Determination of sample size for tests concerning means and variances of normal distributions

The Editor Technometrics

“…We quickly find The solutions for (1) and (2) together with sample size problrms associated with the T and F distribution arc discussed in a paper by me in STATISTICA NEERLANDICA [2]. Narula and Li in their Example 2 use a gamma with parameter 1' (a known integer) for which v = 2nr.…”

The Use of Noncentral F Approximations for Calculation of Power and Sample Size

“…(See Odeh andFox 1975, pp. 38-42 andGuenther 1975. ) For this situation the T and F statistics have noncentral distributions under both the hypothesis and the alternative, and it is more difficult to evaluate power and find critical values.…”

“…Each experimenter will, of course, have to make his or her own selection. One reasonable suggestion (which eliminates (r2 from 0) is to consider situations in which some means are expressed as quantiles of a distribution with another mean (as in the article by Guenther 1977).…”

“…) For this situation the T and F statistics have noncentral distributions under both the hypothesis and the alternative, and it is more difficult to evaluate power and find critical values. Although tables are probably adequate for the T case (Guenther 1975), they are not for the F case. For the latter, Odeh and Fox use their graphs and an iterative procedure, which may yield a conservative solution.…”

“…A useful reference for these problems is the monograph of Odeh and Fox (1975). Two short articles by Guenther (1973Guenther ( , 1977) may also be helpful.…”