Suppose we decide to investigate the efficacy of three forms of therapy (the experimental manipulation). We do this by identifying psychiatric patients who can be divided into two groups on the basis of the severity of their illness (the classificatory variable). Does effectiveness of treatment vary with severity of illness? When all patients are combined, we find that treatment 3 produced the largest improvement, and we are mistakenly led to believe that this treatment is the best. But when we analyze the data according to severity of illness, treatment 3 is not the preferred one for either group of patients. Instead, for patients with less severe problems, treatment 1 is desirable whereas for those with more severe problems, treatment 2 would be preferable.