Testing two variances for superiority/non-inferiority and equivalence

Using the exhaustion algorithm for sample size allocation with cost

Jiin huarng Guo, Wei-Ming Luh

Research output: Contribution to journalArticle

Abstract

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995–1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.

Original languageEnglish
JournalBritish Journal of Mathematical and Statistical Psychology
DOIs
Publication statusPublished - 2019 Jan 1

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Cost Allocation
Non-inferiority
Sample Size
Equivalence
Testing
Percentile
Costs
Unequal
F distribution
Sample Size Determination
Standard Normal distribution
Costs and Cost Analysis
Benchmarking
Test of Hypothesis
Statistical Power
Hypertension
Social Sciences
Type I error
Normal Distribution
Statistical test

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Arts and Humanities (miscellaneous)
  • Psychology(all)

Cite this

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