable. For instance, if we are studying cancer rates among census tracts in a given city local clusters in the rates mean that there are areas that have higher or lower rates than is to be expected by chance alone; that is, the values occurring are above or below those of a random distribution in space.

Global indicators

Notable global indicators of spatial association include:

Global Moran's I: The most commonly used measure of global spatial autocorrelation or the overall clustering of the spatial data developed by Patrick Alfred Pierce Moran. Geary's C (Geary's Contiguity Ratio): A measure of global spatial autocorrelation developed by Roy C. Geary in 1954. It is inversely related to Moran's I, but more sensitive to local autocorrelation than Moran's I. Getis–Ord G (Getis–Ord global G, Geleral G-Statistic): Introduced by Arthur Getis and J. Keith Ord in 1992 to supplement Moran's I.

Local indicators

Notable local indicators of spatial association (LISA) include:

Local Moran's I: Derived from Global Moran's I, it was introduced by Luc Anselin in 1995 and can be computed using GeoDa. Getis–Ord Gi (local Gi): Developed by Getis and Ord based on their global G. INDICATE's IN: Originally developed to assess the spatial distribution of stars, can be computed for any discrete 2+D dataset using python-based INDICATE tool available from GitHub.

See also Spatial analysis Tobler's first law of geography

References

Further reading Bivand, Roger S.; Wong, David W. S. (2018). "Comparing implementations of global and local indicators of spatial association". Test. 27 (3): 716–748. doi:10.1007/s11749-018-0599-x. hdl:11250/2565494. S2CID 125895189.

Illustrations

Worked examples

Example 1 — a first encounter with Indicators of spatial association

Start with the simplest possible case. Write down what Indicators of spatial association 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 Indicators of spatial association 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 Indicators of spatial association 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 Indicators of spatial association

In research: Indicators of spatial association 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 Indicators of spatial association 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: Indicators of spatial association is common in secondary-school and first-year university syllabi. It links to neighbouring topics Spatial analysis, so understanding it makes those chapters shorter.
In everyday life: Look for Indicators of spatial association 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Indicators of spatial association in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Indicators of spatial association 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.
Explain Indicators of spatial association out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Indicators of spatial association in simple terms?

Why does Indicators of spatial association 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 Indicators of spatial association?

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 Indicators of spatial association.