# “-iles” terminology for the top half a percent

The top 25% is the top quartile.
The top 10% is the top decile.
The top 1% is the top percentile.

Is there an equivalent for the top 0.5% i.e. 1-in-200?

Historically, and to the present, the upper or third quartile (for example) is the value exceeded by just 25% of values. (I only ever see informal use of “top” for this meaning.)

By extension, the interval or bin between the upper or third quartile and the maximum is often also called the upper quartile, and sometimes the fourth quartile. More generally, $$k$$ breakpoints define $$k + 1$$ groups. The word “quarter” is also available and perhaps preferable.

Some might quibble at this laxness of terminology and prefer (or even insist on) terminology such as bin or interval whenever bins or intervals are in question. More positively, disambiguation of two related senses is usually not too difficult. If there is talk of people in the top quartile of course performance or BMI or whatever, it is clear what is intended.

Similar comments apply here to deciles and percentiles. Other terms in varying use are tertiles (rare?), quintiles (common), sextiles (rare?) and octiles (uncommon but not rare). The qualifications here are based on my haphazard reading and memory.

Latin is no longer as familiar as its most enthusiastic proponents would like and these terms are challenging to many. More positively, there seems to be a growing convergence on quantile as a standard term and just to expect to see the numerical definitions being explicit. Thus I’d expect to see references to the $$5, 1, 0.5$$% points or quantiles and similarly the upper $$95, 99, 99.5$$% points or quantiles. In practice I see no use of, and in principle see no need for the use of, terms in Latin (or Greek or any other languages) for most such values or the bins they define. Concretely, anyone knowing how to interpret “the top half-percentile” is likely to find “above the 99.5% point” simpler to use.

EDIT 5 October 2016

Aronson (2001) documented first uses of various terms for quantiles. The list here includes some earlier dates from searches of the Oxford English Dictionary and www.jstor.org on 5 October 2016. The dates refer to earliest citations of the terms with their statistical meaning and not to other meanings. The general term quantile itself is often attributed to Kendall (1940) but can be found in Fisher and Yates (1938).

``````English ordinal   Statistical term  Earliest citation 2016+ additions
(Aronson)          (Cox)

Third              Tertile             1931              1911
Tercile             1942

Fourth             Quartile            1879

Fifth              Quintile            1951              1910

Sixth              Sextile             1920

Seventh            Septile             1993              1981

Eighth             Octile              1879

Ninth              Nonile              1968

Tenth              Decile              1881
Decentile (***)     1988

Sixteenth          Suboctile           1880

Twentieth          Vigintile           1936
Ventile (**)

Thirtieth          Trentile                              1958

Hundredth          Percentile          1885
Centile             1902              1894

Thousandth         Permille            1904
``````

Aronson, J. K. 2001. Francis Galton and the invention of terms for quantiles.
Journal of Clinical Epidemiology 54: 1191-1194.

Fisher, R. A. and Yates, F. 1938. Statistical Tables for Biological, Agricultural and Medical Research. Edinburgh: Oliver and Boyd.

Kendall, M. G. 1940. Note on the distribution of quantiles for large samples.
Supplement to the Journal of the Royal Statistical Society 7: 83-85.

EDIT 22 Dec 2016 The historical information above is now written up within Cox, N.J. 2016. Letter values as selected quantiles. Stata Journal 16: 1058-1071 http://www.stata-journal.com/article.html?article=st0465

EDIT 20 June 2017 Added “trentile” reference. Slonim, M.J. 1958. The trentile deviation method of weather forecast evaluation. Journal of the American Statistical Association 53: 398–407. http://www.jstor.org/stable/2281863

EDIT 7 Aug 2019 Another reference for trentile is Panofsky, H.A. and Brier, G.W. 1958. Some Applications of Statistics to Meteorology. University Park, PA: College of Mineral Industries, Pennsylvania State University. They refer to use in World War II.

EDIT 9 Jan 2021 Quartile, sextile and octile are in the first edition of Samuel Johnson’s Dictionary (1755), but with astronomical meanings. None of the other terms is.

EDIT 29 Jan 2021 (*) Hexadecile is recorded from 2001 (link courtesy @whuber).

EDIT 5 Feb 2021 (**) Earliest use of ventile in this sense is hard to spot among quite different meanings.

EDIT 25 Sept 2021 (***) Added decentile (not in OED, some JSTOR hits).