Using Trimmed Means to Compare K Measures Corresponding to Two Independent Groups

Area of Science:

• Statistics
• Robust Statistics

Background:

• Comparing two independent groups with multiple measures (K) presents challenges for hypothesis testing and confidence intervals.
• Conventional mean comparison methods are sensitive to non-normal and skewed distributions, potentially leading to inflated Type I error rates.
• Robust measures of location and bootstrap methods can mitigate issues associated with non-normality and skewness.

Purpose of the Study:

• To compare statistical methods for testing the equality of trimmed means between two independent groups across multiple measures (K).
• To evaluate methods ensuring a specified family-wise error rate and simultaneous confidence interval coverage.
• To investigate an extension of the percentile bootstrap method for improved performance.

Main Methods:

• Utilizes trimmed means as robust estimators of central tendency.
• Employs bootstrap methods, specifically the percentile t bootstrap and an extended version.
• Focuses on scenarios with K=4 measures and a significance level (α) of 0.05.

Main Results:

• Standard mean comparison methods exhibit poor power with minor deviations from normality.
• Trimmed means and bootstrap methods demonstrate superior performance, especially with skewed distributions.
• The extended percentile bootstrap approach shows enhanced accuracy and reliability compared to existing methods.

Conclusions:

• Robust statistical methods, particularly trimmed means combined with bootstrap techniques, are essential for accurate group comparisons.
• The proposed extension of the percentile bootstrap method provides a more reliable approach for hypothesis testing and confidence interval construction.
• These findings are crucial for researchers dealing with non-normally distributed data in multiple comparison scenarios.