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**Application: **This procedure is used to test non-inferiority and superiority that
can be unified by the following hypotheses:

_{}

**
When δ>0, the rejection of the null hypothesis indicates the superiority of the test drug over the control.
**

**
When δ<0, the rejection of the null hypothesis indicates the non-inferiority of the test drug against the control.
**

**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

d) value of *Population variance*

e)
value of ** δ**>0, the superiority margin or
value of

- Click the button “Calculate” to obtain result sample size of
each group
*n*.

**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**: Clinically meaningful difference. The largest

** μ_{2} – μ_{1}**: Value of allowable difference is the
true mean difference between a test drug (

**Examples**

**Example 1:
**Consider the difference of 5% is a difference of
clinical importance, thus the non-inferiority margin is chosen to be 5% (i.e., ** δ=-0.05**).
Also, suppose the true difference in mean of low density lipidproteins
(LDLs) between treatment groups is 0% (i.e.,

**Reference**: Chow, Shao and Wang, *Sample Size Calculations In Clinical
Research*,