Direct Answer
The robust z-score, also called the modified z-score, replaces the mean and standard deviation with the median and the median absolute deviation. This keeps outliers in the window from distorting the scale. The 0.6745 factor makes the score comparable with a standard z-score for normal data.
Robust Z-Score: Formula, Meaning, Signals, Examples and How to Use It
How Is Robust Z-Score Calculated?
The robust z-score, also called the modified z-score, replaces the mean and standard deviation with the median and the median absolute deviation. This keeps outliers in the window from distorting the scale.
Formula: M = 0.6745 * (x - median) / MAD, where MAD is the median of absolute deviations from the median
Inputs:
- Series values
- Window length
- Median and MAD of the window
Worked example. A value of 30 against a median of 20 and a MAD of 5 gives a robust score of 1.349. The inputs are illustrative numbers, not market data.
Reading it. The 0.6745 factor makes the score comparable with a standard z-score for normal data. Iglewicz and Hoaglin suggested treating absolute values above 3.5 as potential outliers.
Limits. If more than half the window takes the same value, MAD is zero and the score is undefined. Real data with fat tails still produces many scores above 3.5 without being errors.
What is Robust Z-Score?
The robust z-score, also called the modified z-score, replaces the mean and standard deviation with the median and the median absolute deviation. This keeps outliers in the window from distorting the scale.
How to use Robust Z-Score
The 0.6745 factor makes the score comparable with a standard z-score for normal data. Iglewicz and Hoaglin suggested treating absolute values above 3.5 as potential outliers. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Median and MAD both ignore the tails, so the scale of the score is set by the typical bulk of the data and not by its extremes.
- The 0.6745 factor aligns the MAD with the standard deviation of normal data, so scores read like conventional z-scores on clean data.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- The MAD uses fewer effective data points than a standard deviation, so the scale itself is noisier in small windows.
- Data with many ties, such as prices rounded to a tick, can make the MAD take only a few discrete values, so scores move in steps.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Robust Z-Score a buy or sell signal?
No. The 0.6745 factor makes the score comparable with a standard z-score for normal data. If more than half the window takes the same value, MAD is zero and the score is undefined. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Robust Z-Score?
Robust Z-Score takes these inputs: series values; window length; median and MAD of the window. There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner.
Can Robust Z-Score be used by itself?
If more than half the window takes the same value, MAD is zero and the score is undefined. Real data with fat tails still produces many scores above 3.5 without being errors. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Robust Z-Score work on every timeframe?
The calculation (M = 0.6745 * (x - median) / MAD, where MAD is the median of absolute deviations from the median) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Robust Z-Score give false signals?
The MAD uses fewer effective data points than a standard deviation, so the scale itself is noisier in small windows. Data with many ties, such as prices rounded to a tick, can make the MAD take only a few discrete values, so scores move in steps. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Robust Z-Score be backtested?
Rebuild Robust Z-Score from series values using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.