**Help Aids** Top

**Application:
**This procedure computes sample size for
non-inferiority and superiority tests in 2×2 cross-over designs in which the
outcome is a continuous normal random variable. A non-inferiority test tests that
the treatment mean is not worse than the reference mean by more than a small
equivalence margin. The actual direction of the hypothesis depends on the
response variable being studied. A superiority test tests that the treatment
mean is better than reference mean by more than a small equivalence margin. The
actual direction of the hypothesis depends on the response variable being
studied. The following hypotheses are usually considered: _{.}

**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 *change
from the reference value (baseline) that is considered to be trivial. *

**μ _{2 }– μ_{1}:**
The true difference between the two mean values at which the power is calculated.

**Population variance:**
*The within mean square error from
the ANOVA table used to analyze the Cross-Over design.*

**Examples**

**Example 1: **Suppose you want
to consider the sample size of a balanced, cross-over design that will be
analyzed the t-test approach. Thus when the non-inferiority margin is *δ*=-0.05, the true difference between the
means under *H _{0}* is assumed
to be 0, with population variance of 0.01 and the
significance level of

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