# Tagged Questions

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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### What is the best way to determine which proteins are significantly bound on a testing chip?

I've got a question about the data from a biological experiment. Three times the same 1024 different proteins are spotted on one testing chip. Target of the experiment is to see whether certain ...
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### What should I use to establish a threshold to detect threshold crossings?

I have data graphed in green here: I want to detect the peaks but I don't know how to define the threshold values. The blue lines are mean ± standard deviation. Using that, I would miss the three ...
239 views

### When the Median Absolute Deviation (MAD) is zero

Suppose my data look like the following: (10, 10, 10, 10, 10, 0) Would it be possible to remove an outlier in this distribution using the median absolute deviation? Of course, you wouldn't need to ...
331 views

### Determine outliers using IQR or standard deviation?

Similar to ... which doesn't have the answer I'm looking for. The data set has a normal distribution. For the project I'm working on, outliers have to be determined over residuals of breeding ...
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### cleaning outliers based on MAD but if MAD == 0.0 then clean by STD?

I'm trying to clean outliers from my features by the following univariate method: calculate median for each feature, and nullify values that are far from it by more than 3*MAD (median absolute ...
275 views

### Identify outliers with median-absolute-deviation for timeseries data

I am having trouble understanding this particular method of detecting outliers in a time series. Below is the problem: I have a region-of-interest containing 15 voxels. Each voxel contains values ...
373 views

### Median absolute deviation: impact/bias when forcing a median of zero

I want to estimate the median absolute deviation (MAD) of a signal. The MAD is defined as the median of the absolute difference between the signal and its median. Now I have a signal that I know for ...
753 views

### Median absolute deviation (MAD) and SD of different distributions

For normally distributed data, the standard deviation $\sigma$ and the median absolute deviation $\text{MAD}$ are related by: $\sigma=\Phi^{-1}(3/4)\cdot \text{MAD}\approx1.4826\cdot\text{MAD},$ ...
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### Bar plot with median +/- median absolute deviation in scientific publication

I know bar plots usually represents mean +/- sem, but if the data is non-normal, is it ok to bar plot median +/- mad? I don't like box plots. Suggestison?
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### Proving the consistancy of the MAD

I am trying to prove that the median absolute deviation from the median (MAD), with k=1.4862, is a consistent estimator of the standard deviation.
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### Alternatives to MAD to find a yardstick to assess data

In a paper by Rousseeuw and Croux from 1993 ("Alternatives to the Median Absolute deviation", page 1274, link to pdf), I came across an indicator I'm considering using. The formula is:  Sn = C\, ...
265 views

### What distribution has the maximum entropy for a known mean absolute deviation?

I was reading the discussion on Hacker News about the use of the standard deviation as opposed to other metrics such as the mean absolute deviation. So, if we were to follow the principle of maximum ...
226 views

I'm using R to calculate the median absolute deviation for a few distributions, but some of the values I'm calculating do not seem realistic at all. I have the following distribution: ...
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### MAD in relation to 95% confidence

MAD (Median Absolute Deviation) is: $\text{MAD} = M_i(|x_i-M_j(x_j)|)$ where $M()$ is the median operator ($M_i(x_i) = \text{median}(x_1,...,x_n)$). I'd like to scale the MAD in such a way as to ...
655 views

### Does a median-unbiased estimator minimize mean absolute deviance?

This is a follow-up but also a different question of my previous one. I read on Wikipedia that "A median-unbiased estimator minimizes the risk with respect to the absolute-deviation loss function, as ...
839 views

### Median + MAD for skewed data

I am trying to figure out what happens if you apply Hampel's outlier detection technique based on the median and the MAD to data that is skewed. Apparently, the advantage of Hampel's method over ...
349 views

### Propagation of errors with median absolute deviation from the median?

Is there a theoretically-sound way to perform propagation of errors with robust statistics? I am trying to characterize the errors inherent in a measurement and propagate the uncertainty through ...
1k views

### Outlier detection for heavy-tailed data

Applying modified z-score for outlier elimination on some data (Iglewicz and Hoaglin, 1993), I discovered that a big proportion of the data (~10%) was outside the range ...
486 views

### Using MAD as a way of defining a threshold for significance testing

If I have a set of terms each term having a particular frequency associated with it (the number of the times the term has appeared in fixed corpus of papers), then is the following method of ...
1k views

### MAD equivalent for standard error

As far as I know, one can calculate the relative standard error from the standard deviation of a data sample. I am looking for the Median Absolute Deviation equivalent for standard error. Does one ...
682 views

### Mean$\pm$SD or Median$\pm$MAD to summarise a highly skewed variable?

I'm working on highly skewed data, so I'm using the median instead of the mean to summarise the central tendency. I'd like to have a measure of dispersion While I often see people reporting mean ...
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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 ...