So what's Type III error? Providing the right answer to the wrong question. Schwartz and Carpenter provide examples showing the consequences in studies of homelessness, obesity, and infant mortality. They focus on the fact (often forgotten) that the cause of differences among individuals within a group may be different from the cause of differences between groups. Here's their conclusion on homelessness.
The causes of interindividual differences within the population may be interesting in and of themselves, but from the public health perspective of trying to decrease the amount of homelessness at any time, the interindividual differences are largely irrelevant. The identification of individual risk factors may benefit certain people by decreasing the probability that they will become homeless. The success of an individual-level intervention is based on the premise that the reduction of a specific risk factor will enhance the ability of the individual to compete for the limited housing resource, all things being equal. From the standpoint of public health, however, explaining interindividual differences in homelessness does not adequately address the goal of decreasing the incidence of homelessness.Why? Well, it would be better to write
Explaining interindividual differences in homelessness will not necessarily lead to decreases in homelessness.If there are more people that need homes than there are homes, interventions based on understanding interindividual differences will change who gets a house, but not how many people get a house.
1If you're a Bayesian, you know that if the variables concerned are continuous, the point null hypothesis is always false, but that's a subject for a different post.