Input 

Results 

α 




β 

N 


Allowable difference_{} 




Population Variance 




Note:
Variables 
Descriptions 
α 
Twosided significance level 
1β 
Power of the test 
Allowable difference 
Acceptable difference between sample mean and known or expected population mean (μ  μ_{0}) 
Population Variance 
Population variance 
N 
Sample size 
Help Aids Top
Application: This
procedure is used to test if there is a statistically significant difference between the mean response of an experimental drug and a constant reference value. 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 expected variance, the population variance.
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.
μ  μ_{0}: The value of allowable difference is the difference value between true mean and reference mean (constant value).
Examples
Example 1: A
pharmaceutical company is interested in investigating the effect of a test drug
on prevention of a progression to osteoporosis in women with osteopenia. We want to show that after treatment, the
change in bone density from mean values is less than 1 unit (δ=1) assuming that the known mean
bone density before the treatment is 1.5 (μ_{0}=1.5).
Now suppose that the mean bone density after treatment is expected to be 2.
Thus we have μ  μ_{0}=0.5,
at α=0.05 with given variance of
1, the required sample size for having an 80% power (β=180%=0.2) for correctly detecting a difference of 0.5
change from pretreatment to posttreatment can be obtained by normal
approximation as N=32.
Reference: Chow, Shao and Wang, Sample
Size Calculations In Clinical Research,