Do Physicians and Pupil-teacher ratio go together across countries?

Across 172 countries the link before adjusting for anything is r = -0.69, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives -0.81.

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 -0.072 (149 countries, 2,181 country-years). Using year-to-year changes, it is -0.010.

Does Physicians 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.

Physicians vs. Pupil-teacher ratio

Holds up after adjusting for income

Across 172 countries, Physicians and Pupil-teacher ratio rise and fall together at r = -0.69 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.20 (q = 0.0071, allowing for the many pairs tested). Much of the first figure is that both measures rise with national income, but a very weak negative link remains.

Comparing countries across the middle half of physicians, 0.413 to 3.4 per 1,000 people, pupil-teacher ratio is better by 15.7 pupils per teacher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 4.44 pupils per teacher.

Link before adjusting (r)-0.694p = 4.6e-26 · 172 countries

After adjusting for national income-0.200p = 0.009 · likely range [-0.34, -0.05]

p, allowing for regions0.000standard error 0.024 · 7 regions

Check for luck (q)0.007across 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.

Physicians · per 1,000 peoplelink with income +0.85 · proxy

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	-0.694	4.6e-26	172
By rank (Spearman), not adjusted	-0.814	6.8e-42	172
Standard (Pearson), adjusted for national income	-0.200	0.009	172
By rank (Spearman), adjusted for national income	-0.368	7.5e-7	172

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 172 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: +0.494 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.247 (without CAF) to -0.178 (without GUY). 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 (-0.047).

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	26	-0.05
Europe & Central Asia	48	-0.33
Latin America & Caribbean	28	-0.24
Middle East, North Africa, Afghanistan & Pakistan	19	-0.23
Sub-Saharan Africa	44	-0.12

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	58	-0.41
Middle third	57	-0.20
Richest third	57	-0.31

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	102	-0.19
Muslims	43	-0.33

By last european coloniser

	n	r
France	23	-0.35
Never a European colony	20	-0.18
Spain	19	-0.32
United Kingdom	56	-0.25

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 = -0.299 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 = -0.072, 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 physicians moved did not tend to see their pupil-teacher ratio move with it.

Across countries (adjusted)-0.200for comparison

Within countries-0.300each country vs itself

…and vs the same year elsewhere-0.072q = 0.261 · 149 countries

Year-on-year changes-0.010q = 0.614

Read with care.

Almost all of this indicator's variation is between countries, not within them, so the within-country estimate rests on a small part of the data.
Much of the within-country association disappears once shared global year effects are removed, which points to a common worldwide trend rather than a country-level relationship.

2,181 country-years (one country in one year), 149 countries, 1990–2019, about 15 years each on average. Share of the variation that happens within countries over time: 8% for Physicians, 9% 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): -0.072. 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 -10), 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

	per 1,000 people	pupils per teacher	Years
Seychelles SYC	6.6	14.5	2022, 2018
Greece GRC	6.58	9.38	2022, 2017
Portugal PRT	5.85	12.4	2022, 2017
Georgia GEO	5.64	8.98	2023, 2018
Austria AUT	5.51	10	2023, 2017
Russian Federation RUS	5.11	21.3	2022, 2017
Andorra AND	5.07	10.5	2023, 2018
Norway NOR	4.97	8.59	2023, 2017
Belarus BLR	4.72	19.2	2023, 2018
Uruguay URY	4.67	11	2022, 2017
San Marino SMR	4.63	6.93	2023, 2018
Germany DEU	4.53	12.3	2022, 2017
Malta MLT	4.51	12.9	2022, 2017
Denmark DNK	4.5	10.7	2021, 2014
Switzerland CHE	4.48	9.93	2022, 2017

World Bank, World Development Indicators
World Bank, World Development Indicators

Sources

Physicians

Physicians (per 1,000 people)

World Health Organization · CC BY 4.0 · updated quarterly

Reported irregularly, so the latest value in the time window used is from a different year for different countries. Hospital beds, already on the site, have no "better" direction, since more beds is not plainly better. More doctors is closer to plainly better, so a direction is set on that basis.

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 2010–2023. 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 Physicians and Pupil-teacher ratio

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