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Z-score (amaZScore)

Version 1.3 September 25, 2017

The 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 current value of a data point is above the mean value or below the mean value as calculated for the selected lookback period.

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 Z-score 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.

One of the main applications of the Z-score 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 introduced by William Eckhardt. However, when the Z-score 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 Z-score.

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