Glossary

Correlation (r)

also: r, Pearson correlation

A single number, written r, for how closely two measures rise and fall together across places. It runs from −1 to +1. At +1 the two always go up together; at −1 one always goes down as the other goes up; at 0 knowing one tells you nothing about the other. On this site 0.7 or more (either sign) is called strong, 0.4 to 0.7 moderate, and below 0.4 weak. A correlation shows that two things go together. It does not show that one changes the other.

p-value

also: p, statistically significant

Even two unrelated measures will show some link just by luck. The p-value is the chance of seeing a link at least as strong as this one if there were really none. A p of 0.05 means a 1-in-20 chance. By custom, 0.05 or less is called “statistically significant”, which only means “unlikely to be chance”. It does not mean the link is large or important. Very small values are written like 3.1e-16, which means 0.00000000000000031.

Standard deviation

also: SD, sd, standardised

How spread out the values are: roughly, how far a typical country sits from the average. If the average life expectancy is 73 years and the standard deviation is 7 years, most countries fall within about 7 years of 73. To put different measures on one scale (“standardising”), each value is turned into how many of these gaps it sits above or below the average. So a score of +1 means one typical gap above average, and −2 means two below.

Median

also: middle value

Put every value in order and take the one in the middle: half are above it, half below. Unlike an average, a few extreme values cannot pull it far. The “middle half” is the range from one quarter of the way up the list to three quarters of the way up.

Percentage terms (log scale)

also: logarithm, log

Some measures, such as income, are compared by how many times bigger one value is than another, not by the gap in dollars. On this scale (a logarithm, or “log”) doubling counts the same wherever it happens: $1,000 to $2,000 is the same step as $10,000 to $20,000. Most country measures line up with income much better this way.

Purchasing power parity (PPP)

also: PPP, international dollars

A dollar buys much more in some countries than others, since prices differ. Figures “at PPP” are adjusted for this, so they show what money actually buys. They are given in “international dollars”: an international dollar buys in each country what a US dollar buys in the United States. GDP per person at PPP is the income measure this site adjusts for.

GDP per person

also: GDP per capita, national income

Gross domestic product (GDP) is the value of all the goods and services a country produces in a year. Divided by the number of people (“per capita” means per person), it is the usual measure of how rich a country is. GNI, gross national income, is close to it but also counts income earned abroad.

Human Development Index (HDI)

also: HDI

A score from the United Nations Development Programme, from 0 to 1 (higher is better). It combines three things: how long people live (life expectancy), how much schooling they get (expected and average years), and income per person. The inequality-adjusted version lowers the score where these are shared unequally.

Gini index

also: Gini coefficient

A measure of how unequally income is shared. At 0 everyone has the same income; at the top of the scale one person has all of it. Some publishers use 0 to 1, others 0 to 100. Most countries fall between about 0.25 and 0.60 (25 and 60). “Market income” Gini is before taxes and government payments; the gap between that and the after-tax figure shows how much taxes and payments even things out.

Partial correlation

also: controlled correlation

A correlation, written r, shows how closely two measures rise and fall together. It runs from −1 (they move in opposite directions) to +1 (they move in step). 0 means no link.

A partial correlation is the same thing after adjusting for a third measure. In effect, it compares countries that are alike in that third measure, so it can’t explain the link. On this site the usual adjustment is for national income: GDP per person, in percentage terms. For example, rich countries have both more internet users and longer lives. The partial correlation asks whether the two still go together among countries with the same income.

How it is worked out: first remove from each measure the part that follows income in a straight line. Then correlate what is left over (the “residuals”). It is written r_xy·z: the link between x and y with z held fixed. The gap between the link before adjusting (the “raw” figure) and after it is the main number on this site.

Development gradient

Almost every country measure moves with national income. Richer countries have longer lives, more schooling, more internet access, less reported corruption and happier survey answers. Since they all follow that one line, any two of them seem linked, even if neither has anything to do with the other. Most published links between country measures are really this income pattern seen from one angle.

Development loading

A number we give each measure: how closely its ranking of countries matches their ranking by income (GDP per person). A measure above 0.80 is, roughly, national income measured another way. Finding that two of those go together tells you very little. A measure below 0.30 mostly doesn’t follow income, so adjusting for income is a real test rather than a formality. It is measured against the same income figures we adjust for. So it describes this set of measures. It is not separate evidence about the world.

