Do HDI and PISA maths go together across countries?

Across 85 countries the link before adjusting for anything is r = +0.81, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.82.

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

Comparing each country only with itself across 2003-2022, and setting aside what happened worldwide in each year, the link is +0.345 (55 countries, 360 country-years). Using year-to-year changes, it is —.

Does HDI cause PISA maths?

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.

HDI vs. PISA maths

Holds up after adjusting for income

Across 85 countries, HDI and PISA maths rise and fall together at r = +0.81 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.44 (q = 0.034, allowing for the many pairs tested). Much of the first figure is that both measures rise with national income, but a moderate positive link remains.

Comparing countries across the middle half of pisa maths, 389 to 482 PISA points, hdi is better by 0.118 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.0391 points.

Link before adjusting (r)+0.815p = 2.4e-21 · 85 countries

After adjusting for national income+0.439p = 2.9e-5 · likely range [+0.25, +0.60]

p, allowing for regions0.013standard error 0.103 · 5 regions

Check for luck (q)0.034across 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.

HDI · index, 0 to 1link with income +0.96 · proxy

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

best-fit line line after adjusting

Four ways to measure the link

Method	r	p	Countries
Standard (Pearson), not adjusted	+0.815	2.4e-21	85
By rank (Spearman), not adjusted	+0.821	7.1e-22	85
Standard (Pearson), adjusted for national income	+0.439	2.9e-5	85
By rank (Spearman), adjusted for national income	+0.425	5.5e-5	85

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 85 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: +0.376 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from +0.384 (without QAT) to +0.495 (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: SGP (+0.056).

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	14	+0.55
Europe & Central Asia	43	+0.25
Latin America & Caribbean	15	+0.52

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	29	+0.44
Middle third	28	+0.19
Richest third	28	+0.52

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	55	+0.39
Muslims	17	+0.16

By last european coloniser

	n	r
Spain	14	+0.71
United Kingdom	14	+0.45

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 = +0.439 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.

Loading…

Over time, within countries

Everything above compares countries with each other at one moment. This section compares each country only with itself over 20years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.

The link shows up within countries over time (r = +0.345) but mostly disappears in year-to-year changes (r = —). That points to slow trends particular to each country, not the two measures moving together from year to year.

Across countries (adjusted)+0.439for comparison

Within countries-0.020each country vs itself

…and vs the same year elsewhere+0.345q = 0.001 · 55 countries

Year-on-year changes—q = —

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.

360 country-years (one country in one year), 55 countries, 2003–2022, about 7 years each on average. Share of the variation that happens within countries over time: 5% for HDI, 10% for PISA maths. 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): +0.345. 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.

The data

	index, 0 to 1	PISA points	Years
Iceland ISL	0.972	459	2023, 2022
Norway NOR	0.97	468	2023, 2022
Switzerland CHE	0.97	508	2023, 2022
Denmark DNK	0.962	489	2023, 2022
Sweden SWE	0.959	482	2023, 2022
Germany DEU	0.959	475	2023, 2022
Australia AUS	0.958	487	2023, 2022
Netherlands NLD	0.955	493	2023, 2022
Hong Kong SAR, China HKG	0.955	540	2023, 2022
Belgium BEL	0.951	489	2023, 2022
Ireland IRL	0.949	492	2023, 2022
Finland FIN	0.948	484	2023, 2022
Singapore SGP	0.946	575	2023, 2022
United Kingdom GBR	0.946	489	2023, 2022
United Arab Emirates ARE	0.94	431	2023, 2022

United Nations Development Programme, Human Development Report 2025
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

HDI

Human Development Index

United Nations Development Programme, Human Development Report Office · via Our World in Data · CC BY 3.0 IGO · updated annual

The geometric mean (a kind of average that multiplies the parts together) of three parts: income per person (GNI per capita), life expectancy, and schooling (expected years and average years). All four inputs are on this site, and each is flagged. So a link between the HDI and any of them is shown for what it is: the index matching a part of itself. For the same reason it is kept out of this site's own topic scores. Those already contain its parts, and adding it would count each twice. It is the most-cited development index there is. It is here mostly so its parts can be read separately.

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 2015–2023. 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 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 HDI and PISA maths

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