ABSTRACT
Values..................................................................................... 497 23.4.4 Role of
β....................................................................................................................... 498
23.4.5 Analogy to Diagnostic Marker Tests ........................................................................... 498 23.4.6 Choice of
β ................................................................................................................... 499
23.5 The Concept of “Power” ........................................................................................................... 500 23.5.1 Statistical Connotation of “Power” .............................................................................. 500 23.5.2 Comparison of “Capacity” and “Power” ..................................................................... 500 23.5.3 Example of Complaints and Confusion ....................................................................... 501 23.5.4 Reciprocity of Z
and Z
.............................................................................................. 501 23.6 Neyman-Pearson Strategy.......................................................................................................... 502
23.6.1 Calculation of “Doubly-Significant” Sample Size....................................................... 502 23.6.2 Example of Calculations .............................................................................................. 504 23.6.3 Use of Tables ................................................................................................................ 504
23.7 Problems in Neyman-Pearson Strategy..................................................................................... 505 23.7.1 Mathematical Problems ................................................................................................ 505 23.7.2 Scientific Problems ....................................................................................................... 506 23.7.3 Additional Scientific Problems..................................................................................... 507
23.8 Pragmatic Problems ................................................................................................................... 508 23.8.1 “Lasagna’s Law” for Clinical Trials ............................................................................ 508 23.8.2 Clinical Scenario........................................................................................................... 508
23.9 Additional Topics....................................................................................................................... 509 23.9.1 The “Power” of “Single Significance”......................................................................... 509 23.9.2 Premature Cessation of Trials with d
<
δ
................................................................... 510 23.9.3 Choice of Relative Values for
α
and
β
........................................................................ 510 23.9.4 Gamma-Error Strategy.................................................................................................. 510 23.9.5 Prominent Statistical Dissenters................................................................................... 511 23.9.6 Scientific Goals for
δ.................................................................................................... 512
23.9.7 Choosing an “Honest”
δ
............................................................................................... 512 References .............................................................................................................................................. 513 Exercises ............................................................................................................................. 513
Type II errors are a common event in stochastic testing. They occur when the investigator concedes the null hypothesis and concludes that the observed results are “not significant,” although the true distinction is really impressive. These errors are the reverse counterpart of the Type I errors, emphasized in all the stochastic discussions so far, that occur when the null hypothesis is rejected although it is actually true.
