Simple "controlling for population size difference" question

#1
Hello,

I just had a ludicrous argument with a friend that we would like your help on settling. Let's assume the following:

California population: 100,000
Nevada population: 60,000

# of toy cars in California: 300
# of toy cars in Nevada: 200

comparing the number of toy cars in california v. nevada would be unfair due to the difference in population size. But by proportioning the number of toy cars per 5000 citizens, you can have a fairer comparison.

300/(100,000/5000)=15
200/(60,000/5000)= 16.66

When controlling for the difference in population size, we can see that Nevada in a sense has more toy cars per 5000 population than california and comparing 15 v. 16.66 would in a sense be "fair" or at least fairer (without becoming too nuanced)

How is this wrong? I don't understand his argument.
 

hlsmith

Omega Contributor
#2
Your logic is good enough. No idea what the counter-argument is, if it is not focusing on controlling for even more details (e.g., age, gender, etc.).


There is a fallacy similar to this. I can't remember the name, but the traditional example usually says something like you are more likely to get in a wreck with a white car than red car. The hitch is there are more white cars.
 

rogojel

TS Contributor
#3
I think this depends on the interpretation of the rather vague term "more". If somebody is interested in the absolute number as in revenue generated by selling toy cars then obviously california is the winner, If the interest is in where do people like toy cars more then nevada , and both answers are right :) So, as very often in stats this boils down to what the research question is.