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). In the 2009 book Dirty rotten strategies by Ian I. chosen the right problem representation" (1974), p. 383. choosing the wrong problem representation. when one should have solved the right problem" or "the error.
They defined type III errors as either "the error. In 1974, Ian Mitroff and Tom Featheringham extended Kimball's category, arguing that "one of the most important determinants of a problem's solution is how that problem has been represented or formulated in the first place". Harvard economist Howard Raiffa describes an occasion when he, too, "fell into the trap of working on the wrong problem" (1968, pp. 264–265). Mathematician Richard Hamming expressed his view that "It is better to solve the right problem the wrong way than to solve the wrong problem the right way". Kimball defined this new "error of the third kind" as being "the error committed by giving the right answer to the wrong problem" (1957, p. 134).
Kimball, a statistician with the Oak Ridge National Laboratory, proposed a different kind of error to stand beside "the first and second types of error in the theory of testing hypotheses". In his discussion (1966, pp. 162–163), Kaiser also speaks of α errors, β errors, and γ errors for type I, type II and type III errors respectively (C.O. 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.
Type II error: "failing to reject the null hypothesis when it is false".Type I error: "rejecting the null hypothesis when it is true".In 1948, Frederick Mosteller argued that a "third kind of error" was required to describe circumstances he had observed, namely: