522 



APPENDIX 



figure A-2. 95% confidence 

 limits (I) for f based on a sin- 

 gle-variable parameter, p. To 

 determine confidence intervals, 

 find p on the vertical scale. 

 Move right to the intersections 

 with the two curves indicating 

 the sample size. Finally, read 

 down to determine on the hori- 

 zontal scale the confidence lim- 

 its of f . ( 2 ) For p based on 

 a single-variable statistic, f. To 

 determine confidence intervals, 

 find f on the horizontal scale. 

 Move upward to the intersec- 

 tions with the two curves indi- 

 cating the sample size. Finally, 

 read left to determine on the 

 vertical scale the confidence lim- 

 its of p. {Courtesy of the Bio- 

 metrika Trustees.) 



wrong 5% of the time. In the penny- 

 tossing example (p = 0.5), if N = 100, s p is 

 approximately 0.05 and 95% of the time 

 we would expect f to be in the interval 

 0.4 - 0.6. If many samples of N = 100 

 are drawn, one can state that 95% of all 

 f's will lie in the interval 0.4 — 0.6. If one 

 draws a single sample of N = 100, it can 

 be stated that f will be in 0.4 — 0.6 and 

 we would have a 95% chance of being right 

 and a 5% chance of being wrong. 



Why should one resign himself to the 

 handicap of being wrong 5% (or any per 

 cent) of the time? In order to be right 

 100% of the time one would have to admit 

 that, 5% of the time, f can lie outside the 

 95% confidence interval. In the example 

 this would mean that 5% of the time f may 

 lie anywhere between (no successes) and 

 0.4 and between 0.6 and 1.0 (all successes). 

 To be 100% correct, to have 100% con- 

 fidence, one would have to predict f to 

 range between and 1. However, electing 



to be 100% right also means that all other 

 values of p would also have an expected 

 range of f's from to 1. Accordingly, the 

 100% range does not provide different ex- 

 pectations of f for different values of p; 

 it provides no power at all to discriminate 

 between different p values. However, by 

 being willing to be wrong 5% of the time, 

 the range of expected f's (when p = 0.5 

 and N = 100) can be reduced from (0 — 1) 

 to (0.4 - 0.6). And were p = 0.3 and 

 N = 100, f would be roughly between 0.2 

 and 0.4 95% of the time. Accordingly, 

 accepting a 5% chance of being wrong per- 

 mits one to have different statistical expec- 

 tations for different p values. In genetics 

 and biology in general, researchers usually 

 agree to the use of the 95% confidence in- 

 terval both for statistics and parameters. 

 Using the expression given on page 521, 

 one can calculate the different values of s p 

 for numerous combinations of p and N. 

 The 95% range for f can be determined 



