Robust regression and outlier detection in the evaluation of robustness tests with different experimental designs

Robustness tests are usually based on an experimental design approach. As designed experiments generally lead to a large variability among the results, erroneous results are often not readily detected. As a consequence, the ordinary least squares (OLS) estimates of the effects of the robustness test can be biased. Here, two robustness tests are studied, which both contain a suspicious result. Moreover, simulated datasets are considered to examine the influence of the extent of the outlier as well as the influence of multiple outliers. On the one hand, different methods are applied to inspect the results of the experiments for outliers: the half-normal plot of the OLS residuals, the normal probability plot of the effects and a method, which is based on experimental design reconstruction. On the other hand, two robust regression methods are applied to calculate the effects with a minimum influence of possible outliers. The different methods are compared and it is evaluated under which circumstances they can be applied.