Previously, CMS carried out a Tukey outlier deletion methodology when calculating Medicare Advantage (MA) and Medicare Part D Prescription Drug Plans (PDP) star ranking. A Final Rule carried out in 2022, nevertheless, eliminated the usage of Tukey outlier deletion from high quality measures. Based on 2020 historic knowledge, 17% of MA plans would have decrease star scores as in comparison with only one% would have larger 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)}
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 seemingly are you to determine an outlier with the Tukey methodology?
The reply to this query relies on (i) how broad 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 Normal, Gumbel and exponential distributions. The outcomes are under. As you may see under, non-normal distributions–particularly exponential–are more likely to have an outlier noticed utilizing the Tukey methodology.
Like all outliers, identification is essential however what to do with them relies on context. If these are knowledge errors or pure anomalous conditions, one might wish to delete them. On the opposite hand, if these are simply outlier values that occur from time-to-time, one ought to go away 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 may generate these values. Either method, the Tukey methodology is a useful, easy strategy for figuring out outliers, however it doesn’t let you know what to do with them as soon as they’re recognized.