Type I and Type II Errors - Etymology

Etymology

In 1928, Jerzy Neyman (1894–1981) and Egon Pearson (1895–1980), both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly drawn from a certain population"p. 1: and, as Florence Nightingale David remarked, "it is necessary to remember the adjective 'random' should apply to the method of drawing the sample and not to the sample itself".

They identified "two sources of error", namely:

(a) the error of rejecting a hypothesis that should have been accepted, and

(b) the error of accepting a hypothesis that should have been rejected.p.31

In 1930, they elaborated on these two sources of error, remarking that:

...in testing hypotheses two considerations must be kept in view, (1) we must be able to reduce the chance of rejecting a true hypothesis to as low a value as desired; (2) the test must be so devised that it will reject the hypothesis tested when it is likely to be false.

In 1933, they observed that these "problems are rarely presented in such a form that we can discriminate with certainty between the true and false hypothesis" (p. 187). They also noted that, in deciding whether to accept or reject a particular hypothesis amongst a "set of alternative hypotheses" (p. 201), H₁, H₂, . . ., it was easy to make an error:

... these errors will be of two kinds:

(I) we reject H₀ when it is true,

(II) we accept H₀ when some alternative hypothesis H_A or H₁ is true.p.187 (There are various notations for the alternative).

In all of the papers co-written by Neyman and Pearson the expression H₀ always signifies "the hypothesis to be tested".

In the same paperp. 190 they call these two sources of error, errors of type I and errors of type II respectively.