Re:Updated IQ and Well-Being Scores for the 50 U.S. States
by SenAnder on Monday July 31, 2023 @05:47PM
(#36949312)
> isn't the difference in population between states going to cause statistical oddities with the biggest states trending to the average and the smallest being potential outliers?
The population sampled for the estimates is not the same as (and probably smaller than) the entire state population. So the potential outliers would be caused by differing sample sizes more than state populations.
It's worth to examine how much variance we can expect due to sample size effects. Per https://en.wikipedia.org/wiki/Standard_error#Standard_error_..., the standard deviation of the measurement (stdev_m) due to sampling effects is stdev_p/sqrt(n), where n is sample size and stdev_p is the standard deviation of the measured variable for the entire population.
So if n=100, then stdev_m is stdev_p/10, and if n=10'000, it is stdev_p/100.
The population sampled for the estimates is not the same as (and probably smaller than) the entire state population. So the potential outliers would be caused by differing sample sizes more than state populations.
It's worth to examine how much variance we can expect due to sample size effects. Per https://en.wikipedia.org/wiki/Standard_error#Standard_error_..., the standard deviation of the measurement (stdev_m) due to sampling effects is stdev_p/sqrt(n), where n is sample size and stdev_p is the standard deviation of the measured variable for the entire population.
So if n=100, then stdev_m is stdev_p/10, and if n=10'000, it is stdev_p/100.