Quantifying and Rejecting Outliers: The Grubbs Test

Sometimes, a data set can have a recorded numerical observation that greatly deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier. To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is known as the Grubbs statistic, 'G.' When the calculated G value exceeds the G critical value for a given confidence level and the number of observations, the questionable observation is considered an outlier and removed from the data set. On the contrary, if the calculated G value is smaller than the critical G value, the questionable observation is not considered an outlier and therefore retained in the data set.