Sample Size Calculator: Two Parallel-Sample Means

Hypothesis: One-Sided Equivalence

 

Data Input: (Help) (Example)

 

Input

 

Results

α

 

 

 

β

 

 

Allowable difference

 

n

Population variance

 

 

 

δ

 

 

 

 

Note:

Variables

Descriptions

α

One-sided significance level

1-β

Power of the test

Allowable difference

Acceptable mean difference between sample two and sample one (µ2-µ1)

Population variance

Population variance

δ

Equivalence limit

n

Sample size of each group

Help Aids Top

 

Application: This procedure is used to test the following hypotheses:

 

The test drug is concluded to be equivalent to the control in average if the null hypothesis is rejected at significance level α.

 

Procedure:

  1. Enter

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.

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

 

Formula:                                                               (*)

 

 

Notations:

 

α:           The probability of type I error is the Probability of rejecting the null hypothesis when null hypothesis is true. The null hypothesis is the two mean values are not equivalent.

 

β:           The probability of type II error is the Probability of failing to reject the null hypothesis when null hypothesis is false.

 

δ:           The largest change from the reference value (baseline) that is considered to be trivial.

 

μ2 – μ1:  Value of allowable difference is the true mean difference between a test drug (μ2) and a placebo control or active control agent (μ1).

 

Examples

 

Example 1: Suppose the true difference is 1% (i.e., μ2–μ1=1%) and the equivalence limit is 5% (i.e., δ=0.05). Thus, by using (*), with the standard deviation is 10% (i.e., population variance is 0.01), the required sample size to achieve an 80% power (β=0.2) at α=0.05 for correctly detecting such difference of 0.05 change obtained by normal approximation as n=108.

 

 

Reference: Chow, Shao and Wang, Sample Size Calculations In Clinical Research, Taylor & Francis, NY. (2003) Pages 59-61.

 

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