Gender discrimination lawsuits based on the discrepancy in pay between men and women could be defeated once it was realized that pay was related to years in service and that women who had only recently arrived on the job market in great numbers simply didn’t have as many years on the job as men.
These same discrimination lawsuits could be won once the gender comparison was made on a years-in-service basis, that is when the salaries of new female employees were compared with those of newly employed men, the salaries of women with three years of service with those of men with the same time in grade, and so forth. Within each stratum, men always had the higher salaries.
If the effects of additional variables other than X on Y are suspected, they should be accounted for either by stratifying or by performing a multivariate regression as described in the next chapter.
The two approaches are not equivalent unless all terms are included in the multivariate model. Suppose we want to account for the possible effects of gender. Let I be an indicator function that takes the value 1 if its argument is true and 0 otherwise. Then, to duplicate the effects of stratification, we would have to write the multivariate model in the following form:
In a study by Kanarek et al.  whose primary focus is the relation between asbestos in drinking water and cancer, results are stratified ...