Methodology

Three ways a link can mislead

1. Wealth explains it

Almost every country measure follows the same rich-to-poor line. Life expectancy, corruption, education, crime, internet use and happiness all move with national income. So any two of them seem linked. A link found by comparing countries is usually just a new way of saying “rich countries differ from poor countries”. Income here is a third factor that goes with both measures.

So every pair on this site is shown twice. First comes the link before adjusting for anything (the “raw” figure). Then comes the link after adjusting for income: in effect, comparing countries with the same GDP per person, so income can’t explain the link. This is called a partial correlation. The gap between the two figures is the main number on the site. We measure income in percentage terms (on a log scale). That is because most measures line up with income more closely that way. Technically, we take out of each measure the part that follows income in a straight line, and then correlate what is left. The line is drawn the standard way (ordinary least squares), which picks the line that comes closest to all the countries at once.

Each measure’s development loading is how closely it follows income on its own. It tells you how much work the income adjustment is doing. Two measures that both score above 0.80 are mostly two ways of measuring national income.

2. Countries are not separate, unrelated cases

Neighbours share history, laws, language and ideas. If you treat 195 countries as 195 unrelated cases, the usual math makes results look far more certain than they are. This is known as Galton’s problem. So we also give a more careful measure of uncertainty (“clustered standard errors”; a standard error is how much a result could wobble by chance). It allows for countries in the same region being alike. The site’s wording follows this more careful figure. We also show the link worked out separately inside each region. A link that holds inside Sub-Saharan Africa and inside Western Europe is far more believable than one that only shows up when you compare the two.

There are only seven World Bank regions, which is a small number of groups. So the standard small-sample correction is used, and pairs covering fewer than five regions are flagged.

3. Testing thousands of pairs at once

With 163 measures there are 12,497 different pairs. At the usual 5% cut-off, about 625of them would look real (“significant”) by chance alone. So every list of findings here is ranked by a figure that allows for this, called a q-value (the Benjamini–Hochberg method). It is adjusted for every pair tested. Each page also says how many pairs were tested. An adjusted figure means nothing unless you know how many tests it was adjusted for.

Within countries, over time

Everything above compares countries with each other at one moment. That can’t rule out anything fixed about a country, such as its history, geography, laws, religion or colonial past. It also can’t tell “democracies have more X” apart from “X rises when a country becomes democratic”. So every pair is also checked within countries across 1990–2025. This compares each country only with itself over the years.

That view has its own trap, much like the wealth trap. Almost every measure here rises over time. Life expectancy, internet use, city living and schooling all go up nearly everywhere. Two measures that both rise in every country will look almost perfectly linked within countries, whether or not they are related. Comparing each country only with itself would create links out of shared world-wide progress.

So three versions are shown. Each one rules out one more thing:

• Country fixed effects: compares each country only with its own average. Still open to world-wide trends.
• Two-way fixed effects (country and year): also compares each year only with the same year in other countries. That rules out whatever happened to the whole world in a given year. This is the main within-country figure.
• First differences(with year adjustments): compares one year’s changein one measure with the same year’s change in the other. This also rules out each country’s own steady trend, which the two-way version leaves in. It is the strictest of the three.

A link that shows in the first version but not the second is a shared world-wide trend. One that shows in the second but not the third is likely a trend inside each country. Neither tells you how the world works. Across this data, 1762 pairs lose most of their within-country link once each year is compared only with the same year elsewhere. And for 2799 of them the link flips direction between the first two versions.

The uncertainty allows for each country’s years resembling each other (standard errors are clustered by country). The math also counts every adjustment made. Year-to-year changes are only taken between back-to-back years with data, never across a gap. A pair needs at least 25 countries, each with five or more years of data, before any within-country figure is shown.

First differences are strict, not final. Looking at year-to-year changes rules out each country’s own trend. But small measuring errors loom large in those changes, which pulls the results toward zero. So a result near zero is weak evidence that there is no link. It is not proof.

Links across years, and why nothing is ranked by them

Pair pages show the link between one measure and the other from 10 years before to 10years after (“lags” from −10 to +10). It uses the same two-way comparison as above. It is a check, and on purpose it is notused to find anything. No pair is ranked by its lag, no “best lag” is reported, and the lag points carry no q-values.

