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I am reading a paper where users have a score $> 0$, and the authors want to assign users to groups Low, Medium, and High. Here is what they do:

  1. Users' scores are first sorted in ascending order.
  2. Scores are then summed from the beginning until reaching 1/3 of total sum. These users are the Low group.
  3. Scores are then summed from the value at which (2) left off until reaching 2/3 of the total sum. These users are the Medium group.
  4. The rest of the users are the high group.

It is not quite a percentile ranking, right? What is this method called?

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  • $\begingroup$ I assume the word you are thinking of is "ordinal"... $\endgroup$
    – usεr11852
    Commented Aug 26, 2022 at 22:12
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    $\begingroup$ This looks a bit similar to tantile. $\endgroup$
    – ttnphns
    Commented Aug 26, 2022 at 22:16
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    $\begingroup$ Very closely related: stats.stackexchange.com/questions/137931. $\endgroup$
    – whuber
    Commented Aug 26, 2022 at 22:20

1 Answer 1

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EDIT: My initial answer was incorrect because as ttphns and whuber point out, this is a type of tantile and not a quantile. I have now updated the answer.


If you were dividing the number of users into 3 equal-sized groups (assuming the total is divisible by 3), this would be a tertile (more common) or tercile, which is a type of quantile. Definitions from wiktionary:

  1. (statistics) Either of the two points that divide an ordered distribution into three parts, each containing a third of the population.
  2. (statistics) Any one of the three groups so divided.

However, since you are diving the users into 3 groups so that they have an equal sum of the scores and not and equal number of users, you may create differently-sized groups. These groups are tantiles and not quantiles. I am not aware of a specific term for tantiles of different values such as 3 that is analogous to tertiles for quantiles.

The following thread mentioned by whuber is one of the rare places I've even seen tantiles mentioned. The discussion in the comments there is useful: When would we use tantiles and the medial, rather than quantiles and the median?

Nick Cox makes the valuable point that this type of metric only makes sense for a variable where a sum is meaningful, like income. For other variables like temperature, summing doesn't give rise to a useful quantity.

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    $\begingroup$ I am not aware of a name, but a concrete application might be to an additive variable like income or wealth, where the 90% poorest have 1/3 of the total; the next 9% have 1/3 too; and the last richest 1% have 1/3 too. (The numbers here are invented, but intended to be plausible.) $\endgroup$
    – Nick Cox
    Commented Aug 27, 2022 at 8:27

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