Determining sample size when assessing mean equivalence

Abstract

Background. When we want to assess whether two analytical methods are equivalent, we could test if the difference between the mean results is within the specification limits of 0 ± an acceptance criterion. Testing the null hypothesis of zero difference is less interesting, and so is the sample size estimation based on testing that hypothesis. Power function curves for equivalence testing experiments are not widely available. In this paper we present power function curves to help decide on the number of measurements when testing equivalence between the means of two analytical methods. Methods. Computer simulation was used to calculate the probability that the 90% confidence interval for the difference between the means of two analytical methods would exceed the specification limits of 0 ± 1, 0 ± 2 or 0 ± 3 analytical standard deviations (SD_a), respectively. Results. The probability of getting a nonequivalence alarm increases with increasing difference between the means when the difference is well within the specification limits. The probability increases with decreasing sample size and with smaller acceptance criteria. We may need at least 40–50 measurements with each analytical method when the specification limits are 0 ± 1 SD_a, and 10–15 and 5–10 when the specification limits are 0 ± 2 and 0 ± 3 SD_a, respectively. Conclusions. The power function curves provide information of the probability of false alarm, so that we can decide on the sample size under less uncertainty.

Key Words::

• Chemistry techniques
• analytical/methods
• quality control
• reproducibility of results
• sample size
• systematic bias

Declaration of interest: The authors report no conflict of interest. The authors alone are responsible for the content and writing of the paper.