Fixed broadband vs. Pupil-teacher ratio
Fades after adjusting for income
Across 178 countries, Fixed broadband 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 -0.09, which could easily be chance (q = 0.40, 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. Caution: direction is not consistent across regions.
Comparing countries across the middle half of pupil-teacher ratio, 13.7 to 28.9 pupils per teacher, fixed broadband is worse by 13.3 per 100 people at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 1.67 per 100 people.
Link before adjusting (r)-0.687p = 3.7e-26 · 178 countries
After adjusting for national income-0.093p = 0.217 · likely range [-0.24, +0.05]
p, allowing for regions0.111standard error 0.050 · 7 regions
Check for luck (q)0.396across 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.
Fixed broadband · per 100 peoplelink with income +0.88 · 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 | -0.687 | 3.7e-26 | 178 |
| By rank (Spearman), not adjusted | -0.791 | 2.5e-39 | 178 |
| Standard (Pearson), adjusted for national income | -0.093 | 0.217 | 178 |
| By rank (Spearman), adjusted for national income | -0.219 | 0.003 | 178 |
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 178 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: +0.593 (a minus sign means it grew).
How solid is it?
Leaving out one country at a time, r ranges from -0.143 (without CAF) to -0.068 (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 (-0.049).
Fragile: this link may not hold up.
- direction is not consistent across regions
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 | 28 | -0.18 | |
| Europe & Central Asia | 48 | -0.11 | |
| Latin America & Caribbean | 31 | -0.32 | |
| Middle East, North Africa, Afghanistan & Pakistan | 19 | +0.22 | |
| Sub-Saharan Africa | 44 | -0.14 |
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 | 60 | -0.32 | |
| Middle third | 59 | -0.29 | |
| Richest third | 59 | -0.05 |
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 | 104 | -0.14 | |
| Muslims | 43 | +0.00 |
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 | -0.10 | |
| Never a European colony | 20 | -0.05 | |
| Spain | 19 | -0.35 | |
| United Kingdom | 56 | -0.19 |
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 = -0.214 after dropping 7 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 22years. 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 = +0.171) but mostly disappears in year-to-year changes (r = +0.035). That points to slow trends particular to each country, not the two measures moving together from year to year.
Across countries (adjusted)-0.093for comparison
Within countries-0.295each country vs itself
…and vs the same year elsewhere+0.171q = 0.008 · 164 countries
Year-on-year changes+0.035q = 0.308
The direction flips. Comparing each country only with itself gives -0.29. Also taking out what happened to the whole world each year gives +0.17. 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 this indicator's variation is between countries, not within them, so the within-country estimate rests on a small part of the data.
2,089 country-years (one country in one year), 164 countries, 1998–2019, about 13 years each on average. Share of the variation that happens within countries over time: 5% for Fixed broadband, 33% 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): +0.171. 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
per 100 people | pupils per teacher | Years | |
|---|---|---|---|
| Cayman Islands CYM | 56.4 | 15.7 | 2022, 2018 |
| Andorra AND | 52.4 | 10.5 | 2024, 2018 |
| Bermuda BMU | 51.3 | 10.4 | 2024, 2015 |
| France FRA | 48.9 | 18.2 | 2024, 2013 |
| Korea, Rep. KOR | 47.8 | 16.3 | 2024, 2017 |
| China CHN | 47.2 | 16.4 | 2024, 2018 |
| Switzerland CHE | 47 | 9.93 | 2024, 2017 |
| St. Kitts and Nevis KNA | 46.7 | 13.9 | 2022, 2016 |
| Germany DEU | 45.6 | 12.3 | 2024, 2017 |
| Portugal PRT | 45.2 | 12.4 | 2024, 2017 |
| Norway NOR | 45.2 | 8.59 | 2024, 2017 |
| Greece GRC | 44.7 | 9.38 | 2024, 2017 |
| Malta MLT | 44.5 | 12.9 | 2024, 2017 |
| Belgium BEL | 44.2 | 11.3 | 2024, 2017 |
| Saudi Arabia SAU | 44.1 | 13.8 | 2024, 2018 |
World Bank, World Development Indicators
World Bank, World Development Indicators
Sources
Fixed broadband
Fixed broadband subscriptions (per 100 people)
International Telecommunication Union · CC BY 4.0 · updated quarterly
Subscriptions, not people. A household line counts once, however many people use it. A country that went straight to mobile data can be well connected with few of these lines. Internet users, already on the site, is the measure of people.
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 2010–2024. 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 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 Fixed broadband and Pupil-teacher ratio
This page shows that two measures go together. It does not show that Fixed broadband changes Pupil-teacher ratio, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.
More links with Fixed broadband or Pupil-teacher ratio
- Fixed broadband vs Researchers before +0.77 → after adjusting +0.49
- Fixed broadband vs Frequent prayer before -0.74 → after adjusting -0.45
- Confidence in religious institutions vs Fixed broadband before -0.62 → after adjusting -0.43
- Fixed broadband vs Informal employment before -0.86 → after adjusting -0.42
- Fixed broadband vs Public social spending before +0.58 → after adjusting +0.41
- Adult literacy vs Pupil-teacher ratio before -0.73 → after adjusting -0.41
- Pupil-teacher ratio vs Secondary enrollment before -0.75 → after adjusting -0.40
- Alcohol consumption vs Fixed broadband before +0.59 → after adjusting +0.38