

American Cancer Society
Please feel free to forward
your comments, suggestions, and corrections to Dr. James L. Kepner 

Sample Size Calculator: OneSample Designs
Background
This program determines the sample size necessary to attain a specified size and power for an
exact test of one proportion. The hypotheses to be tested are of the form:
H0: p=p0
H1: p>p0
The user must submit a value for p0, an upper bound for alpha (i.e., the probability of committing a Type I error),
and a lower bound for the power at the point p = p0+delta, where 0 < delta < (1p0).
Upon taking these study constraints into consideration, the calculator will then recommend a design that is optimal
by the following criteria:
 The first stage sample size, n1, is as small as possible.
 The second stage sample size (if a twostage design is requested), n2, is as small as possible and satisfies
n2 <= n1.
 The third stage sample size, (if a threestage design is requested), n3, is as small as possible and
satisfies n3 <= n2.
 The actual significance level, or size, of the test satisfies size <= alpha, where alpha
is the significance level specified by the user.
 The actual power at p = p0+delta, apower, satisfies apower >= power, where power is the userspecified minimum
acceptable power.
Step One
Enter the following information from your study*: