Examination of the Spencer-McCuen Outlier-Detection Test for Log-Pearson Type 3 Distributed Data

Identification of outliers in flood records can be an important step in a robust flood frequency analysis procedure. Bulletin 17B includes the Grubbs-Beck test (with =10%) as an objective criterion of whether the smallest observations in a flood record are outliers. The Spencer-McCuen test extends the Grubbs-Beck test to consider explicitly whether the three smallest observations are outliers in log-Pearson Type 3 (or equivalently Pearson Type 3) distributed samples with log-space skew coefficients between [-1,1], and three significance levels [1, 5, and 10%]. Presented here are Monte Carlo experiments evaluating the performance of the Spencer-McCuen test. When that test relies on the sample skew coefficient as an estimate of the population skew, the test generally fails to achieve the nominal significance levels. The same is true when used with a generalized (weighted) skew coefficient. Thus, the test will often be inappropriate if used as originally proposed. More fundamentally, when a proposed test relies on the skew coefficient of a sample to test for outliers in that sample, it is no longer clear what it means for an observation to be an outlier.