Mathematician finds a strong correlation between the presence of mobile phone masts and the number of children born
The match between mobile phone towers and birth rates is an extremely strong correlation and it is highly statistically significant. There is no doubting the mathematical finding that more mobile phone masts mean that there will also be more births. This is about as rigorous as statistics can get.
Mobile phone masts, however, have absolutely no bearing on the number of births. There is no causal link between the masts and the births despite the strong correlation. Both the number of mobile phone transmitters and the number of live births are linked to a third, independent factor: the local population size. As the population of an area goes up, so do both the number of mobile phone users and the number people giving birth.
I remember my economics and statistics teacher coming up with a similar example: it’s in towns that have the highest number of churches that you’ll find the highest number of alcoholics. Because those towns are bigger. Duh!