[2] Florence Nightingale David,[3] a sometime colleague of both Neyman and Pearson at the University College London, making a humorous aside at the end of her 1947 paper, suggested that, in the case of her own research, perhaps Neyman and Pearson's "two sources of error" could be extended to a third: I have been concerned here with trying to explain what I believe to be the basic ideas [of my "theory of the conditional power functions"], and to forestall possible criticism that I am falling into error (of the third kind) and am choosing the test falsely to suit the significance of the sample.In 1948, Frederick Mosteller[b] argued that a "third kind of error" was required to describe circumstances he had observed, namely: According to Henry F. Kaiser, in his 1966 paper extended Mosteller's classification such that an error of the third kind entailed an incorrect decision of direction following a rejected two-tailed test of hypothesis.
Harvard economist Howard Raiffa describes an occasion when he, too, "fell into the trap of working on the wrong problem" (1968, pp. 264–265).
In the 2009 book Dirty rotten strategies by Ian I. Mitroff and Abraham Silvers described type III and type IV errors providing many examples of both developing good answers to the wrong questions (III) and deliberately selecting the wrong questions for intensive and skilled investigation (IV).
[4] In 1969, the Harvard economist Howard Raiffa jokingly suggested "a candidate for the error of the fourth kind: solving the right problem too late" (1968, p. 264).
In 1970, L. A. Marascuilo and J. R. Levin proposed a "fourth kind of error" – a "type IV error" – which they defined in a Mosteller-like manner as being the mistake of "the incorrect interpretation of a correctly rejected hypothesis"; which, they suggested, was the equivalent of "a physician's correct diagnosis of an ailment followed by the prescription of a wrong medicine" (1970, p. 398).