There is a good reason for this. Trying 21 gaps per pair and keeping the biggest means picking the best of many similar tries. That always makes the result look stronger than it is. Across the 2468 published curves, the gain from picking the best gap over the same-year figure is small for most pairs. The middle value is 0.04 in the size of r. But it reaches 0.14 for the top tenth of pairs and 0.44 at worst. More to the point: 1122 pairs have a same-year link below 0.1 either way. Of those, 616 — 55% — reach 0.1 at some gap. A site that ranked by gap could turn more than a third of its own “no link” pairs into findings, while every single page still looked careful.

The shape of the curves says the same thing. If one measure really moved ahead of the other, peaks would sit somewhere in the middle of the range. Instead 580curves peak at exactly ±10 years. That is the edge of the search, where the curve is still moving when it runs out. Only 244 peak at zero. That pattern means the measures change slowly, not that one comes first. Pair pages flag it when it happens, and the lag study page shows every pair with both summaries.

Even a sharp peak in the middle of the range would not show which way things run. One measure moving before another does not prove cause. Two measures that both follow a third factor at different speeds give exactly that shape.

Shared ingredients and shared constructs

Two more ways a link can be real and still tell you nothing.

Shared ingredients: the scores literally contain each other. V-Dem’s liberal democracy score is built on top of its electoral democracy score. The six Worldwide Governance Indicators come from one shared pool of surveys. V-Dem is itself one of the sources Transparency International blends into its Corruption Perceptions Index (CPI). These scores are built from the same numbers, so they are bound to match partly. That part of the link is just arithmetic. The pair page says so and names the shared part.

Shared constructs: different groups, different raw material, same idea being measured. Freedom House and V-Dem both rate how democratic a country is. That they agree shows they measure well. It is not a discovery about the world. Without this check, the site’s “strongest findings” list would just be scores agreeing with themselves.

Checking that results hold up

Every pair carries four checks a doubtful reader would run:

• Leave-one-country-out: worked out again with each country left out in turn. Is this Luxembourg, or is it the world?
• Outlier-trimmed: extreme values on either measure are removed. (Technically, values more than 1.5 times the spread of the middle half, or 1.5×IQR, beyond that middle half.)
• Within region: see above.
• By income third: countries split into poorest, middle and richest thirds. A link that exists only in the richest third is a feature of rich countries, not a general one.

The data

163 measures across 218 countries. Each snapshot takes most recent value in 2010-2025. The year each value came from is recorded. Where a pair mixes years from different countries, the page says so.

We are strict about matching countries. Groups of countries (“World”, “Sub-Saharan Africa”, “High-income countries”) never enter a link. Countries that no longer exist are dropped, not stitched onto the countries that followed them. Putting the USSR’s figures onto Russia is a choice with real effects, and we will not make it quietly. Unclear names are never guessed. “Congo” and “Korea” each name two countries. So a source that spells them unclearly is rejected, rather than giving one country’s data to another. Breaks where a source changed its method are strict filters, not footnotes. Corruption Perceptions Index scores from before 2012 use a different scale, so they never enter the data at all.

What is worked out where

The full data set is small enough to send to your browser. So the explorer works out the links on your own computer as you change the adjustments. Nothing is sent to a server. The stored results, q-values and robustness checks come from a Python program when the site is built. Both versions are tested against each other on every build. If they ever disagree to eight decimal places, the build fails.

What this does not do

• No claims of cause. No special methods that try to prove cause (such as instrumental variables or difference-in-differences). No wording that says one measure moves another. Only wording about things going together, and a test enforces it.
• Nothing about individual people. Links between countries say nothing about people. If countries with more of X have more of Y, that does not mean people with X have more Y. Treating it that way is called the ecological fallacy. This site describes places, not individual people.
• No forecasting, and no data for regions inside countries.
• Fixed effects do not prove cause. Comparing each country with itself rules out everything about it that stays the same. But something that changes over time, and moves with both measures, could still create a link. It is a better test than comparing countries at one moment, but it does not show cause.
• Missing data is not random. Poorer and less democratic countries report fewer measures. So every link is worked out on a group of countries that is richer and freer than the world as a whole. In this data, how many measures a country reports goes with democracy more closely than with income.