Repeated measures one-way ANOVA based on a modified one-step M-estimator

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Trimmed means offer advantages over traditional means for dependent groups, especially with non-normal distributions.
• Existing trimmed mean methods face practical challenges and may lack Type I error control in small samples.
• Robust M-estimators can address some trimmed mean limitations but may also struggle with small sample sizes.

Purpose of the Study:

• To evaluate a modified one-step M-estimator for comparing trimmed means of dependent groups.
• To assess the performance of this new method in terms of Type I error control and statistical power.
• To compare the proposed method against other omnibus tests for dependent group comparisons.

Main Methods:

• Simulation studies were conducted to compare statistical methods.
• The study examined trimmed means and robust M-estimators for dependent samples.
• A modified one-step M-estimator was developed and tested.

Main Results:

• Trimmed means demonstrated good performance in simulations, particularly with heavy-tailed distributions.
• The modified M-estimator showed improved Type I error control compared to standard trimmed means, especially in small samples.
• One tested omnibus test performed well even with a sample size as small as 11.

Conclusions:

• Modified M-estimators provide a viable alternative to trimmed means for dependent groups, addressing practical concerns.
• The proposed method offers better control over Type I errors in small sample situations.
• Further research into robust statistical methods for dependent data is warranted.