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A note on permutation tests of significance for multiple regression coefficients.

Michael A Long¹, Kenneth J Berry, Paul W Mielke

¹Department of Sociology, Colorado State University, Fort Collins, CO 80523-1784, USA. Michael.Long@colostate.edu

Psychological Reports

|June 15, 2007

Summary

Traditional multiple regression analysis often relies on asymptotic probability values. This study shows these estimates can be inaccurate, proposing a resampling permutation procedure for more reliable standard error estimation in psychological research.

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Area of Science:

Psychology
Statistics

Background:

Multiple regression analysis is widely used in psychological research.
Asymptotic probability values are commonly reported for standard errors in these analyses.

Purpose of the Study:

To demonstrate the potential inaccuracy of asymptotic standard error estimates in multiple regression.
To introduce and evaluate a resampling permutation procedure for more accurate standard error estimation.

Main Methods:

Employed a resampling permutation procedure.
Estimated standard errors using this novel method.
Compared results with traditional least squares regression estimates.

Main Results:

Asymptotic estimates of standard errors in multiple regression are not always accurate.
The resampling permutation procedure provided substantially different results in some cases.
This highlights potential discrepancies from traditional methods.

Conclusions:

Standard error estimation in psychological research using multiple regression may require more robust methods.
Resampling permutation procedures offer a viable alternative for accurate statistical inference.
Researchers should consider alternative methods to ensure the reliability of their findings.