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India - district map

Shades India by district - 641 of them, at ten times the resolution of the state map. The level at which most Indian administrative data is published and most within-state variation lives: a state average hides the fact that its richest district is often several times its poorest.

What it needs

The intuition

A district map is a state map with more regions and less data behind each one. Finer geography looks more precise and is usually less reliable: the same survey spread over 700 districts instead of 30 states gives each unit a twentieth of the sample, so the extremes on the map are mostly the districts where the fewest people were asked.

When to use it

Any district-level Indian data, which is most of what the census, NREGA, the NFHS and the district statistical abstracts publish. Also the honest first look before any within-state claim, because a state average hides the thing you usually want: the richest district of a large state is often several times its poorest.

Where the estimator comes from

For a district with n_d observations the sampling variance of its mean is \sigma^2/n_d, so the SPREAD of estimates across districts is inflated by sampling noise, not just by real variation. The map's extremes are therefore biased outward, and systematically so: the smallest n_d produce the most extreme \bar{v}_d in both directions. Empirical Bayes shrinkage is the standard repair, pulling each district towards the overall mean by a factor that depends on its own sample size - exactly the credibility weight Z=n/(n+k) used in insurance.

What it assumes

Statistical properties

How to read the output

A worked reading

A district map of a rare outcome will always put its darkest colours on the least populous districts, because one event in a district of 5,000 is a rate of 20 per 100,000 while the same event in a district of 500,000 is 0.2. The map appears to show a geographic pattern and is showing a population pattern. Shrinkage fixes it arithmetically, and the diagnostic is simple: plot each district's rate against its denominator, and if the extremes all sit at the left of that plot the map is displaying sample size.

Symptom → diagnosis → what to do

If you see thisIt meansDo this
A few districts far darker than the restSmall samples, most likelyMap the sample size beside it
Salt-and-pepper patternNoise dominatingShrink towards the regional mean
Districts missing from the mapBoundary vintage or a failed name joinJoin on codes and report unmatched counts
A very smooth mapAlready shrunk, or a modelled surfaceCheck what was mapped
A striking clusterMultiple comparisons across hundreds of unitsTest it, do not just point at it
Rates from tiny denominatorsOne event in a small district gives a huge rateSuppress below a minimum denominator

Common mistakes

Where to read this properly

See also

Credibility theory, which is this shrinkage in an insurance setting. State map, for the same data at a coarser scale.

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