Modified Z-Score

Modified Z Score applying the the mean absolute deviation

The Modified Z-score applies the median calculation instead of the mean. Furthermore, the signed number of standard deviations is replaced by the Mean Absolute Deviation (around the Median).

Indicator Description

The standard Z-score will show you how far removed a data point is from the mean, measured in standard deviations. The modified Z-score applies the median and the standard deviations has been replaced by the Mean Absolute Deviation (around the Median).

For a normally distributed sample, 95.8% of the Z-scores of all data points fall within the range [-2, +2]. A Z-score of 0 indicates that the data point is identical with the arithmetic mean of the data set.

The modified Z-score is a normalized oscillator and will show extreme readings of the input series. The modified Z-score divides the absolute difference between a data point and the median by the Mean Absolute Deviation (around the Median).

As with the standard Z-score, the modified version will normalize the oscillator values. For example, the MACD is not a normalized oscillator. However, by applying the MACD to the Modified Z-score it will plot on a normalized scale. Therefore, the resulting MACD will pass the c-test. To do that, set the MACD as an input series for the modified Z-score.

More information on the process of normalization and the Z-score was discussed in our Indicator Spotlight.

Other Library Indicators

You may want to review other indicators in the Multi Points Statistics category, featuring the Moving Mean TPOMoving Mean VWTPO, Moving MedianTPO, Moving Median VWTPO, Moving Mode TPO and the Moving Mode VWTPO.

You may want to review other indicators in Statistical Analysis category, including the  Mean Absolute Deviation (around the Mean and Median), the Moving Median, the Median Absolute Deviation (around the Median), the Standard DeviationVolume Weighted Standard Deviation, the Volume Weighted Mean Absolute Deviation and the Interquartile Range indicator. Finally, this category also contains the Standard Z Score indicator. The Z-Score was also discussed in the Indicator Spotlight newsletter.

The most frequently used institutional price benchmark to establish the Volume Weighted Average Price was discussed in our Indicator Spotlight.

The Modified Z-score indicator is available for NinjaTrader 8.