**Help Aids **Top

**Application: **The determination of the sample size to control the power and to
control the length of the confidence interval, following hypotheses are
usually used:

where anddenote the success probabilities of interest.

**Procedure**:

- Enter

a) value of α, the probability of type I error

b) value of P_{1}, the observed proportion of success in arm 1

c) value of P_{2}, the observed proportion of success
in arm 2

d) value of L_{0}, the bound of expected length of 100(1- α)% confidence interval.

- Click the button “Calculate” to obtain

a) value of n, the sample size per arm

b) value
of N, the
total sample size

** **

**Formula:**

Let *n _{L}*
donotes the sample size required to have, a specified positive value.

where is the expected length, , of (1- α) confidence interval of .

where ,is the upper
100(1-p) percentile of the standard normal distribution.

**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.*

**Examples** Top

**Example 1:**

A clinical trial was planned to compare two
active treatments for a certain type of cancer, with respect to their response
rates *P _{1}* and

**Reference**: *Statistics in Medicine*, 8 (1988):803-811. Print.