I know the original post is over a year old, but I would like some more information on this topic. I currently run a proficiency program for manure testing and soil testing laboratories. A colleague, who knows much more about statistics than I do, suggested the following to get a 95% confidence interval using the MAD and median.
- Calculate the median and MAD values.
- Remove results exceeding plus or minus 4.0 MAD units from the median as outliers.
- Recalculate the median and MAD values on the reduced data set.
- Results exceeding plus or minus 2.9 MAD units from the second median are outside the 95% confidence interval.
There is one other kicker. I use the statistical program R. When calculating MAD I use the following:
mad(x, constant = 1)
The default in R is: constant = 1.4826.
Typically, we have from 140 to 200 datapoints for each analysis. Often, the results are right skewed, occasionally left skewed, and rarely normally distributed. After removing the 4.0 MAD outliers, we have a much more normally distributed histogram. I suspect at that point we might be able to use mean and SD to calculate the confidence interval.
For a number of years, we just ran the data one time. Labs were flagged for accuracy if their results deviated by more than 2.5 MAD units from the median. I have compared both methods, and usually 2.5 MAD units from the median (just one calculation) is quite close to the two-step method using 2.9 MAD units from the median after removing the 4.0 outliers.
I hope this method gives us a 95% confidence interval. But, if anyone has a better suggestion, I'd like to hear it.