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Beforehand, CMS applied a Tukey outlier deletion methodology when calculating Medicare Benefit (MA) and Medicare Half D Prescription Drug Plans (PDP) star score. A Last Rule applied in 2022, nonetheless, eliminated using Tukey outlier deletion from high quality measures. Based mostly on 2020 historic knowledge, 17% of MA plans would have decrease star rankings as in comparison with just one% would have larger star rankings 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 – ok(IQR), Q3+ok(IQR)}
Right here Q1 and Q3 are the primary and third quartiles of the information respectively and IQR is the interquartile vary (i.e., the distinction between the third and first quartile). The time period ok is a multiplier, which describes how delicate you’d need to be to outliers. John Tukey proposed that ok = 1.5 signifies an “outlier”, and ok = 3 signifies knowledge that’s “far out”.
How probably are you to establish an outlier with the Tukey methodology?
The reply to this query is dependent upon (i) how large your Tukey vary is (i.e., the worth of ok) and (ii) the form of your distribution. Andrey Akinshin created simulations to reply this query for Regular, Gumbel and exponential distributions. The outcomes are beneath. As you may see beneath, 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 is dependent upon context. If these are knowledge errors or pure anomalous conditions, one could need to delete them. However, 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 might generate these values. Both manner, the Tukey methodology is a useful, easy strategy for figuring out outliers, but it surely doesn’t inform you what to do with them as soon as they’re recognized.
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