Comparing two ratios - Which test should I use?

#1
It has been years since I attempted statistics and I would appreciate any form of help.
I am looking at data, and I want to see if one rate influences another rate. I want to know if two rates are correlated and significance of that correlation. The data looks similar to something like this (made up numbers and ratio names)

A, B, C, D, E, F
City, Officers, Pop, Crimes, Pop/Crime, Pop/Officer,
city1, 50, 50562, 123, 411.07, 1011.24
city2, 100, 250022, 861, …., ….
city3, 76, 100574, 435, …., ….

I would want to find out if more police officers would decrease crime rates. So if smaller pop/officer ratio would increase population/crime.
Or perhaps, a greater officer/pop ratio would decrease crime/pop?

I would like to consider population as a factor for correlation, which is why I am not just testing officers and crimes. I don't know if this is necessary or not.
Anyhow, what test would I use to compare E to F in both correlation and statistical significance?

I sincerely appreciate any and all help.
 

Karabiner

TS Contributor
#2
If you don't necessarily want to take into accounte the respectve population
sizes, then why don't you just calculate and test a Spearman rank correlation?

With kind regards

K.
 
#3
I agree that a Spearman correlation should work. Two additional thoughts: (1) Most crime and other rates are reported with population as the denominator (crimes per 1,000 or per 100,000, say). You might want to go that route for both ratios. These are probably both a bit more stable than ratios with population in the numerator and also more interpretable, (2) beware of confounding and reverse causality. A city with a high crime rate may hire more police! Answering your underlying question is challenging given that crime rates and decisions about police are made in context ... a wealthy city with low crime may have a lot of cops because it can afford them. A poor city with high crime may also have a lot of cops because it has no choice!
 
#4
Thank you very much, for some reason I thought it would need to be more complicated and am very relieved I can just use the Spearman rank correlation.

Many Thanks