Note:
Variables

Descriptions

α

Onesided significance level

1β

Power of the test

Allowable difference

Acceptable mean difference between sample
two and sample one (µ_{2}µ_{1})

Population variance

Population variance

δ

Equivalence limit

n

Sample size of each group

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Application: This procedure is used to test the following hypotheses:
The test drug is concluded to be equivalent
to the control in average if the null hypothesis is rejected at significance
level α.
Procedure:
 Enter
a)
value
of α,
the probability of type I error
b)
value
of β,
the probability of type II error
c)
value of allowable difference
d) value of Population
variance
e)
value of δ>0, the equivalence limit.
 Click the button “Calculate” to obtain result sample size of
each group n.
Formula:
_{} (*)
Notations:
α: The probability of type I error is the Probability of rejecting the null hypothesis when null hypothesis is true. The null hypothesis is the two mean values are not equivalent.
β: The probability of type II error is the Probability of failing to reject the null hypothesis when null hypothesis is false.
δ: The largest change
from the reference value (baseline) that is considered to be trivial.
μ_{2} – μ_{1}: Value of allowable difference is the
true mean difference between a test drug (μ_{2})
and a placebo control or active control agent (μ_{1}).
Examples
Example 1:
Suppose the true difference is 1% (i.e., μ_{2}–μ_{1}=1%)
and the equivalence limit is 5% (i.e., δ=0.05). Thus, by using (*), with
the standard deviation is 10% (i.e., population variance is 0.01), the
required sample size to achieve an 80% power (β=0.2) at α=0.05
for correctly detecting such difference of 0.05 change obtained by normal
approximation as n=108.
Reference: Chow, Shao and Wang, Sample Size Calculations In
Clinical Research, Taylor & Francis, NY.
(2003) Pages 5961.
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