Do Free and fair elections and PISA science go together across countries?

Across 84 countries the link before adjusting for anything is r = +0.53, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.61.

Does the link hold within countries over time, not just across countries?

Comparing each country only with itself across 2006-2022, and setting aside what happened worldwide in each year, the link is +0.113 (55 countries, 324 country-years). Using year-to-year changes, it is —.

Does Free and fair elections cause PISA science?

This analysis cannot answer that. It shows only that the two go together. A link between two country measures, adjusted or not, does not show that either one changes the other. Country figures also say nothing about individual people.

Free and fair elections vs. PISA science

Fades after adjusting for income

Across 84 countries, Free and fair elections and PISA science rise and fall together at r = +0.53 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.31, which could easily be chance (q = 0.46, allowing for the many pairs tested, and allowing for countries in the same region being alike). So the first figure mostly shows richer countries differing from poorer ones, not a link between these two things.

Comparing countries across the middle half of pisa science, 403 to 491 PISA points, free and fair elections is better by 0.238 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.198 points.

Link before adjusting (r)+0.529p = 2.4e-7 · 84 countries

After adjusting for national income+0.313p = 0.004 · likely range [+0.10, +0.50]

p, allowing for regions0.165standard error 0.184 · 5 regions

Check for luck (q)0.465across 12,497 pairs

How to read these.r runs from −1 (one goes up as the other goes down) to +1 (they rise together), and 0 means no link. Adjusting for national income means comparing countries with the same GDP per person, so differences in wealth can’t explain the link. Income is used in percentage terms, since an extra $1,000 means more to a poor country than to a rich one. p is how likely a link this strong would be if there were really none. Below 0.05 means it is unlikely to be chance. Very small values are written in short form: 1.1e-32 means a decimal point followed by 31 zeros and then 11, so very close to zero. The likely range is where the true figure probably lies, and a range that crosses zero means the link could easily be chance. Countries in the same region tend to resemble each other, so the third figure allows for that, which gives a fairer p. The standard error is the typical size of the error in r. Finally, testing this many pairs means some will look strong by luck alone. A q below 0.05 means this link is unlikely to be one of those.

Free and fair elections · index (0-1)link with income +0.61 · high

PISA science · PISA pointslink with income +0.78 · high

Both of these rise and fall closely with national income, so a strong link between them before adjusting was close to certain. Read the adjusted figure, not the first one.

“Link with income” is how closely each measure tracks GDP per person across countries, from −1 to +1.

Every country as a dot

best-fit line line after adjusting

Four ways to measure the link

Method	r	p	Countries
Standard (Pearson), not adjusted	+0.529	2.4e-7	84
By rank (Spearman), not adjusted	+0.609	8.0e-10	84
Standard (Pearson), adjusted for national income	+0.313	0.004	84
By rank (Spearman), adjusted for national income	+0.328	0.002	84

The rank version uses only each country’s place in line, from lowest to highest, so a few extreme countries count for less. The adjusted and unadjusted versions use the same 84 countries: those that report both measures and GDP per person. So the gap between them comes from the adjustment, not from a change in which countries are counted. Drop in the size of r after adjusting: +0.215 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from +0.226 (without QAT) to +0.354 (without HKG). The bar above shows that range on a scale from −1 to +1, with the solid line at the full result. The single country that moves r most: QAT (-0.088).

Within each region

Countries are not separate, unrelated cases, and neighbors share a lot. A link that holds inside each region is far more believable than one that shows up only when comparing regions.

	n	r
East Asia & Pacific	13	+0.37
Europe & Central Asia	44	+0.16
Latin America & Caribbean	15	+0.47

By income third

If the link shows up only in the richest third of countries, it is a feature of rich countries, not a general pattern.

	n	r
Poorest third	28	+0.26
Middle third	28	-0.07
Richest third	28	+0.52

By largest religious group

Countries grouped by a label they share, such as main religion, rather than by a number. Groups of fewer than twelve countries are not shown. These groups differ in income, region and history all at once. So a gap between them is a place to start asking questions, not an answer.

	n	r
Christians	55	+0.06
Muslims	16	+0.24

By last european coloniser

	n	r
Spain	14	+0.41
United Kingdom	13	+0.70

Without outliers (countries far outside the middle half of countries on either measure, by more than one and a half times the width of that middle half): r = +0.313 after dropping 0 countries.

