If there are three population groups and data is collected for three groups.
How do we come to know whether these three populations are capable of being pooled for a valid statistical analysis of data?
Statistics is about what we can know about things. And knowledge abouth things influences the way of statistical analysis. If we know something, it is often sensible to acknowledge this knowledge and consider it in an appropriate statistical analysis.But it can also be that this knowledge is quite irrelevant for the analysis we want to do; then we can ignore it.
A simple example:
We know that the body heights of 30-year-old males and females are systematically different. If we want to say something about 30-year-old human body heights (say to give a summary like statistics for location [mean] and dispersion [variance]), it would be rather silly to ignore this knowledge. The same applies if we had individuals of different ages. We know that the height change with age, especially during the first years of life, and so it would be silly to ignore this. A statistical analysis of such data should include the "age-effect".
We may have data of body weights of newborns, and such data never showes some relevant systematic difference between boys and girls. The analysis of the heights of newborns may thus simply ignore the gender (you would say we can pool the data from boys and girls).
Often there might be influential factors we are not aware of or would not expect. A statistical analysis may then reveal that there is some influential factor that should be considered.
There is no "valid" vs. "invalid" analysis. The analysis (given it is technically ok) is always "valid", ignoring irrelevant information will not make an analysis "invalid", and considering additional relevant information will make an analysis more "specific", more "precise", and possibly more "useful". What is "relevant" depends on how much the consideration of the respective information will improve the specificity, precision, or usefulness of the analysis results. This is not a statistical question.
I feel that populations are fit to be analysed as far as they are 'classified by same criteria and methods'. The statistical analysis may be significant or insignifant, but may stil be important in descriptive sense
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