Across 185 countries, Infrastructure score and Out of school, primary rise and fall together at r = -0.57 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.37 (q = 0.032, allowing for the many pairs tested). Much of the first figure is that both measures rise with national income, but a weak negative link remains. Caution: correlation moves sharply once outliers are trimmed.
Comparing countries across the middle half of out of school, primary, 1.06% to 10.4% of primary-age children, infrastructure score is worse by 0.319 typical gaps at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.0999 typical gaps.
Link before adjusting (r)-0.572p = 1.8e-17 · 185 countries
After adjusting for national income-0.374p = 1.7e-7 · likely range [-0.49, -0.24]
p, allowing for regions0.021standard error 0.120 · 7 regions
Check for luck (q)0.032across 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.
Infrastructure score · typical gaps (standard deviations)link with income +0.90 · proxy
Out of school, primary · % of primary-age childrenlink with income -0.45 · 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
-0.572
1.8e-17
185
By rank (Spearman), not adjusted
-0.531
7.9e-15
185
Standard (Pearson), adjusted for national income
-0.374
1.7e-7
185
By rank (Spearman), adjusted for national income
-0.331
4.5e-6
185
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 185 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: +0.198 (a minus sign means it grew).
How solid is it?
Leaving out one country at a time, r ranges from -0.402 (without CPV) to -0.297 (without GNQ). 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: GNQ (+0.078).
Fragile: this link may not hold up.
correlation moves sharply once outliers are trimmed
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
30
-0.03
Europe & Central Asia
50
-0.19
Latin America & Caribbean
34
-0.30
Middle East, North Africa, Afghanistan & Pakistan
18
-0.53
Sub-Saharan Africa
44
-0.40
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
62
-0.20
Middle third
61
-0.55
Richest third
62
-0.54
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
109
-0.34
Muslims
44
-0.55
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
France
23
-0.46
Never a European colony
19
-0.65
Spain
20
-0.90
United Kingdom
59
-0.07
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 = -0.163 after dropping 20 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 0years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.
Not enough history inside each country to look at this over time. That needs countries measured for several years in a row, and at least one of these measures is measured too rarely.
PlaceStats · via PlaceStats · Derived work; each member keeps its own licence · updated recomputed with the panel
The average of 5 measures from 1 publisher. Each measure is first put on a common scale: 0 is the average country in an average year, and 1 is a typical gap between countries (a standard deviation). Each is turned so that higher is better. Measures are averaged within each publisher first, so a publisher with many measures does not count for more. Members: Electricity access, Slum share of urban population, Mobile subscriptions, Fixed broadband, Internet users.
UNESCO Institute for Statistics · CC BY 4.0 · updated quarterly
Children of primary-school age not enrolled at any level. Treated as measuring the same thing as gross primary enrolment, which is on the site. They are two ways of asking whether children are in school, so their agreement is not a finding.
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 Infrastructure score and Out of school, primary
This page shows that two measures go together. It does not show that Infrastructure score changes Out of school, primary, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.
More links with Infrastructure score or Out of school, primary