Do One-person households and Pupil-teacher ratio go together across countries?

Across 140 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 -0.61.

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 -0.095 (32 countries, 218 country-years). Using year-to-year changes, it is —.

Does One-person households 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.

One-person households vs. Pupil-teacher ratio

Fades after adjusting for income

Across 140 countries, One-person households 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 -0.03, which could easily be chance (q = 0.69, 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 one-person households, 6.93% to 22.7% of households, pupil-teacher ratio is better by 11.2 pupils per teacher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.455 pupils per teacher.

Link before adjusting (r)-0.553p = 1.4e-12 · 140 countries

After adjusting for national income-0.028p = 0.745 · likely range [-0.19, +0.14]

p, allowing for regions0.505standard error 0.039 · 7 regions

Check for luck (q)0.686across 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

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	-0.553	1.4e-12	140
By rank (Spearman), not adjusted	-0.612	1.0e-15	140
Standard (Pearson), adjusted for national income	-0.028	0.745	140
By rank (Spearman), adjusted for national income	-0.051	0.551	140

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 140 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: +0.525 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.056 (without CAF) to -0.005 (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: CAF (-0.028).

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	21	-0.17
Europe & Central Asia	37	-0.05
Latin America & Caribbean	25	-0.40
Sub-Saharan Africa	39	-0.21

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	47	+0.03
Middle third	46	-0.13
Richest third	47	-0.25

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	87	-0.08
Muslims	32	+0.13

By last european coloniser

	n	r
France	21	+0.28
Never a European colony	14	-0.17
Spain	15	-0.47
United Kingdom	39	-0.06

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 = -0.089 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 = -0.095, 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 one-person households moved did not tend to see their pupil-teacher ratio move with it.

Across countries (adjusted)-0.028for comparison

Within countries-0.189each country vs itself

…and vs the same year elsewhere-0.095q = 0.409 · 32 countries

Year-on-year changes—q = —

218 country-years (one country in one year), 32 countries, 1990–2019, about 7 years each on average. Share of the variation that happens within countries over time: 20% for One-person households, 13% 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): -0.095. 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.

This curve peaks at the edge of the window (lag -4), so it is still drifting where the search stops. That pattern usually reflects a slow trend left over in the data, not a link with real timing. The peak value should not be read as the “true” link at the right lag.

The data

	% of households	pupils per teacher	Years
Latvia LVA	41.1%	11.5	2021, 2017
Finland FIN	41%	13.7	2010, 2017
Norway NOR	39.6%	8.59	2011, 2017
Belarus BLR	38%	19.2	2019, 2018
Germany DEU	37.3%	12.3	2011, 2017
Austria AUT	36.3%	10	2011, 2017
France FRA	35.5%	18.2	2015, 2013
Japan JPN	34.5%	15.7	2015, 2017
Bermuda BMU	34.1%	10.4	2016, 2015
Belgium BEL	34%	11.3	2011, 2017
Turks and Caicos Islands TCA	33.6%	17.7	2019, 2018
Luxembourg LUX	33.3%	8.3	2011, 2016
Slovenia SVN	32.6%	13.8	2015, 2016
Czechia CZE	32.5%	18.9	2011, 2013
Hungary HUN	32.1%	10.8	2011, 2016

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

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.

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 2010–2021. 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 One-person households and Pupil-teacher ratio

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