PISA science vs. Small government (Fraser)
Fades after adjusting for income
Across 83 countries, PISA science and Small government (Fraser) 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 -0.26, 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 small government (Fraser), 5.82 to 7.31 points, PISA science is worse by 40.2 PISA points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 14.7 PISA points.
Link before adjusting (r)-0.548p = 8.2e-8 · 83 countries
After adjusting for national income-0.258p = 0.019 · likely range [-0.45, -0.04]
p, allowing for regions0.136standard error 0.139 · 5 regions
Check for luck (q)0.302across 17,292 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.
PISA science · PISA pointslink with income +0.78 · high
Small government (Fraser) · rating (0-10)link with income -0.32 · moderate
“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 | -0.548 | 8.2e-8 | 83 |
| By rank (Spearman), not adjusted | -0.547 | 8.5e-8 | 83 |
| Standard (Pearson), adjusted for national income | -0.258 | 0.019 | 83 |
| By rank (Spearman), adjusted for national income | -0.271 | 0.014 | 83 |
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 83 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: +0.290 (a minus sign means it grew).
How solid is it?
Leaving out one country at a time, r ranges from -0.309 (without DZA) to -0.229 (without DOM). 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: DZA (-0.050).
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 | -0.49 | |
| Europe & Central Asia | 42 | -0.43 | |
| Latin America & Caribbean | 15 | -0.44 |
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 | 28 | -0.34 | |
| Middle third | 27 | -0.39 | |
| Richest third | 28 | +0.06 |
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 | -0.44 | |
| Muslims | 15 | +0.15 |
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.
| n | r | ||
|---|---|---|---|
| Spain | 14 | -0.37 | |
| United Kingdom | 14 | +0.26 |
By official ideology
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 | ||
|---|---|---|---|
| No strong official ideology | 63 | -0.26 |
By party system
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 | ||
|---|---|---|---|
| No parties banned | 69 | -0.27 |
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 = -0.258 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 17years. 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 = +0.002, 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 PISA science moved did not tend to see their small government (Fraser) move with it.
Across countries (adjusted)-0.258for comparison
Within countries+0.026each country vs itself
…and vs the same year elsewhere+0.002q = 0.991 · 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.
324 country-years (one country in one year), 55 countries, 2006–2022, about 6 years each on average. Share of the variation that happens within countries over time: 9% for PISA science, 5% for Small government (Fraser). 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): +0.002. 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 largest value on this curve (+0.16 at lag +5) is higher than the same-year one by 0.15. That gap is not a finding. It is the largest of 16 closely related estimates, and picking the biggest of many tests always makes it look bigger. That is exactly why nothing on this site is ranked or chosen by lag.
The data
PISA points | rating (0-10) | Years | |
|---|---|---|---|
| Singapore SGP | 561 | 7.39 | 2022, 2024 |
| Japan JPN | 547 | 5.93 | 2022, 2024 |
| Korea, Rep. KOR | 528 | 6.45 | 2022, 2024 |
| Estonia EST | 526 | 6.21 | 2022, 2024 |
| Hong Kong SAR, China HKG | 520 | 7.31 | 2022, 2024 |
| Canada CAN | 515 | 6.32 | 2022, 2024 |
| Finland FIN | 511 | 4.94 | 2022, 2024 |
| Australia AUS | 507 | 6.18 | 2022, 2024 |
| New Zealand NZL | 504 | 6.28 | 2022, 2024 |
| Ireland IRL | 504 | 6.26 | 2022, 2024 |
| Switzerland CHE | 503 | 7.68 | 2022, 2024 |
| Slovenia SVN | 500 | 4.83 | 2022, 2024 |
| United Kingdom GBR | 500 | 6.09 | 2022, 2024 |
| United States USA | 499 | 7.4 | 2022, 2024 |
| Poland POL | 499 | 5.62 | 2022, 2024 |
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
Gwartney, J., Lawson, R., Murphy, R. and others, Economic Freedom of the World: 2026 Annual Report, Fraser Institute. Data from the EFW panel dataset (efotw-2026-master-index-data-for-researchers-iso.xlsx).
Sources
PISA science
PISA mean science score
OECD · via Our World in Data · CC BY 4.0 (OECD terms and conditions) · updated annual, except the snapshots noted per indicator
Small government (Fraser)
Economic freedom, area 1, size of government (Fraser Institute)
Fraser Institute · No licence stated; used with citation · updated annual
Scores higher the smaller the government's role: less government spending, fewer transfers and subsidies, fewer state-owned businesses and lower top tax rates. A country with a large welfare state scores low here even if its markets are otherwise free. No "better" direction is set.
How this was computed
Data used: most recent value in 2010-2025; values come from 2015–2024. 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 17,292 pairs at once, using the Benjamini–Hochberg method. Underlying data last updated V-Dem v16; V-Party v2. How the country data works · explore PISA science and Small government (Fraser)
This page shows that two measures go together. It does not show that PISA science changes Small government (Fraser), or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.
More links with PISA science or Small government (Fraser)
- PISA science vs Religiously unaffiliated before +0.68 → after adjusting +0.63
- PISA science vs Researchers before +0.81 → after adjusting +0.60
- Redistribution vs Small government (Fraser) before -0.65 → after adjusting -0.55
- Family benefits spending vs Small government (Fraser) before -0.60 → after adjusting -0.53
- Gender Inequality Index vs PISA science before -0.81 → after adjusting -0.51
- One-person households vs PISA science before +0.71 → after adjusting +0.49
- HDI vs PISA science before +0.82 → after adjusting +0.46
- Confidence in religious institutions vs PISA science before -0.59 → after adjusting -0.46