Significance testing between ratios

[trwib]

Hi,

I'm working with employment data to compare my local region with Pennsylvania's employment as a whole. I'd like to determine whether differences from the overall ratio are significant,
e.g. my region has 20.23% of PA's 5,426,530 jobs. But in, say, the Air Transportation sector, we have 4,445 of PA's 11,619 jobs, or 38.26%. That seems like a significant difference. But since the two ratios are dependent and just one number each instead of a set of observations, I don't know how to determine it statistically.

 

[eyesack_kn]

I don't know if you can "test" this because you're asking about individuals, not a group of individuals. But for each sector-region you can ask whether the difference between the two ratios falls within a particular threshhold. To do this, generate a variable containing the difference between the ratio of total jobs in a region and ratio of (say) Air Transportaiton sector jobs in that region. Standardize the variable by dividing by its standard deviation and you should be able to obtain a z-score for each sector-region combination. You could then ask whether the magnitude of the difference is greater than the population mean at a 90%, 95%, 99%, or some other level just using the z score.

 

[eyesack_kn]

Oh and of course, you could test whether the mean of the difference was difference within a subpopulation. For instance, you could test whether the difference in the areas in the southwest region of Pennsylvania had a higher mean concentration of Air Transportation jobs than regions in the rest of Pennsylvania, but you would need to have at least two observations in each group and it sounds like your regions are really big, so it wouldn't be a very powerful test.

 

[trwib]

@eyesack_kn, I think I see what you mean. So the method you first suggested would be a measure of how extreme the deviation was based on all of the employment sectors' deviation? It wouldn't depend at all on the one ratio but only on the distribution of ratios: 38.26% could either be extreme or not depending on the ratios for the other sectors. That's too bad, I was hoping for some measure that would take into account the size of the sector (b/c if all of PA only has 10 XX jobs it's not that surprising that my region would have 3 instead of 2, whereas a small deviation in a huge sector seems more significant) to arrive at a significance level that wouldn't vary with different sector distributions.