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#116709 - 11/27/03 05:42 AM quartile variations
jennieho Offline
stranger

Registered: 10/23/03
Posts: 2
I have a report which has grouped ranges into lower, middle and upper quartiles. Does anyone know whether quartile can only be used for four groups, and if so, what the equivalent word should be for three sections. Thanks.


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#116710 - 11/27/03 08:38 AM Re: quartile variations
wwh Offline
Carpal Tunnel

Registered: 01/18/01
Posts: 13858
quartile
n : (statistics) any of three points that divide an ordered
distribution into four parts each containing one quarter
of the scores


Source: Webster's Revised Unabridged Dictionary (1913)

Quartile \Quar"tile\, n. [F. quartile aspect, fr. L. quartus the
fourth. See Quart.] (Astrol.)
Same as Quadrate.


I found severalsites on Internet that used "tertile" to mean data divided by two points into three groups, but was
unable to find a dictionary definition.

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#116711 - 11/27/03 08:05 PM Re: quartile variations
stales Offline
old hand

Registered: 11/13/00
Posts: 866
Loc: Perth, Western Australia
You asked for it.....

"The quartiles allow for a more detailed description of a distribution than it is possible with only one measure of location, like the median, for example. Analogous to the latter the three quartiles are defined as those values which divide the distribution into four parts containing ideally all the same amount of data. Like the median, the quartiles can only be determined on at least an ordinal level of scale. Simply speaking, the lower, middle and upper quartile QR(x) are defined as those values being larger than 25%, 50% and 75% of the remaining data as well as smaller than 75%, 50% and 25% of the remaining data, resp. Thus, each quartile cuts the set of data into two sub-sets, which comprise proportions of x resp. 1-x of the remaining data, whereby x takes values of 0.25 (25%, first or lower quartile), 0.5 (50%, second or middle quartile, i.e. median) and 0.75 (75%, third or upper quartile). Thus, a proportions ratio pr = x / (1-x) can be defined, which ideally takes the values of 1/3, 1 and 3 for the lower, middle and upper quartile, resp.
When determining the quartiles, problems similar to those for the median will usually occur, because most probably the set won't contain a variable value that divides the distribution exactly into proportions of x and 1-x, resp. Then either that variable value can be taken as quartile which leads to proportions most closely to the required ones (this is the only possible strategy on an ordinal level of scale). Thus an error in the proportions has to be accepted but the quartile is realised by a measured value. Or an interpolation rule can be applied onto those two variable values leading to the two proportions closest to the required ones. Thus only a virtual value for the quartile is calculated but it has the advantage of diving the distribution exactly as it was required. The less data a set contains, the bigger these problems become.
The definition of the quartiles implies a generalisation to those proportions with no restriction on the value x, these are called quantiles."


Taken from: http://www.drgst.de/STAT/2_3-quartil-en.html

Translation: Quartiles, by definition, are 4 separate groups of quantifiable data; each with the same number of data points. To work out what the quartiles are, one lists the scores/values/data points in order, from top to bottom then splts the data set in half - and then the halves in half again.

In total the 4 quartiles constitute one's data population.

Despite the fact there's four quartiles (upper, upper middle, lower middle & lower), they are usually treated as three, upper (or top), middle and lower (or bottom).

This usage is valid for statistical purposes but grammatically inaccurate in that the "middle quartile" is not a quartile at all.

In this case, the upper quartile consists of the the highest 25% of scores, the lower quartile consists of the lowest 25% of scores and the middle quartile contains the remaining 50% of scores - those that fall 25% above and below the middle or median value.

phew

stales


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#116712 - 11/28/03 01:56 AM quantiles
Jenet Offline
journeyman

Registered: 11/22/03
Posts: 81
There seems to be a systematic ambiguity. The quartiles are the three values that divide a probability distribution into four parts; but loosely, "quartile" is also used for any one of the four parts so created.

The only terms I've seen are quartile, decile, and percentile, and I think these are all subject to the same ambiguity. People talk of something being in the top percentile, meaning it's in the top 1%. Strictly this is above the top percentile, which is the 99th percentile.

If n is an integer, an n-ile is a value that divides the data into n equal parts, so there are n - 1 n-iles altogether. The first n-ile separates the lower 1/n from the remaining (n - 1)/n. So the first quartile separates the lower quarter from the upper three-quarters, the middle quartile separates the upper and lower halves, and the upper quartile separates the lower three-quarters from the upper quarter.

