Sample Size Calculator: One Sample Mean

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 difference between sample mean and known or population mean (µ-µ0)

Population variance

Population variance

δ

Equivalence limit

N

Sample size

Help Aids Top

 

Application: The test drug is determined to be equivalent to a gold standard on average if the null hypothesis is rejected at significance level α. The following hypotheses are usually considered:

 

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

 

μ – μ0:       The value of allowable difference is the difference value between true mean and reference mean (constant value).

 

Examples

 

Example 1:  Concerning the effect of a test drug on body weight change in terms of body mass index (BMI) before and after the treatment, we consider that a less than 5% change in BMI from pre-treatment is not safety concern for the indication of the disease under study. Thus, δ=5% as the equivalence limit and to demonstrate safety by testing equivalence in mean BMI between pre-treatment and post-treatment of the test drug. Now, if true BMI difference is 0 (μ–μ0=0) and the population variance is 0.01, by (*) with α=0.05, we required the sample size of N=35 to achieve an 80% power (β=0.2).

 

 

Reference: Chow, Shao and Wang, Sample Size Calculations In Clinical Research, Taylor & Francis, NY. (2003) Pages 52-53.

 

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