Type III Error

Other Definitions of Type III Error

Kimball was neither the first nor the only statistician to provide a definition of Type III error. In fact, Type III error has several definitions with none appearing to enjoy wide acceptance. Frederick Mosteller described Type III error with respect to the null hypothesis as correctly rejecting the null hypothesis for the wrong reason. Henry F. Kaiser argued that a Type III error is an incorrect decision of the direction of rejection in a two-tailed NHST. In addition, S. Schwartz and K. M. Carpenter defined Type III error as a discrepancy between the causal components of a theory and how they are operationalized. For instance, the rate of homelessness in any country is structural—based on policies related to housing and poverty—but if researchers focused on the demographics of homeless individuals, they would miss the structural component and believe that individual differences might contribute to or control the phenomenon. Similarly, Schwartz and Carpenter argued that obesity is a result of gene and environment interplays, but research that focuses on individual difference contributions to obesity (e.g., gender, age) will routinely miss or underplay the environmental factors.

The Commonality Among the Type III Error Definitions

Although disparately focused, each of the definitions of Type III error provided in the previous section can reasonably be subsumed under Kimball’s axiom of giving the right answer to the wrong problem. The misspecification errors of Mosteller, Kaiser, and Schwartz and Carpenter can be viewed as correctly answering another question—just the wrong problem for the investigation at hand. In this way, Type III errors appear to be focused on how theories become operationalized for empirical research. Stated differently, Type III errors focus on methodological implementation errors.

The Need for a Fourth Type of Error

If one can argue for giving the right answer to the wrong problem as an epistemic decision error (i.e., Type III error), then it is worth asking: Can one demonstrate that giving the wrong answer to the right problem also exists as another kind of epistemic decision error? The answer appears to be yes insofar as there are existing definitions of Type IV error that focus on the incorrect interpretation of an interaction term in regression or analysis of variance.

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