When to use Bootstrap-F in One-Way Repeated Measures ANOVA: Type I Error and Power

With repeated measures, the traditional ANOVA F-statistic requires fulfillment of normality and sphericity. Bootstrap-F (B-F) has been proposed as a procedure for dealing with violation of these assumptions when conducting a one-way repeated measures ANOVA. However, evidence regarding its robustness and power is limited. Our aim is to extend knowledge about the behavior of B-F with a wider range of conditions.

A simulation study was performed, manipulating the number of repeated measures, sample sizes, epsilon values, and distribution shape.

B-F may become conservative with higher values of epsilon, and liberal under extreme violation of both normality and sphericity and small sample sizes. In these cases, B-F may be used with a more stringent alpha level (.025). The results also show that power is affected by sphericity: the lower the epsilon value, the larger the sample size required to ensure adequate power.

B-F is robust under non-normality and non-sphericity with sample sizes larger than 20-25.