I'll try to explain my question with an easy example.
Very often you can read in the papers that researchers have compared the IQs of different countries. But, it's a known fact that the intelligence tests are standardized in each country so that the average is 100. How is it possible, then, to compare the IQs of different countries, if each country will have an average of 100?
The intelligence is just used here as a catchy example, my question is more broad and concerns comparing different groups in variables that have been standardized.
E.g. let's say that you have data from previous independent researchers who have measured a personality trait in two countries. They used the same questionnaire, however, the researchers from the first country used a 4-point Likert scale, while the researchers from the second country have used a 5-point Likert scale. Obviously, the "raw" scores cannot be compared to infer if the countries differ in the measured trait. However, if we standardize the scores, we will also be unable to compare the countries because their average would be exactly the same.
So, how would we go on about this issue?