A comparison of efficiency of test statistics for detecting outliers in normal population

Abstract

The objective of this research was to compare the efficiency among the test statistics which are used to detect outliers by testing hypothesis methods. The test statistics considered were Dixon’s test, Ferguson’s test, Grubbs’ test, Tw-test, and Tietjen-Moore’s test. The outliers were divided, by how far they are, into two groups: mild and extreme outliers. The efficiency of the test statistics was measured by the probability of type I error and the power of the test. The results showed that Tietjen-Moore’s test can control the probability of type I error according to Cochran and Bradley criteria in every situation. Tw-test has highest sensitivity in detecting one outlier when the sample size is small or moderate but, if the sample size is large, Grubbs’ test performs better. In the case of detecting one extreme outlier, the power of four tests tend to increase as the sample size increases at the significance level 0.01. Given that k outliers are detected, Tietjen-Moore’s test provides higher power than Tw-test when k equals 10% of sample size when the outliers are both mild and extreme, contrary to the case when k make up for 20%.