Do PISA maths and Pupil-teacher ratio go together across countries?

Across 81 countries the link before adjusting for anything is r = -0.56, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives -0.53.

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

There are not enough years of data within countries to check this over time.

Does PISA maths 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.

PISA maths vs. Pupil-teacher ratio

Fades after adjusting for income

Across 81 countries, PISA maths and Pupil-teacher ratio rise and fall together at r = -0.56 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.11, which could easily be chance (q = 0.72, 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. Caution: direction is not consistent across regions.

Comparing countries across the middle half of pisa maths, 389 to 482 PISA points, pupil-teacher ratio is better by 5.35 pupils per teacher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 1.23 pupils per teacher.

Link before adjusting (r)-0.556p = 7.2e-8 · 81 countries

After adjusting for national income-0.107p = 0.346 · likely range [-0.32, +0.12]

p, allowing for regions0.553standard error 0.165 · 5 regions

Check for luck (q)0.721across 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.

PISA maths · PISA pointslink with income +0.79 · 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	-0.556	7.2e-8	81
By rank (Spearman), not adjusted	-0.535	2.7e-7	81
Standard (Pearson), adjusted for national income	-0.107	0.346	81
By rank (Spearman), adjusted for national income	-0.102	0.369	81

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 81 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: +0.449 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.136 (without MNG) to -0.066 (without ARE). 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: ARE (+0.041).

Fragile: this link may not hold up.

direction is not consistent across regions

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	14	+0.26
Europe & Central Asia	42	+0.01
Latin America & Caribbean	13	-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	27	-0.27
Middle third	27	-0.13
Richest third	27	+0.02

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	50	-0.28
Muslims	17	-0.10

By last european coloniser

	n	r
Spain	13	-0.28

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 = -0.140 after dropping 3 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 0years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.

Not enough history inside each country to look at this over time. That needs countries measured for several years in a row, and at least one of these measures is measured too rarely.

The data

	PISA points	pupils per teacher	Years
Singapore SGP	575	14.7	2022, 2017
Macao SAR, China MAC	552	13.5	2022, 2018
Hong Kong SAR, China HKG	540	13.3	2022, 2018
Japan JPN	536	15.7	2022, 2017
Korea, Rep. KOR	527	16.3	2022, 2017
Estonia EST	510	11.3	2022, 2017
Switzerland CHE	508	9.93	2022, 2017
Netherlands NLD	493	11.8	2022, 2017
Ireland IRL	492	16.1	2022, 2012
Belgium BEL	489	11.3	2022, 2017
Denmark DNK	489	10.7	2022, 2014
United Kingdom GBR	489	15.1	2022, 2017
Poland POL	489	10.2	2022, 2017
Russian Federation RUS	488	21.3	2018, 2017
Austria AUT	487	10	2022, 2017

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
World Bank, World Development Indicators

Sources

PISA maths

PISA mean mathematics score

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

The average score of 15-year-olds on the same test in every country taking part. It is scaled so the OECD average in the starting year was 500, with a standard deviation (a typical gap between students) of 100. Held every three years. The 2021 round was held in 2022, and the OECD says it can still be compared with earlier rounds despite the pandemic. The three subjects are treated as measuring the same thing. Their links with each other are above 0.95, and that close match is a fact about the test, not about schooling.

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 2012–2022. 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 PISA maths and Pupil-teacher ratio

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