Input 

Results 

α 




β 




Allowable difference_{} 


N 

Population variance 




δ 




Note:
Variables 
Descriptions 
α 
Onesided significance level 
1β 
Power of the test 
Allowable difference 
Acceptable difference between sample mean and known or population mean (µµ_{0}) 
Population variance 
Population variance 
δ 
Equivalence limit 
N 
Sample size 
Help
Aids Top
Application: The test drug is determined to be equivalent to a gold standard on average if the null hypothesis is rejected at significance level α. The following hypotheses are usually considered:
Procedure:
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.
Formula:
_{} (*)
Notations:
α: The
probability of type I error (significance level) is the probability of rejecting the true null
hypothesis.
β: The
probability of type II error (1 – power of the test) is the probability of
failing to reject the false null hypothesis.
δ: The largest change from the reference value (baseline) that is considered to be trivial.
μ – μ_{0}: The value of allowable difference is the difference value between true mean and reference mean (constant value).
Examples
Example 1: Concerning
the effect of a test drug on body weight change in terms of body mass index
(BMI) before and after the treatment, we consider that a less than 5% change in
BMI from pretreatment is not safety concern for the indication of the disease
under study. Thus, δ=5% as the
equivalence limit and to demonstrate safety by testing equivalence in mean BMI
between pretreatment and posttreatment of the test drug. Now, if true BMI
difference is 0 (μ–μ_{0}=0)
and the population variance is 0.01, by (*) with α=0.05, we required the sample
size of N=35 to achieve an 80% power (β=0.2).
Reference: Chow, Shao and Wang, Sample Size Calculations In
Clinical Research,