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Use ANOM to compare group means to the overall mean. This method assumes that your data are approximately normally distributed. See Example of an Analysis of Means Chart.
This is the nonparametric version of the ANOM analysis. Use this method if your data is clearly nonnormal and cannot be transformed to normality. ANOM with Transformed Ranks compares each group’s mean transformed rank to the overall mean transformed rank. The ANOM test involves applying the usual ANOM procedure and critical values to the transformed observations.
Suppose that there are n observations. The transformed observations are computed as follows:
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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. For details, see Nelson et al. (2005).