More powerful tests of predictor subsets in regression analysis under nonnormality

Area of Science:

• Statistics
• Statistical Modeling
• Data Analysis

Background:

• Parametric tests are statistically optimal for normally distributed data.
• Nonparametric tests can offer greater statistical power than parametric tests when normality assumptions are violated.
• Limited availability of nonparametric tests for complex designs has restricted their use.

Purpose of the Study:

• To investigate the statistical power of nonparametric tests compared to parametric tests under non-normal error distributions.
• To evaluate the performance of nonparametric tests for predictor subset selection in multiple regression analysis.
• To assess the utility of nonparametric procedures for complex experimental designs with realistic data conditions.

Main Methods:

• A Monte Carlo simulation study was employed.
• The study focused on tests of predictor subsets within multiple regression models.
• Performance was evaluated based on statistical power and Type I error rate control.

Main Results:

• Nonparametric tests demonstrated greater statistical power than the traditional F test for skewed and heavy-tailed data.
• Nonparametric tests effectively controlled the Type I error rate.
• The studied nonparametric tests are computable using readily available statistical software.

Conclusions:

• Nonparametric tests are a powerful alternative to parametric tests when data deviates from normality, particularly in regression analysis.
• These findings encourage the broader application of nonparametric methods in complex statistical analyses.
• The accessibility of software for these nonparametric tests removes a significant barrier to their adoption.