Modified Z-Score

The Z-score method relies on the mean and standard deviation of a group of data to measure central tendency and dispersion. This is troublesome, because the mean and standard deviation are highly affected by outliers – they are not robust. In fact, the skewing that outliers bring is one of the biggest reasons for finding and removing outliers from a dataset! Another drawback of the Z-score method is that it behaves strangely in small datasets – in fact, the Z-score method will never detect an outlier if the dataset has fewer than 12 items in it.

This motivated the development of a modified Z-score method, which does not suffer from the same limitation. This method works well for skewed data or data that is not normally distributed & where the number of observations is less. MAD is Median Absolute Deviation. A further benefit of the modified Z-score method is that it uses the median and MAD rather than the mean and standard deviation. The median and MAD are robust measures of central tendency and dispersion, respectively.


Modified Z-score example