Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test...

Area of Science:

• Neuroimaging
• Statistical Inference
• Brain Signal Analysis

Background:

• Neuroimaging studies commonly employ the general linear model (GLM) for statistical inference.
• Testing regression coefficients (H₀:β=0) is crucial for identifying brain signal relationships.
• Existing permutation methods often rely on the F ratio, which can be unreliable with heteroscedastic errors.

Purpose of the Study:

• To compare the performance of the F test statistic and the robust W (Wald) test statistic in permutation tests.
• To evaluate the validity and accuracy of these statistics under both homoscedastic and heteroscedastic error conditions.
• To recommend a reliable test statistic for nonparametric hypothesis testing in neuroimaging.

Main Methods:

• Comparison of the F ratio and W test statistics within eight distinct permutation methods.
• Simulation or analysis under conditions of both homoscedastic (constant variance) and heteroscedastic (non-constant variance) errors.
• Assessment of false positive rates and statistical power for each test statistic and permutation method.

Main Results:

• Permutation tests using the F ratio yielded accurate results with homoscedastic errors but exhibited high false positive rates with heteroscedastic errors.
• Permutation tests employing the W test statistic demonstrated valid results under homoscedasticity and asymptotically valid results under heteroscedasticity.
• While the W statistic showed slightly lower power with homoscedastic errors, this difference diminished with increasing sample size.

Conclusions:

• The W test statistic is recommended for robust nonparametric hypothesis testing of regression coefficients in neuroimaging.
• The W statistic provides a more reliable approach, particularly when error variance is non-constant (heteroscedastic).
• This finding enhances the validity of statistical inference in neuroimaging research, especially in complex models.