A Z-score or standard score is a numerical measurement of a value’s relationship to the arithemic mean of the data set. The Z-score is the signed number of standard deviations by which the value of a data point is above the mean or below the mean value of the data set.

### Indicator Description

The Z score indicator is a normalized oscillator that can be used to identify extreme readings of the input series. The Z-score is calculated by dividing the absolute difference between a data point and the arithmetic mean by the standard deviation.

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.

One of the main applications of the Z Score indicator is that it can be used to normalize any oscillator. For example, the MACD is a non normalized oscillator which does not pass the c-test intorudced by William Eckhardt. However, when the Z Score indicator is used to normalize the MACD, the resulting oscillator uses a normalized scale and will pass the c-test. The normalized MACD is obtained, when the MACD is used as the input series for the standard score.

#### Other Library Indicators

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

Other indicators in the Statistical Analysis category, include the Mean Absolute Deviation (around the Mean and Median), the Moving Median, the Median Absolute Deviation (around the Median), the Standard Deviation, Volume Weighted Standard Deviation, the Volume Weighted Mean Absolute Deviation and the Interquartile Range indicator.

The library also contains a Modified Z Score. It 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).

The indicator is available for NinjaTrader 8.