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The field of research I'm in uses ranked data a lot. We often refer to deciles to mean the group of units that make up one-tenth of a population or sample. Recently I saw a paper which made the point that the word deciles should be used to refer to the singular values that define the edges of those groups, not the groups themselves. The OED states:

  1. Statistics. Each of the ten groups produced by dividing a frequency distribution into groups containing one tenth of the total population. Also occasionally: each of the nine values of a variate which divide a frequency distribution in this way.

Is this just a case of language evolving naturally? Is it acceptable to use the first half of the OED defintion in research papers?

Bradford
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  • That first definition works well with the preposition “in”: “people in the top percentile of wealth”, “houses in the bottom quartile of cost per square foot”, etc. The phrase “the middle quintile of income” is also clear, and is a common figure in income statistics from the US census, but not used much elsewhere. – Matt F. Jul 19 '23 at 13:20

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There is a potential for confusion and both are used. You just need to be clear. I try to use the words point and group to clarify which I am talking about.

To take an example, the UK Office for National Statistics published an Excel workbook of data for effects of taxes and benefits on household income in the financial year April 2021-March 2022 where Table 2a gives

  • Breakpoints for the quintile groups of equivalised household disposable income (row 5); as you might expect, there are four breakpoints between the five groups

          £19,542     £27,874     £37,230     £51,164

  • Mean equivalised household disposable income in each quintile group (row 48); as you might expect, there are five quintile groups and so five means

      £13,218     £23,750     £32,419     £43,567     £83,687

I think it is reasonable to call £27,874 the second breakpoint the "second quintile point" or $q_{0.4}$.

I also think it reasonable to call £23,750 the "mean of the second quintile group". As you would expect, this is between the first quintile point of £19,542 and the second quintile point of £27,874, i.e. the range of the second quintile group (it is slightly more than halfway between them).

Henry
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