Statistical Details for ANOM

Transformed Ranks

Suppose that there are n observations. The transformed observations are computed as follows:

• Rank all observations from smallest to largest, accounting for ties. For tied observations, assign each one the average of the block of ranks that they share.

• Denote the ranks by R1, R2,..., Rn.

• The transformed rank corresponding to the ith observation is:

The ANOM procedure is applied to the values Transformed Ri. Since the ranks have a uniform distribution, the transformed ranks have a folded normal distribution. See Nelson et al. (2005).

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