On robust testing for normality in chemometrics

• Classic tests for normality can falsely reject normality because of a single outlier.
• Robust tests for normality are less sensitive to outliers.
• New robust tests that have high power are proposed.

The assumption that the data has been generated by a normal distribution underlies many statistical methods used in chemometrics. While such methods can be quite robust to small deviations from normality, for instance caused by a small number of outliers, common tests for normality are not and will often needlessly reject normality. It is therefore better to use tests from the little-known class of robust tests for normality. We illustrate the need for robust normality testing in chemometrics with several examples, review a class of robustified omnibus Jarque–Bera tests and propose a new class of robustified directed Lin–Mudholkar tests. The robustness and power of several tests for normality are compared in a large simulation study. The new tests are robust and have high power in comparison with both classic tests and other robust tests. A new graphical method for assessing normality is also introduced.