Outlier Treatment in Data Merging

Abstract

Experience with a variety of diffraction data-reduction problems has led to several strategies for dealing with mismeasured outliers in multiply measured data sets. Key features of the schemes employed currently include outlier identification based on the values y median = median(| F i | 2 ), σ median = median[ σ (| F i | 2 )], and | Δ | median = median(| Δ i |) = median[|| F i | 2 -median (| F i | 2 )|] in samples with i = 1, 2 ..... n and n ≥ 2 measurements; and robust/resistant averaging weights based on values of | z i | = | Δ i |/max{ σ median , | Δ | median [ n /( n −1)] 1/2 }. For outlier discrimination or down-weighting, sample median values have the advantage of being much less outlier-based than sample mean values would be.