> That aside, 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?
I don't think so. That would be plausible if the sample sizes (not the population sizes, which are quite large) from which the average state IQs are calculated were too small in the smaller states for some reason. The population of even the least populous state [1] is relatively large.
> 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.
About 2% of the US population moves to a new state each year. Also states are very large, any most of them encompass radically different socioeconomic regions (try comparing Florida swampland to Miami highrises...) Any study that buckets people by state isn't going to be very useful.
It’s interesting data but the analysis is pretty weak IMHO. Religious groups tend to drink less, yet the author supposed that they had found an invalid correlation and could not list a reason as to why. It also doesn’t acknowledge the bias built into the IQ exam, and it fails to reason about causality to my satisfaction.
These data do show a positive correlation between state alcohol consumption and state IQ. However, the children taking IQ tests and academic assessments is a different population than the one used for measuring alcohol consumption.
In general, I think the relationship between all of these measures could make a good example of Simpson’s paradox. It’s likely completely different correlations could be supported if the data were analyzed at the county level or if it were possible to completely disaggregate down to individuals.
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[ 2.5 ms ] story [ 43.2 ms ] threadI don't think so. That would be plausible if the sample sizes (not the population sizes, which are quite large) from which the average state IQs are calculated were too small in the smaller states for some reason. The population of even the least populous state [1] is relatively large.
[1]: Currently Wyoming, with an estimated population of 581,381. (https://en.wikipedia.org/wiki/List_of_U.S._states_and_territ...)
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 whole thing is kind of misleading because the correlation exists but isn't through the roof.
In general, I think the relationship between all of these measures could make a good example of Simpson’s paradox. It’s likely completely different correlations could be supported if the data were analyzed at the county level or if it were possible to completely disaggregate down to individuals.