Inferential procedures based on the weighted Pearson correlation coefficient test statistic

Area of Science:

• Statistics
• Biostatistics

Background:

• The t-test is widely used for hypothesis testing.
• Weighted Pearson correlation is employed in various analyses.
• Existing t-test methods show poor Type I error control with weighted Pearson correlation.

Purpose of the Study:

• To evaluate the Type I error control of the t-test for weighted Pearson correlation.
• To propose novel methods for accurate hypothesis testing in this context.

Main Methods:

• Derived the large sample variance of the weighted Pearson correlation coefficient.
• Developed an asymptotic test and studentized permutation tests.
• Conducted extensive simulation studies with varying sample sizes and distributions.

Main Results:

• The standard t-test demonstrates severely inflated Type I error rates.
• The proposed studentized permutation test, particularly using Fisher's Z statistic, effectively controls Type I errors.
• Robust performance was observed even in small sample sizes and non-normal data scenarios.

Conclusions:

• The studentized permutation test offers a reliable solution for hypothesis testing with weighted Pearson correlation.
• This method ensures accurate statistical inference, addressing limitations of standard t-tests.