Title: Sample Size Determination for the Test of One Proportion
Author: Keith M. Bower
Publication Source: International Society of Six Sigma Professionals, EXTRAOrdinary Sense, Vol. 3 No. 1, February 2002, pp. 6-7
Abstract
Type I and Type II errors are discussed, as well as the relationship between the sample size and the statistical power of a test. A practical illustration of sample size determination is shown. This topic is also discussed in Podcast 1.
Notes
There are several side issues that went into the creation of this paper. As well as addressing the issue of obtaining "usefully" high sample sizes to make an investigation worthwhile, I was also interested in mentioning:
(1) Type I and Type II errors
(2) The association between Power and Type II error (i.e. Power = 1 - β)
(3) The use of α = 0.05 for the significance level of a test
(4) Using a one-tailed alternative hypothesis
In particular, the consistent (and somewhat unquestioned) use of α = 0.05 by practitioners as the significance level was something I wanted to highlight. Of course, altering the significance level of the test has direct consequences on the sample size required in this procedure. Though such an extension is not addressed directly in the paper, my hope is that it would lead to further individual research, possibly by exploring the implications with the functionality in a statistical software package.
Incidentally, this paper was adjusted to consider the one-sample t-test procedure. The paper "Sample Size Determination for the One-Sample t-Test" is available by clicking here.
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© Keith M. Bower. All rights reserved.