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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Multiple-comparison procedures are crucial for controlling Type I errors in statistical analyses.
  • Evaluating the performance of these procedures, particularly in two-group designs, is essential for accurate inference.
  • Existing methods vary in their control of different error rates, such as familywise and per-family error rates.

Purpose of the Study:

  • To evaluate the statistical power and Type I error control of various multiple-comparison procedures in two-group designs.
  • To compare stepwise Bonferroni-based methods against other procedures concerning familywise Type I error rate (FWER) and per-family error rate (PFER).
  • To highlight the importance of PFER control and identify methods that achieve it.

Main Methods:

  • Computer simulations were employed to assess the performance of different multiple-comparison procedures.
  • The simulations focused on two-group designs with varying numbers of outcome variables.
  • Statistical power and Type I error rates (FWER and PFER) were the primary metrics evaluated.

Main Results:

  • Stepwise Bonferroni-based procedures demonstrated higher statistical power but failed to control the PFER.
  • Only the classical Bonferroni procedure and a modified MANOVA-protection method effectively controlled the PFER.
  • The relative power of these two PFER-controlling methods was contingent upon several factors, including the number of outcome variables.

Conclusions:

  • The choice of a multiple-comparison procedure is context-dependent.
  • Factors influencing the decision include the number of outcome variables, the priority of PFER control, the need for confidence intervals, and the desired emphasis on multiple versus single variable significance.
  • Greater attention to PFER is recommended, particularly for stepwise Bonferroni-type procedures.