placestats

One-person households vs. PISA maths

Fades after adjusting for income

Across 73 countries, One-person households and PISA maths rise and fall together at r = +0.67 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.42, which could easily be chance (q = 0.30, 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 maths, 383 to 479 PISA points, one-person households is 11.8% of households higher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 9.79% of households.

Link before adjusting (r)+0.671p = 8.0e-11 · 73 countries
After adjusting for national income+0.421p = 0.000 · likely range [+0.21, +0.59]
p, allowing for regions0.051standard error 0.152 · 5 regions
Check for luck (q)0.302across 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.

One-person households · % of householdslink with income +0.70 · high
PISA maths · PISA pointslink with income +0.79 · 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

One-person households · % of households →PISA maths · PISA points →1.61%41.1%336575Albania: 9.95% of households, 368 PISA pointsArgentina: 22.8% of households, 378 PISA pointsAustralia: 22.8% of households, 487 PISA pointsAustria: 36.3% of households, 487 PISA pointsBelgium: 34% of households, 489 PISA pointsBulgaria: 30.8% of households, 417 PISA pointsBosnia and Herzegovina: 11.5% of households, 406 PISA pointsBelarus: 38% of households, 472 PISA pointsBrazil: 12% of households, 379 PISA pointsBrunei Darussalam: 7.22% of households, 442 PISA pointsCanada: 28.2% of households, 497 PISA pointsChile: 20.2% of households, 412 PISA pointsColombia: 11.1% of households, 383 PISA pointsCosta Rica: 12.1% of households, 385 PISA pointsCyprus: 20.8% of households, 418 PISA pointsCzechia: 32.5% of households, 487 PISA pointsGermany: 37.3% of households, 475 PISA pointsDominican Republic: 20.1% of households, 339 PISA pointsAlgeria: 1.61% of households, 360 PISA pointsSpain: 23.2% of households, 473 PISA pointsFinland: 41% of households, 484 PISA pointsFrance: 35.5% of households, 474 PISA pointsUnited Kingdom: 30.6% of households, 489 PISA pointsGeorgia: 15% of households, 390 PISA pointsGreece: 25.7% of households, 430 PISA pointsGuatemala: 4.33% of households, 344 PISA pointsHong Kong SAR, China: 18.3% of households, 540 PISA pointsCroatia: 24.6% of households, 463 PISA pointsHungary: 32.1% of households, 473 PISA pointsIndonesia: 7.1% of households, 366 PISA pointsIreland: 22% of households, 492 PISA pointsItaly: 31.1% of households, 471 PISA pointsJamaica: 28.2% of households, 377 PISA pointsJordan: 4.36% of households, 361 PISA pointsJapan: 34.5% of households, 536 PISA pointsKazakhstan: 15.5% of households, 425 PISA pointsCambodia: 3.37% of households, 336 PISA pointsKorea, Rep.: 31.8% of households, 527 PISA pointsLithuania: 31.7% of households, 475 PISA pointsLuxembourg: 33.3% of households, 483 PISA pointsLatvia: 41.1% of households, 483 PISA pointsMacao SAR, China: 15.1% of households, 552 PISA pointsMorocco: 7.2% of households, 365 PISA pointsMoldova: 22.6% of households, 414 PISA pointsMexico: 10.1% of households, 395 PISA pointsNorth Macedonia: 11.8% of households, 389 PISA pointsMalta: 22.6% of households, 466 PISA pointsMontenegro: 15.4% of households, 406 PISA pointsMongolia: 8.96% of households, 425 PISA pointsNorway: 39.6% of households, 468 PISA pointsNew Zealand: 21.9% of households, 479 PISA pointsPanama: 13.4% of households, 357 PISA pointsPeru: 16.8% of households, 391 PISA pointsPhilippines: 9.18% of households, 355 PISA pointsPoland: 24% of households, 489 PISA pointsPortugal: 21.4% of households, 472 PISA pointsParaguay: 10.4% of households, 338 PISA pointsWest Bank and Gaza: 4.31% of households, 366 PISA pointsQatar: 6.98% of households, 414 PISA pointsRomania: 26% of households, 428 PISA pointsRussian Federation: 25.7% of households, 488 PISA pointsSingapore: 16.1% of households, 575 PISA pointsEl Salvador: 8.46% of households, 343 PISA pointsSerbia: 21.8% of households, 440 PISA pointsSlovak Republic: 25.3% of households, 464 PISA pointsSlovenia: 32.6% of households, 485 PISA pointsThailand: 21.6% of households, 394 PISA pointsTunisia: 6.27% of households, 367 PISA pointsUkraine: 25% of households, 441 PISA pointsUruguay: 17.6% of households, 409 PISA pointsUnited States: 27.9% of households, 465 PISA pointsViet Nam: 10.5% of households, 469 PISA pointsKosovo: 3.32% of households, 355 PISA pointsBGRDOMDZAFINGTMHKGJAMJPNKHMLVAMACSGP

best-fit line line after adjusting

Four ways to measure the link

MethodrpCountries
Standard (Pearson), not adjusted+0.6718.0e-1173
By rank (Spearman), not adjusted+0.7111.9e-1273
Standard (Pearson), adjusted for national income+0.4210.00073
By rank (Spearman), adjusted for national income+0.4673.5e-573

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 73 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: +0.250 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from +0.352 (without QAT) to +0.481 (without SGP). 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 (-0.070).

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+0.47
Europe & Central Asia36+0.67
Latin America & Caribbean14+0.31

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 third25+0.35
Middle third24+0.63
Richest third24+0.16

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
Christians49+0.59
Muslims12+0.56

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
Spain14+0.18

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 = +0.421 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 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


% of households
PISA points		Years
Latvia LVA41.1%4832021, 2022
Finland FIN41%4842010, 2022
Norway NOR39.6%4682011, 2022
Belarus BLR38%4722019, 2018
Germany DEU37.3%4752011, 2022
Austria AUT36.3%4872011, 2022
France FRA35.5%4742015, 2022
Japan JPN34.5%5362015, 2022
Belgium BEL34%4892011, 2022
Luxembourg LUX33.3%4832011, 2018
Slovenia SVN32.6%4852015, 2022
Czechia CZE32.5%4872011, 2022
Hungary HUN32.1%4732011, 2022
Korea, Rep. KOR31.8%5272020, 2022
Lithuania LTU31.7%4752011, 2022

United Nations, Department of Economic and Social Affairs, Population Division (2022). Database on Household Size and Composition 2022.
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

One-person households

Share of one-person households

United Nations Department of Economic and Social Affairs, Population Division · via Our World in Data · CC BY 3.0 IGO · updated irregular (2017, 2019 and 2022 editions)

Households of one person, from the same UN collection as the single-parent share and with the same limits: one to three readings per country, from sources that sort households differently, and few after 2019. It rises with age and with income, and falls with family size. That is three different things in one number. No "better" direction is set.

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.

How this was computed

Data used: most recent value in 2010-2025; values come from 2010–2022. 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 One-person households and PISA maths

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

More links with One-person households or PISA maths