Grubbs' Test for Outlier Detection Code Implementation

Grubbs' test is a classical outlier detection method suitable for datasets following normal distribution. It identifies potential outliers by calculating the maximum deviation between extreme values (either maximum or minimum) and the mean of the dataset. The core principle assumes that the data point showing the largest deviation from the mean in a dataset is most likely to be an outlier.

Implementing Grubbs' test in MATLAB typically involves these key steps: first compute the mean and standard deviation of the dataset, then identify the data point with the maximum absolute deviation from the mean. The Grubbs' statistic is calculated as G = max|X_i - mean| / standard_deviation. The implementation requires comparing this statistic against critical values from Grubbs' table based on significance level (commonly α=0.05) and sample size. If the calculated statistic exceeds the critical value, the point is flagged as an outlier.

Important practical considerations: Grubbs' test is sensitive to data normality assumptions and is designed for univariate datasets. When outliers are detected, manual verification of data logical合理性 is recommended before removal. This method finds wide applications in industrial quality control and experimental data analysis.

Extended considerations: For non-normal distributions, Tukey's boxplot method serves as an alternative approach. When multiple outliers are suspected, iterative detection should be implemented - removing one outlier at a time and recalculating the test statistic for the remaining data points until no more outliers are detected.