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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Traditional repeated measures ANOVA F-statistic assumes normality and sphericity.
  • Bootstrap-F (B-F) is a proposed alternative for violations of these assumptions.
  • Limited evidence exists on B-F's robustness and power across diverse conditions.

Purpose of the Study:

  • To evaluate the behavior of Bootstrap-F (B-F) under various conditions.
  • To extend understanding of B-F's robustness and power in repeated measures ANOVA.
  • To provide guidance on using B-F with assumption violations.

Main Methods:

  • A simulation study was conducted.
  • Key variables manipulated included number of repeated measures, sample sizes, sphericity (epsilon values), and distribution shape.
  • The performance of B-F was analyzed under these simulated conditions.

Main Results:

  • B-F can be conservative with high epsilon values.
  • B-F may be liberal with severe violations of normality and sphericity, especially with small sample sizes.
  • Statistical power is influenced by sphericity; lower epsilon requires larger sample sizes for adequate power.

Conclusions:

  • Bootstrap-F (B-F) demonstrates robustness against non-normality and non-sphericity.
  • B-F is reliable for sample sizes exceeding 20-25.
  • A more stringent alpha level (e.g., .025) may be considered when B-F is liberal.