Ecological fallacy

The mistake of judging individual people from a pattern among groups. If countries with more of X have more of Y, that does not mean people with more of X have more of Y. The pattern among countries can even be the opposite of the pattern among people. Everything on this site is measured for whole countries. It describes places, not individual people, so nothing here supports a claim about people.

Galton's problem

also: spatial autocorrelation, non-independence

Named after a point Francis Galton made at a meeting in 1888: societies are not separate, unrelated cases. They copy each other and grow out of each other. Neighbouring countries look alike. If you treat 195 countries as 195 unrelated cases, the usual math makes the results look far more certain than they are. So this site also gives a more careful measure of uncertainty that allows for countries in the same region being alike. It also shows each link worked out separately inside each region.

Clustered standard errors

A standard error says how much a result could wobble by chance. The usual kind assumes every country is unrelated to every other. The clustered kind allows for countries in the same group being alike. Here the group is the World Bank region. Clustered errors are usually larger, sometimes several times larger. The chance figure that comes from them (the p-value) is the honest one. With only seven regions, a small extra correction is used. Pairs covering fewer than five regions are flagged.

False discovery rate (FDR)

also: Benjamini-Hochberg, q-value

Test enough things and some will look real just by luck. The false discovery rate is the share of “real-looking” results you would expect to be flukes. With 163 measures there are 12,497 pairs. At the usual 5% cut-off, about 625 would look real by chance alone. A method called Benjamini–Hochberg adjusts each chance figure (p-value) for how many tests were run. The result is called a q-value. An adjusted figure means nothing unless you know how many tests it was adjusted for. So every page here says how many pairs were tested.

Shared ingredient

Many measures are combined scores, and they often 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. When two measures are built from the same numbers, they are bound to match partly. That part of the link is just arithmetic, and the pair page names the shared part.

Convergent measurement

also: shared construct, convergent validity

Different groups, different raw material, same idea being measured. Freedom House and V-Dem both rate how democratic a country is, and they agree closely (r ≈ 0.93). That tells you both tools do their job well. It does not mean you have found a link between two different things. This is not the same as a shared ingredient, where the scores are built from literally the same parts.

Fixed effects

also: within-country estimate, two-way fixed effects

Comparing each country only with itself over the years. We take away each country’s own average first, so only its ups and downs count. This rules out anything about a country that stays the same: its history, geography, laws and culture. “Two-way” also compares each year only with the same year elsewhere. That rules out whatever happened to the whole world in a given year. This matters because most measures here rise everywhere over time. Any two rising lines will look linked, whether or not they are. This is a better test, but it still does not prove cause. Something else that changed over the same years could still explain the link.

First differences

Comparing how much X changed from one year to the next with how much Y changed, rather than comparing their levels. For example: did a country’s schooling rise in the same years its income rose? This rules out each country’s own steady trend, which fixed effects leave in. It is the strictest test on the site. It also tends to give the weakest numbers. Small measuring errors loom large in year-to-year changes, and that pulls results toward zero. So a result near zero is weak evidence that there is no link. It is not proof.

Spearman rank correlation

A correlation worked out from each country’s rank (1st, 2nd, 3rd…) rather than its actual value. It picks up any pattern where one measure keeps rising (or keeps falling) as the other rises, not just a straight line. A single extreme country can’t dominate it. The usual kind, Pearson, uses the actual values. When the two differ a lot, the pattern is curved or a few extreme countries are steering it. That is why both are always shown.

Lag selection

also: lag shopping, time-shifted correlation

Comparing X in one year with Y some years later, and reporting whichever gap gives the strongest link. Picking the best of many similar tries makes the result look stronger than it is, every time. Among the pairs here whose same-year link is below 0.1, more than a third reach 0.1 at some gap. Pair pages show these lag curves as a check. They are good for seeing that a link is absent, or how fast it fades over the years. But nothing is ranked or picked by them. A peak at the very end of the range searched is a warning sign. It means the curve was still moving when the search stopped.

Leave-one-out

Working out the correlation again with each country left out in turn. The spread of the results shows whether the finding holds across the world or rests on one unusual country. If leaving out Luxembourg or Rwanda changes the correlation a lot, the pair page says so and names the country.