Do Health coverage index and Tertiary enrollment go together across countries?

Across 170 countries the link before adjusting for anything is r = +0.74, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.78.

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

Comparing each country only with itself across 2000-2023, and setting aside what happened worldwide in each year, the link is -0.102 (166 countries, 2,896 country-years). Using year-to-year changes, it is -0.012.

Does Health coverage index cause Tertiary enrollment?

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.

Health coverage index vs. Tertiary enrollment

Fades after adjusting for income

Across 170 countries, Health coverage index and Tertiary enrollment rise and fall together at r = +0.74 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.29, which could easily be chance (q = 0.11, 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 tertiary enrollment, 17.2% to 71.8% gross, health coverage index is better by 18.6 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 5.36 points.

Link before adjusting (r)+0.741p = 7.7e-31 · 170 countries

After adjusting for national income+0.292p = 0.000 · likely range [+0.15, +0.42]

p, allowing for regions0.003standard error 0.062 · 7 regions

Check for luck (q)0.109across 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.

Health coverage index · index, 0 to 100link with income +0.88 · proxy

Tertiary enrollment · % grosslink with income +0.75 · 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

best-fit line line after adjusting

Four ways to measure the link

Method	r	p	Countries
Standard (Pearson), not adjusted	+0.741	7.7e-31	170
By rank (Spearman), not adjusted	+0.785	1.1e-36	170
Standard (Pearson), adjusted for national income	+0.292	0.000	170
By rank (Spearman), adjusted for national income	+0.324	1.8e-5	170

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 170 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 +0.269 (without GUY) to +0.323 (without GRC). 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: GRC (+0.031).

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	24	+0.28
Europe & Central Asia	50	+0.11
Latin America & Caribbean	27	+0.42
Middle East, North Africa, Afghanistan & Pakistan	20	+0.60
Sub-Saharan Africa	41	+0.24

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	57	+0.61
Middle third	56	+0.17
Richest third	57	+0.27

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	99	+0.23
Muslims	44	+0.52

By last european coloniser

	n	r
France	23	+0.72
Never a European colony	21	+0.18
Spain	17	+0.09
United Kingdom	54	+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 = +0.330 after dropping 2 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 24years. 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 = -0.102, 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 health coverage index moved did not tend to see their tertiary enrollment move with it.

Across countries (adjusted)+0.292for comparison

Within countries+0.481each country vs itself

…and vs the same year elsewhere-0.102q = 0.187 · 166 countries

Year-on-year changes-0.012q = 0.652

The direction flips. Comparing each country only with itself gives +0.48. Also taking out what happened to the whole world each year gives -0.10. So the first figure was picking up a trend both measures share with worldwide progress, not a link between them.

Read with care.

Almost all of the second indicator's variation is between countries, 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.

2,896 country-years (one country in one year), 166 countries, 2000–2023, about 17 years each on average. Share of the variation that happens within countries over time: 14% for Health coverage index, 8% for Tertiary enrollment. 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): -0.102. 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

	index, 0 to 100	% gross	Years
Canada CAN	92	76.3%	2023
Iceland ISL	90	76.5%	2023
New Zealand NZL	89	77.2%	2023, 2024
Norway NOR	89	95.5%	2023, 2024
Australia AUS	89	108%	2023, 2024
United States USA	88	79.4%	2023, 2022
Singapore SGP	88	97.3%	2023
Korea, Rep. KOR	88	112%	2023, 2024
United Kingdom GBR	88	80.4%	2023
Germany DEU	87	76.7%	2023, 2024
Switzerland CHE	87	73.5%	2023, 2024
Japan JPN	86	64.5%	2023
Finland FIN	86	110%	2023, 2024
Belgium BEL	86	82.1%	2023
Uruguay URY	85	80%	2023

World Health Organization, Global Health Observatory
World Bank, World Development Indicators

Sources

Health coverage index

Universal health coverage service coverage index

World Health Organization · via Our World in Data · CC BY-NC-SA 4.0 · updated annual

Fourteen "tracer" measures of basic health services, combined by WHO into one index. They include vaccination, care during pregnancy, treatment of tuberculosis and HIV, and hospital beds and staff. Several of those measures are on the site on their own. So a link with any of them is partly the index matching a part of itself.

Tertiary enrollment

School enrollment, tertiary (% gross)

UNESCO Institute for Statistics · CC BY 4.0 · updated quarterly

How this was computed

Data used: most recent value in 2010-2025; values come from 2010–2025. 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 Health coverage index and Tertiary enrollment

This page shows that two measures go together. It does not show that Health coverage index changes Tertiary enrollment, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.