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Parametric Methods I: The Grubb’s Test

  • Univariate outlier detection: The Grubb's test (maximum normed residual test) ─ another statistical method under normal distribution
    • For each object x in a data set, compute its z-score: x is an outlier if 
    \[ z\geq \frac{N-1}{\sqrt{N}}\sqrt{\frac{t^{2}_{\alpha/(2N),N-2 }}{N-2+t^{2}_{\alpha/(2N),N-2}}} \]
    where
    \[ t^{2}_{\alpha/(2N),N-2 } \]
    is the value taken by a t-distribution at a significance level of α/(2N), and N is the # of objects in the data set


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