Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size...

Area of Science:

• Statistics
• Biostatistics
• Psychometrics

Background:

• Null hypothesis significance testing (NHST) for group means faces criticism.
• There's growing interest in alternative hypothesis tests like superiority, non-inferiority, and equivalence.
• Sample size estimation for these advanced tests is often overlooked, particularly with unequal costs or group sizes.

Purpose of the Study:

• To develop an optimized sample size determination method for equivalence tests.
• To address challenges of unequal sampling unit costs and unequal group sizes.
• To maximize statistical power while minimizing total research costs.

Main Methods:

• Approximated F distribution percentiles using standard normal distribution percentiles for initial allocation.
• Employed an exhaustion algorithm to identify optimal group size combinations.
• Ensured designated statistical power levels are met with maximal efficiency.

Main Results:

• The proposed method achieves optimized sample size planning for equivalence tests.
• Simulations demonstrate efficiency in controlling Type I errors and maintaining statistical power.
• An illustrative example using hypertension data from the Health Survey for England is provided.

Conclusions:

• The developed sample size determination is broadly applicable and efficient.
• Four R Shiny applications are provided for practical implementation.
• Benchmarks for setting equivalence margins are suggested to aid researchers.