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PISA science vs. Pupil-teacher ratio

Fades after adjusting for income

Across 81 countries, PISA science 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 -0.10, which could easily be chance (q = 0.64, 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 science, 403 to 491 PISA points, pupil-teacher ratio is better by 5.29 pupils per teacher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 1.17 pupils per teacher.

Link before adjusting (r)-0.553p = 8.6e-8 · 81 countries
After adjusting for national income-0.102p = 0.367 · likely range [-0.31, +0.12]
p, allowing for regions0.448standard error 0.121 · 5 regions
Check for luck (q)0.640across 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 science · PISA pointslink with income +0.78 · 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

PISA science · PISA points →Pupil-teacher ratio · pupils per teacher →3475618.341.7Albania: 376 PISA points, 17.6 pupils per teacherUnited Arab Emirates: 432 PISA points, 24.5 pupils per teacherAustria: 491 PISA points, 10 pupils per teacherBelgium: 491 PISA points, 11.3 pupils per teacherBulgaria: 421 PISA points, 15.2 pupils per teacherBosnia and Herzegovina: 398 PISA points, 16.9 pupils per teacherBelarus: 471 PISA points, 19.2 pupils per teacherBrazil: 403 PISA points, 20.2 pupils per teacherBrunei Darussalam: 446 PISA points, 9.9 pupils per teacherSwitzerland: 503 PISA points, 9.93 pupils per teacherChile: 444 PISA points, 17.8 pupils per teacherColombia: 411 PISA points, 23.3 pupils per teacherCosta Rica: 411 PISA points, 12.2 pupils per teacherCyprus: 411 PISA points, 12 pupils per teacherCzechia: 498 PISA points, 18.9 pupils per teacherGermany: 492 PISA points, 12.3 pupils per teacherDenmark: 494 PISA points, 10.7 pupils per teacherDominican Republic: 360 PISA points, 18.9 pupils per teacherAlgeria: 376 PISA points, 24.3 pupils per teacherSpain: 485 PISA points, 13.1 pupils per teacherEstonia: 526 PISA points, 11.3 pupils per teacherFinland: 511 PISA points, 13.7 pupils per teacherFrance: 487 PISA points, 18.2 pupils per teacherUnited Kingdom: 500 PISA points, 15.1 pupils per teacherGeorgia: 384 PISA points, 8.98 pupils per teacherGreece: 441 PISA points, 9.38 pupils per teacherGuatemala: 373 PISA points, 20.3 pupils per teacherHong Kong SAR, China: 520 PISA points, 13.3 pupils per teacherCroatia: 483 PISA points, 13.5 pupils per teacherHungary: 486 PISA points, 10.8 pupils per teacherIndonesia: 383 PISA points, 17 pupils per teacherIreland: 504 PISA points, 16.1 pupils per teacherIceland: 447 PISA points, 10.1 pupils per teacherIsrael: 465 PISA points, 12.1 pupils per teacherItaly: 477 PISA points, 11.5 pupils per teacherJamaica: 403 PISA points, 24.8 pupils per teacherJordan: 375 PISA points, 18.5 pupils per teacherJapan: 547 PISA points, 15.7 pupils per teacherKazakhstan: 423 PISA points, 17.2 pupils per teacherCambodia: 347 PISA points, 41.7 pupils per teacherKorea, Rep.: 528 PISA points, 16.3 pupils per teacherLebanon: 384 PISA points, 12.5 pupils per teacherLithuania: 484 PISA points, 13.5 pupils per teacherLuxembourg: 477 PISA points, 8.3 pupils per teacherLatvia: 494 PISA points, 11.5 pupils per teacherMacao SAR, China: 543 PISA points, 13.5 pupils per teacherMorocco: 365 PISA points, 26.8 pupils per teacherMoldova: 417 PISA points, 17.9 pupils per teacherMexico: 410 PISA points, 26.6 pupils per teacherNorth Macedonia: 380 PISA points, 14.9 pupils per teacherMalta: 466 PISA points, 12.9 pupils per teacherMongolia: 412 PISA points, 30.4 pupils per teacherMalaysia: 416 PISA points, 11.7 pupils per teacherNetherlands: 488 PISA points, 11.8 pupils per teacherNorway: 478 PISA points, 8.59 pupils per teacherNew Zealand: 504 PISA points, 14.9 pupils per teacherPanama: 388 PISA points, 22 pupils per teacherPeru: 408 PISA points, 17.4 pupils per teacherPhilippines: 356 PISA points, 29.1 pupils per teacherPoland: 499 PISA points, 10.2 pupils per teacherPortugal: 484 PISA points, 12.4 pupils per teacherParaguay: 368 PISA points, 24.2 pupils per teacherWest Bank and Gaza: 369 PISA points, 24.5 pupils per teacherQatar: 432 PISA points, 12.2 pupils per teacherRomania: 428 PISA points, 19.3 pupils per teacherRussian Federation: 478 PISA points, 21.3 pupils per teacherSaudi Arabia: 390 PISA points, 13.8 pupils per teacherSingapore: 561 PISA points, 14.7 pupils per teacherEl Salvador: 373 PISA points, 26.9 pupils per teacherSerbia: 447 PISA points, 14.3 pupils per teacherSlovak Republic: 462 PISA points, 15.5 pupils per teacherSlovenia: 500 PISA points, 13.8 pupils per teacherSweden: 494 PISA points, 12.2 pupils per teacherThailand: 409 PISA points, 16.6 pupils per teacherTunisia: 386 PISA points, 16.9 pupils per teacherTurkiye: 476 PISA points, 17 pupils per teacherUkraine: 450 PISA points, 13 pupils per teacherUruguay: 435 PISA points, 11 pupils per teacherUnited States: 499 PISA points, 14.2 pupils per teacherUzbekistan: 355 PISA points, 21.5 pupils per teacherViet Nam: 472 PISA points, 20.3 pupils per teacherESTGEOKHMLBNMACMARMKDMNGPHLSGP

best-fit line line after adjusting

Four ways to measure the link

MethodrpCountries
Standard (Pearson), not adjusted-0.5538.6e-881
By rank (Spearman), not adjusted-0.5158.9e-781
Standard (Pearson), adjusted for national income-0.1020.36781
By rank (Spearman), adjusted for national income-0.0680.54681

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: +0.451 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.139 (without GEO) to -0.053 (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 (+0.049).

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.

nr
East Asia & Pacific14+0.13
Europe & Central Asia42+0.00
Latin America & Caribbean13-0.29

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.

nr
Poorest third27-0.24
Middle third27-0.16
Richest third27+0.06

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.

nr
Christians50-0.20
Muslims17-0.10

By last european coloniser

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.

nr
Spain13-0.34

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 = -0.092 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 SGP56114.72022, 2017
Japan JPN54715.72022, 2017
Macao SAR, China MAC54313.52022, 2018
Korea, Rep. KOR52816.32022, 2017
Estonia EST52611.32022, 2017
Hong Kong SAR, China HKG52013.32022, 2018
Finland FIN51113.72022, 2017
New Zealand NZL50414.92022, 2017
Ireland IRL50416.12022, 2012
Switzerland CHE5039.932022, 2017
Slovenia SVN50013.82022, 2016
United Kingdom GBR50015.12022, 2017
United States USA49914.22022, 2017
Poland POL49910.22022, 2017
Czechia CZE49818.92022, 2013

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 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

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 science and Pupil-teacher ratio

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

More links with PISA science or Pupil-teacher ratio