Detection of outliers in processing of small size data

Abstract

This article describes the criteria for detection of outliers power depending on a small size sample. Removing outliers is one of the stages of signals pre-processing. A statistical experiment, in which using a random number generator were received arrays of data, containing several thousand samples with normal distribution, with the given mean averages and standard deviation for each n-value, was conducted to solve this problem. Thus, we researched and vividly illustrated the possibility of Grubbs, Dixon, Tietjen — Moore, Irving, Chauvenet, Lvovsky and Romanovsky criteria at studied data sizes from 5 to 20 meterages. Conclusions about the applicability of each criterion for the outliersdetection in processing of small size data were made. Lvovsky criterion was recognized the optimal criterion. Dixon’s criterion was recommended for n ≤ 10. Irwin’s criterion was recommended when n ≥ 10. Tietjen—Moore’scriterion can be recommended for the detection of outliers in small samples for n > 5, since it recognizes errors well in the values of a ¯x + 4σ and has the least amount of I type mistakes. Grubb’s with an unknown standard deviation may be used in samples for n ≥ 15. Chauvenet and Romanovsky criteria cannot be recommended for the detection of outliers in small size data.