Beforehand, CMS carried out a Tukey outlier deletion technique when calculating Medicare Benefit (MA) and Medicare Half D Prescription Drug Plans (PDP) star score. A Ultimate Rule carried out in 2022, nevertheless, eliminated the usage of Tukey outlier deletion from high quality measures. Primarily based on 2020 historic knowledge, 17% of MA plans would have decrease star scores as in comparison with just one% would have increased star scores after eradicating the Tukey outlier deletion. This begs the query, what’s a Tukey Outlier.
Tukey Outlier Definitions.
Tukey outliers are knowledge factors that lie exterior the next vary;
- {Q1 – okay(IQR), Q3+okay(IQR)}
Right here Q1 and Q3 are the primary and third quartiles of the info respectively and IQR is the interquartile vary (i.e., the distinction between the third and first quartile). The time period okay is a multiplier, which describes how delicate you’ll wish to be to outliers. John Tukey proposed that okay = 1.5 signifies an “outlier”, and okay = 3 signifies knowledge that’s “far out”.
How doubtless are you to determine an outlier with the Tukey technique?
The reply to this query depends upon (i) how extensive your Tukey vary is (i.e., the worth of okay) and (ii) the form of your distribution. Andrey Akinshin created simulations to reply this query for Regular, Gumbel and exponential distributions. The outcomes are under. As you’ll be able to see under, non-normal distributions–particularly exponential–are more likely to have an outlier noticed utilizing the Tukey technique.
Like all outliers, identification is essential however what to do with them depends upon context. If these are knowledge errors or pure anomalous conditions, one could wish to delete them. However, if these are simply outlier values that occur from time-to-time, one ought to depart them within the knowledge and simply attempt to higher perceive if there’s a knowledge producing course of which differs from the common one which might generate these values. Both method, the Tukey technique is a useful, easy method for figuring out outliers, however it doesn’t let you know what to do with them as soon as they’re recognized.