Two series, one country

Both measures over the years for one country you pick. The two charts are stacked so they share only the years along the bottom.

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Over time, within countries

Everything above compares countries with each other at one moment. This section compares each country only with itself over 17years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.

Within countries over time, there is no link that is clearly more than chance (r = +0.113, comparing each country only with itself over the years, and each year only with the same year elsewhere). Whatever the cross-country picture shows, countries whose free and fair elections moved did not tend to see their pisa science move with it.

Across countries (adjusted)+0.313for comparison

Within countries+0.142each country vs itself

…and vs the same year elsewhere+0.113q = 0.619 · 55 countries

Year-on-year changes—q = —

Read with care.

Almost all of this indicator's variation is between countries, not within them, so the within-country estimate rests on a small part of the data.

324 country-years (one country in one year), 55 countries, 2006–2022, about 6 years each on average. Share of the variation that happens within countries over time: 5% for Free and fair elections, 7% for PISA science. The margins of error allow for each country appearing many times, and for each year’s value being close to the year before.

Year-to-year changes are a cautious test, not a final answer. Looking only at changes from one year to the next removes each country’s own trends. But it also makes measurement mistakes louder, which pulls the results toward zero. A near-zero result here is weak evidence of no link, not proof.

With one measure years behind the other

Same year (lag 0): +0.113. A peak away from zero does not show which comes first. These series change slowly — this year’s value is close to last year’s. That makes the curve smooth and nearly symmetric, whatever produced the data. Even a sharp peak at one lag (a gap of some years) would not prove that one measure changes the other.

The largest value on this curve (+0.23 at lag -6) is higher than the same-year one by 0.12. That gap is not a finding. It is the largest of 18 closely related estimates, and picking the biggest of many tests always makes it look bigger. That is exactly why nothing on this site is ranked or chosen by lag.

The data

	index (0-1)	PISA points	Years
Belgium BEL	0.968	491	2025, 2022
Norway NOR	0.966	478	2025, 2022
Australia AUS	0.962	507	2025, 2022
Finland FIN	0.961	511	2025, 2022
Denmark DNK	0.961	494	2025, 2022
Germany DEU	0.957	492	2025, 2022
Spain ESP	0.956	485	2025, 2022
Chile CHL	0.956	444	2025, 2022
New Zealand NZL	0.954	504	2025, 2022
Netherlands NLD	0.954	488	2025, 2022
Estonia EST	0.952	526	2025, 2022
Uruguay URY	0.947	435	2025, 2022
Sweden SWE	0.945	494	2025, 2022
Italy ITA	0.945	477	2025, 2022
Ireland IRL	0.945	504	2025, 2022

Coppedge, M. et al., V-Dem Dataset, Varieties of Democracy (V-Dem) Project
OECD databases as named on each indicator: PISA, Social Expenditure Database (SOCX), Income Distribution Database, Development Assistance Committee statistics, Family Database, Government at a Glance, Corporate Tax Statistics, employment and environment statistics

Sources

Free and fair elections

Free and fair elections index

V-Dem Institute, University of Gothenburg · via Our World in Data · CC BY 4.0 · updated annual

Whether elections are run without voter-registration fraud, widespread irregularities, government threats against the opposition, vote buying or election violence. This asks a narrower question than whether a country is a democracy, and one that is easier to answer. A state can run clean elections while barring the opposition from standing. It can also run dirty elections and still change government. It is the clean-elections part of the electoral democracy index. So its pair with that index, and with liberal and participatory democracy, is built from the same numbers and flagged as such.

PISA science

PISA mean science score

OECD · via Our World in Data · CC BY 4.0 (OECD terms and conditions) · updated annual, except the snapshots noted per indicator

How this was computed

Data used: most recent value in 2010-2025; values come from 2015–2025. To adjust for income, each measure is first predicted from GDP per person (in percentage terms, on a log scale) with a straight-line fit. Only what is left over is then compared. This is called a partial correlation. The line is drawn the standard way (ordinary least squares), which picks the line that comes closest to all the countries at once. The error margins allow for countries in the same region resembling each other, using 5 World Bank regions. The q-value corrects for testing all 12,497 pairs at once, using the Benjamini–Hochberg method. Underlying data last updated DYB 2024. How the country data works · explore Free and fair elections and PISA science

This page shows that two measures go together. It does not show that Free and fair elections changes PISA science, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.