<P> 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 fail to reject, or reject a particular hypothesis amongst a "set of alternative hypotheses" (p. 201), H, H,..., it was easy to make an error: </P> <Dl> <Dd>... (and) these errors will be of two kinds: <Dl> <Dd> (I) we reject H (i.e., the hypothesis to be tested) when it is true, </Dd> <Dd> (II) we fail to reject H when some alternative hypothesis H or H is true . (There are various notations for the alternative). </Dd> </Dl> </Dd> </Dl> <Dd>... (and) these errors will be of two kinds: <Dl> <Dd> (I) we reject H (i.e., the hypothesis to be tested) when it is true, </Dd> <Dd> (II) we fail to reject H when some alternative hypothesis H or H is true . (There are various notations for the alternative). </Dd> </Dl> </Dd> <Dl> <Dd> (I) we reject H (i.e., the hypothesis to be tested) when it is true, </Dd> <Dd> (II) we fail to reject H when some alternative hypothesis H or H is true . (There are various notations for the alternative). </Dd> </Dl>

Type 1 error type 2 error power of the test