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I have data being grouped into 3 ranges: 80-89%; 90-109% 110-120%

Can I call these 3 Terciles? I believe a tercile is the data split into 3 equal sized groups - is there another term I can use instead of tercile (for uneven groups)?

Nick Cox
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Aaron Guthrie
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    What about the group of 0-79% and what about the group >120% ? It seems you have five groups out of which you explicitly mention three. Did you read https://en.wikipedia.org/wiki/Percentile ? – Nikolas Rieble Jun 12 '17 at 12:27
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    Thanks I'll check the reference. For more context, the ranges relate to relativity to market salaries where the compa ratio = 100 (if paid a compa ratio of 100, that is equivalent to 100% of the market rate) Compa ratio 80-89 indicates paid less than market 90-110 paid at market (+/- 10%) 110+ shows paid above market Our policy limits salary as being +/- 20% of the median i.e. range of 80-120 – Aaron Guthrie Jun 12 '17 at 12:30
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    *Why* do you need another term if one already exists? You can always talk about "equally sized groups". – Tim Jun 12 '17 at 12:31
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    They are not equally sized, hence the question - the middle group has a wider range, otherwise I could use "tercile" – Aaron Guthrie Jun 12 '17 at 12:33
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    You have three groups that you mention. They are **not** tertile (more common term in my experience) or tercile groups unless 89 or 90 and 109 or 110 are tertiles of the data, i.e. 1/3 of values are less than 89 or 90 and 2/3 less than 109 or 110. Clearly your groups are not equal intervals on your variable scale; it's not impossible that they have equal frequencies on your information, but it seems highly unlikely. So, you have three groups or intervals and no need to reach for any other term. – Nick Cox Jun 12 '17 at 12:38
  • See also https://stats.stackexchange.com/questions/235330/iles-terminology-for-the-top-half-a-percent for comments on terminology of values defined by whatever fraction is smaller or large and the bins or intervals they delimit. – Nick Cox May 08 '19 at 16:13

3 Answers3

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From my understanding, and as you pointed out, terciles are three intervals containing 1/3 of the observations each. My suggestion to you would thus be to instead use another word to describe your intervals with, in order to avoid misunderstandings. Perhaps "partitions", "discretisations", or "chosen intervals" would suffice?

Phil
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A tercile contains one-third of the data with the cuts being lower third, middle third and upper third. A tercile is an element of that particular subset of data divided into three groups that is either lower, middle or upper thirds. Generally, if the number of data entries is not a multiple of three, interpolation is used to calculate the tercile parameters.

The other term the OP wants is merely, "data divided into three groups," which although not implying interpolation at face value, does not exclude it either.

Carl
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A term which I have seen used for groups formed by cutting at the tertiles is "tertile categories". The advantage of this over saying thirds is that it makes precise how the categories were arrived at. Of course quintile categories and so on are also in use.

mdewey
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  • I can't quite see this. _Top third_ and so forth are likely to be clear informally. So, "in the top third of our students" is not hard to decipher. (Mind you, 90% of testimonials report a student as being in the top third....) I tend to use the term _categories_ for categories that are nominal or possibly ordinal, not subdivisions of a measured or counted scale: even though the latter are also ordinal categories, I still think the term is better avoided. – Nick Cox May 09 '19 at 17:19