Median Absolute Deviation (MAD) is a measure of variability in a sample of data, and is often used as an alternative to measures like standard deviation since it is more resistant to outliers. Use [tag:mae] if you are asking about the point forecast accuracy measure called MAD or MAE.

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### Convert median absolute deviation (MAD) to SD for log-normal distribution

How do I convert the $\text{MAD}$ (median absolute deviation from the median) of data that is drawn from a log-normal distribution to the standard deviation of a log-normal distribution? To clarify, ...
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### What's the best method to measure relative variability for non normal data?

I have a set of data that states the volume required each month for the next 12 for 750 raw materials. I would like to determine the variability in the demand for each material, and categorise the ...
54 views

### Inference using robust statistics

I'm simulating the overall usage of a cluster using historic deployment data. Due to the nature of the simulation, there are some heavy points (i.e. very low overall usage). As a result, the variance ...
117 views

### Modified Z score of a sample

I would like advice on how to calculate a modified Z score for multiple samples drawn from a population. I understand that when working with standard Z score the standard error of the mean woudl be ...
78 views

### Welch t-test using the median and MAD

Can the Welch t-test be used with the median and MAD instead of mean and variance? I think outliers are causing problems and the median places less weight on extreme outliers. I'm using this to test ...
442 views

### Median absolute deviation outlier detection for new data points

I have been reading this article for outlier detection and the method proposed works really well when applied over my data set. However, it would be great if i could run outlier check for new data ...
272 views

Am I correct in saying that you can only use the formula for approximating the standard deviation from MAD, i.e $$\text{SD } = K \times \text{ MAD }$$ if you know the actual probability ...
165 views

### How to prove 'For a symmetric distribution with zero mean, the population MAD is the 75th percentile of the distribution'

For a symmetric distribution with zero mean, the population MAD is the 75th percentile of the distribution I came across this statement in the wikipedia page for MAD(Median Absolute Deviation) but ...
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### Robust Regression

The Median Absolute Deviation (MAD) is often used as a measure of dispersion of the residuals in robust regression. For univariate data, MAD is computed by first finding the median of the data, then ...
224 views

### Interpretation of the least absolute deviations linear regression coefficient

In linear regression of $y$ onto $x$, one finds a $\beta_0$ and $\beta_1$ minimizing $\sum \|y - (\beta_1 x + \beta_0)\|^2$. One can show that $$\beta_1 = \rho(x,y) \frac{\sigma(y)}{\sigma(x)},$$ ...
58 views

### Only four values per site - how do I detect outliers (with MAD)?

I have four weights. I want to test if there is an outlier within those four weights. To me, the number seems quite small to detect outliers. I thought that the Median Absolute Deviation (MAD) ...
368 views

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### Use of robust spread measures such median average deviation and median filters for time series

I have a time series where I need to detect gross anomalies due to coding errors, not small shifts in the structure of the series. I am interested in the most recent data points, not historical data ...