Do Free and fair elections and Pupil-teacher ratio go together across countries?

Across 155 countries the link before adjusting for anything is r = -0.55, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives -0.59.

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

Comparing each country only with itself across 1990-2019, and setting aside what happened worldwide in each year, the link is -0.055 (163 countries, 3,293 country-years). Using year-to-year changes, it is +0.018.

Does Free and fair elections cause Pupil-teacher ratio?

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. Pupil-teacher ratio

Fades after adjusting for income

Across 155 countries, Free and fair elections and Pupil-teacher ratio rise and fall together at r = -0.55 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.22, which could easily be chance (q = 0.22, 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 free and fair elections, 0.271 to 0.869 points, pupil-teacher ratio is better by 13.1 pupils per teacher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 3.62 pupils per teacher.

Link before adjusting (r)-0.547p = 1.7e-13 · 155 countries

After adjusting for national income-0.216p = 0.007 · likely range [-0.36, -0.06]

p, allowing for regions0.069standard error 0.098 · 7 regions

Check for luck (q)0.218across 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

Pupil-teacher ratio · pupils per teacherlink with income -0.83 · proxy

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	-0.547	1.7e-13	155
By rank (Spearman), not adjusted	-0.586	1.1e-15	155
Standard (Pearson), adjusted for national income	-0.216	0.007	155
By rank (Spearman), adjusted for national income	-0.214	0.008	155

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 155 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: +0.331 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.238 (without MWI) to -0.196 (without LBR). 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: MWI (-0.022).

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	20	-0.22
Europe & Central Asia	46	-0.27
Latin America & Caribbean	20	-0.72
Middle East, North Africa, Afghanistan & Pakistan	18	-0.25
Sub-Saharan Africa	44	-0.29

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	52	-0.34
Middle third	51	-0.04
Richest third	52	-0.19

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	93	-0.35
Muslims	41	-0.28

By last european coloniser

	n	r
France	23	-0.11
Never a European colony	20	-0.16
Spain	18	-0.59
United Kingdom	42	-0.15

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 = -0.262 after dropping 6 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 30years. 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 = -0.055, 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 pupil-teacher ratio move with it.

Across countries (adjusted)-0.216for comparison

Within countries-0.183each country vs itself

…and vs the same year elsewhere-0.055q = 0.424 · 163 countries

Year-on-year changes+0.018q = 0.704

Read with care.

Almost all of the second indicator's variation is between countries, so the within-country estimate rests on a small part of the data.

3,293 country-years (one country in one year), 163 countries, 1990–2019, about 20 years each on average. Share of the variation that happens within countries over time: 13% for Free and fair elections, 10% for Pupil-teacher ratio. 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): -0.055. 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 data

	index (0-1)	pupils per teacher	Years
Belgium BEL	0.968	11.3	2025, 2017
Norway NOR	0.966	8.59	2025, 2017
Finland FIN	0.961	13.7	2025, 2017
Denmark DNK	0.961	10.7	2025, 2014
Germany DEU	0.957	12.3	2025, 2017
Spain ESP	0.956	13.1	2025, 2017
Chile CHL	0.956	17.8	2025, 2017
New Zealand NZL	0.954	14.9	2025, 2017
Netherlands NLD	0.954	11.8	2025, 2017
Estonia EST	0.952	11.3	2025, 2017
Uruguay URY	0.947	11	2025, 2017
Sweden SWE	0.945	12.2	2025, 2017
Italy ITA	0.945	11.5	2025, 2017
Ireland IRL	0.945	16.1	2025, 2012
Luxembourg LUX	0.944	8.3	2025, 2016

Coppedge, M. et al., V-Dem Dataset, Varieties of Democracy (V-Dem) Project
World Bank, World Development Indicators

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.

Pupil-teacher ratio

Pupil-teacher ratio, primary

UNESCO Institute for Statistics · CC BY 4.0 · updated quarterly

The World Bank's copy stops at 2019.

How this was computed

Data used: most recent value in 2010-2025; values come from 2010–2025. 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 7 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 Pupil-teacher ratio

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