Outliers are a common problem in statistical analysis. It is critical to ensure that bias is not accidentally introduced when any dataset is filtered for datapoints that are outside of an expected range. Generally speaking, removing outliers follows a guideline that datapoints may be removed if they incorrectly influence the analysis in a way that is not consistent with the experimental design. Criteria for filtering should always be established ahead of time, and never be changed after the fact.
Several methods exist for filtering. One is Cook's Test, or Cook's Distance, which measures the affect outlier datapoints have on the remaining datapoints, and if that change is outside a predetermined threshold. Cook's Distance can be implemented in R, Graphpad Prism, and other statistical analysis software.
In this instance, the dataset was being tested for normalcy as part of a larger workflow. A QQ-plot was created, and the data reasonably fit, however, the plot failed the Shapiro-Wilk normality test. Graphpad Prism has created a strikingly good description of normalcy tests, as well as the methods it uses to detect outliers.
The dataset was imported into Graphpad Prism, and the ROUT method was used with a Q cutoff of 0.5% , which eliminated 12 outliers. Next, Column Analyes -> Column Tests was run on the outlier-filtered dataset, and all three normalcy tests (D'Agostino-Pearson, Shapiro-Wilk, and Kolmogorov-Smirnov) were run on the dataset from David Baker. The output showed that it passed the D'Agostino-Pearson normalcy test, likely due to more sensitive comparison of datapoints to a Gaussian distribution, as well as correct filtering with ROUT.