Related Experiment Video
Updated: Aug 17, 2026
A Two-interval Forced-choice Task for Multisensory Comparisons
Published on: November 9, 2018
Sample size determination for proving equivalence based on the ratio of two means for normally distributed data
D Hauschke1, M Kieser, E Diletti
1Department of Biometry, Byk Gulden Pharmaceuticals, Konstanz, Germany.
Abstract:
Equivalence trials aim to demonstrate that two treatments do not differ by more than a prespecified clinically irrelevant amount. We consider the problem when equivalence is defined in terms of the ratio of population means and the original (untransformed) data are normally distributed. Application of the intersection-union principle to the test proposed by Sasabuchi results in a two one-sided tests procedure of size alpha. We give the associated 100 (1-2 alpha) per cent confidence interval and derive the exact methods for calculation of power and sample sizes for the parallel group design and the two-period cross-over. We present tables and figures of required sample sizes and achieved power.
Related Concept Videos
01:24Testing a Claim about Population Proportion
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
01:11Testing a Claim about Mean: Known Population SD
Estimating a population mean requires the samples to be distributed normally. The data should be collected from the randomly selected samples having no sampling bias. The sample size needed to be higher than 30, and most importantly, the population standard deviation should be already known.
In most realistic situations, the population standard deviation is often unknown, but in rare circumstances, when it...
01:19Testing a Claim about Standard Deviation
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
01:15One-Way ANOVA: Equal Sample Sizes
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
01:15One-Way ANOVA: Unequal Sample Sizes
01:21Testing a Claim about Mean: Unknown Population SD
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used; instead...