Modified z score

The modified z score is a standardized score that measures outlier strength or how much a particular score differs from the typical score. Using standard deviation units, it approximates the difference of the score from the median.

The modified z score might be more robust than the standard z score because it relies on the median for calculating the z score. It is less influenced by outliers when compared to the standard z score.

The standard z score is calculated by dividing the difference from the mean by the standard deviation. The modified z score is calculated from the mean absolute deviation (MeanAD) or median absolute deviation (MAD). These values must be multiplied by a constant to approximate the standard deviation.

Depending on the value of MAD, the modified z score is calculated in one of two ways:

If MAD does equal 0

Subtract the median from the score and divide by 1.253314*MeanAD. 1.253314*MeanAD approximately equals the standard deviation: (X-MED)/(1.253314*MeanAD).

If MAD does not equal 0

Subtract the median from the score and divide by 1.486*MAD: (X-MED)/(1.486*MAD). 1.486*MAD approximately equals the standard deviation.