Oh I admit I don't know in all those cases. What I tried to state and I used cognitive index which would not be accurate, but I was in a hurry is the following: Essentially, there is data. Data can be aggregated where variables thought to be important can be put into a model. That doesn't mean the variables are, just that they would be in the data and the relationship of those variables could be studied however many there are. You just should have some repeated measure of the variables or essentially you eliminate the error term and falsely provide an extremely high if not perfect correlation which to many would be very misleading. Completed as such you have many variables in the model that allow a weighting of all the variables in the model.
In other words, were the variables studied an effective predictor of the sought measure? The sought measure might be the delta of growth over some time or something else. Perhaps the overall model is NOT as effective as desired or the variables thought to be in play affect the sought measure little...that weighing is in the data.
Bottom line considered variables in play can be studied relative to the sought measure and an understanding of the contributing weighing of each variable as well as any "error" due to variables considered to be important, but are not, will be removed as important variables and grow the error term. The goal is to understand what affects the sought measure and if you for example were one of the data points, and your wealth as measured was comparible to other data points, your data increases the value the model and if not, then your variables weaken the model. As a quick approximation in many cases is the R^2 of the correlation is what is explained by the total model and yet 80% of that model may lie in a single variable? A correlation of .7 for the model may only explain .49 of the sought measure.
Once you understand the variables in play, you would try to control for those between the different categories. It doesn't have to be an us versus them but could be more than two demographics for study and test for significance between teh demographics. Now, yuor ability to test for significance is a function of how well your variables affect the sought meaure. Poor model and you will have much greater difficulty in proving significance between the demographics. The relationship may ver well be there, but the noise due to other factors grow the error term and make the significance of the model not shown. Lastly, if you show significance between demographics...that is all it shows. What contributing explanation for that difference could be wrong, but the weighing of the individual variables might be a good place to start to explain any difference. BTW, my house due to the insurance policy I just got in the mail is too high, but elevating the false value allows for more coverage and expense to me for a statistically unliekly event that the actuaries know...and again will require another phone call on my end to counter the elevated value so they can make more money.