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Determining sample size when assessing mean equivalence.

Arne Asberg1, Kristine B Solem, Gustav Mikkelsen

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Summary

Determining analytical method equivalence requires careful sample size estimation. This study introduces power function curves to guide the number of measurements needed for reliable equivalence testing, reducing uncertainty in method validation.

Keywords:
Chemistry techniquesanalytical/methodsquality controlreproducibility of resultssample sizesystematic bias

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Area of Science:

  • Analytical Chemistry
  • Method Validation
  • Statistical Analysis

Background:

  • Assessing analytical method equivalence often involves testing if the mean difference falls within specified limits.
  • Traditional hypothesis testing for zero difference and associated sample size estimations are less informative for equivalence assessments.
  • Power function curves for equivalence testing are not widely available, hindering experimental design.

Purpose of the Study:

  • To present power function curves for equivalence testing between the means of two analytical methods.
  • To aid researchers in determining the appropriate number of measurements for reliable method comparison.
  • To reduce uncertainty in sample size selection for equivalence studies.

Main Methods:

  • Computer simulations were employed to calculate probabilities.
  • The study focused on the 90% confidence interval for the difference between method means.
  • Specification limits were set at 0 ± 1, 0 ± 2, and 0 ± 3 analytical standard deviations (SDa).

Main Results:

  • The probability of a false non-equivalence alarm increases with the mean difference, smaller sample sizes, and tighter acceptance criteria.
  • Recommended sample sizes range from 40-50 for ±1 SDa limits, 10-15 for ±2 SDa limits, and 5-10 for ±3 SDa limits.
  • These results highlight the impact of acceptance criteria and sample size on the reliability of equivalence testing.

Conclusions:

  • Power function curves offer crucial insights into the probability of false alarms in equivalence testing.
  • These curves enable more informed decisions regarding sample size determination.
  • Utilizing power curves reduces uncertainty in the validation of analytical methods.