Those quarters are also loosely referred to as quartiles, under the natural (mis)apprehension that there must be four quartiles.

If q is a proportion 0 < q < 1, the q-quantile is the point such that the amount of data under it is q. So the first quartile is the 0.25-quantile.

As quartus is a Latin ordinal, and as the old month names were Quintilis and Sextilis, probably "tertile" is a good name for the two points dividing data into three.

http://www.riskglossary.com/articles/quantile.htm


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#116713 - 11/28/03 06:51 AM Re: quantiles
Buffalo Shrdlu Offline
Carpal Tunnel

Registered: 06/24/02
Posts: 7210
Loc: Vermont
most of this is going one ear(eye?) and out the other, but I had a difficult time visualizing what was meant by three points separating four ranges, because I was seeing a circle divided by two lines making four quarters. I had never heard the word quartiles. how many other numbers can be used to make four?
and when I see tertiles I can't but help think of turtles...


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#116714 - 11/28/03 07:59 AM Re: quantiles
Faldage Offline
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Registered: 12/01/00
Posts: 13803
%          0        25       50      75      100
quartile 1 2 3

Does that help?




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#116715 - 11/28/03 08:04 AM Re: quantiles
Buffalo Shrdlu Offline
Carpal Tunnel

Registered: 06/24/02
Posts: 7210
Loc: Vermont
Does that help?

no.

hahaha!
actually, I had figured it out, but I appreciate the effort. I realized I had to see between the ranges, a sort of figure-ground idea...

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#116716 - 11/28/03 08:07 AM Re: quantiles
Faldage Offline
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Registered: 12/01/00
Posts: 13803
Or either
%          0         25        50        75        100
quartile 0 1 2 3 4

There you got four quartiles (if you don't mind starting counting at zero).


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#116717 - 11/28/03 08:24 AM Re: quantiles
Buffalo Shrdlu Offline
Carpal Tunnel

Registered: 06/24/02
Posts: 7210
Loc: Vermont
or
1-25   26-50   51-75   76-100
1 2 3

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#116718 - 11/28/03 02:54 PM Re: quartiles
Jackie Offline

Carpal Tunnel

Registered: 03/15/00
Posts: 11609
Loc: Louisville, Kentucky
Jenet, a belated welcome aBoard to you! Nice to have you.Those quarters are also loosely referred to as quartiles Thank you for that clarification: I'd been wondering, because it was fairly easy for me to picture a circle with 3 horizontal lines dividing the circle into four equal parts. (Hmm, dunno why I didn't picture a square, come to think of it...) And I was wondering how one might distinguish between the line and the part.
'Nother question--can quartiles be...er, visual? Or are they as Faldage put: simply an understood demarcation point? Could I, looking at my circle, point to one of those lines and call it a quartile?



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#116719 - 11/28/03 03:58 PM Re: quartiles
Buffalo Shrdlu Offline
Carpal Tunnel

Registered: 06/24/02
Posts: 7210
Loc: Vermont
fairly easy for me to picture a circle with 3 horizontal lines dividing the circle into four equal parts

really?!? the spaces would need to be of two unequal widths, no? (boy, that's hard to describe...)

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#116720 - 11/28/03 06:48 PM circiles
Jenet Offline
journeyman

Registered: 11/22/03
Posts: 81
All you people thinking of circles are just laying up trouble for yourselves. :)


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#116721 - 11/28/03 09:37 PM Re: circiles
Jackie Offline

Carpal Tunnel

Registered: 03/15/00
Posts: 11609
Loc: Louisville, Kentucky
circiles Ok, I wondered before, and now am inclined to think you did put quantiles on purpose... I'd much rather lay up treasures, but seem to accumulate plenty of the other nonetheless.

Yes, eta, the top and bottom segments of the circle would have to be wider/deeper/fatter than the center two.


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#116722 - 11/30/03 07:00 PM more -iles
wofahulicodoc Offline
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Registered: 08/06/01
Posts: 4838
Loc: Worcester, MA
The concrete example usually used is the fence/fenceposts.

Four fenceposts (including the beginning and the end) are needed to divide a fence into three sections. Unless, as pointed out, it's circular fence, in which case the beginning and the end are identical.

I've seen tertiles, quartiles, quintiles, noniles, and deciles used in medical or psychology papers of varying degrees of scholarship (and/or pretentiousness). Often the choice seems to be driven by what measurement will render the conclusion "significant." Caveat lector. [Did I get that right?]



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