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        riddles >> general problem-solving / chatting / whatever >> Quartiles.
        
(Message started by: Noke Lieu on Aug 30^th, 2005, 8:12pm)

Title: Quartiles.
Post by Noke Lieu on Aug 30^th, 2005, 8:12pm

Just stirring here. My limited stats knowledge may have a big hole in it, but this seems a bit... curious.

Imagine a population.
Imagine that they sit a test.
Imagine that a directive comes out that their results are to be ranked and put into quartiles.
No problem so far.
Now, here comes the tricky bit, label these quartiles A, B, C, D or E.
Eh?

Title: Re: Quartiles.
Post by towr on Aug 31^st, 2005, 12:37am

I think I'll label them all A ;D

Title: Re: Quartiles.
Post by Grimbal on Aug 31^st, 2005, 2:47pm

So you want to label all 5 quartiles? ::)

Title: Re: Quartiles.
Post by Noke Lieu on Aug 31^st, 2005, 6:11pm

Hmmmn, background... Like I said, could be stirring here

Last school I was in in tasmania, a teacher said I'd find this funny. Certain powers that be have said that there needs to be a new system of measuring students abilities. It is putting them into quartiles and then labelling them abcde.

He was right. I did find it very funny.
Wondering who supplied the numeracy advice to these powers...

Title: Re: Quartiles.
Post by Icarus on Aug 31^st, 2005, 6:31pm

Probably the Magliozzi brothers (Tom and Ray of "Car Talk"). Who, with tongue firmly in cheek, divide their show into three halves, regularly making mention of what is coming up in the "third half" of the show.

Title: Re: Quartiles.
Post by JocK on Sep 1^st, 2005, 10:57am

on 08/31/05 at 18:11:50, Noke Lieu wrote:

Wondering who supplied the numeracy advice to these powers...

Obviously, there is three kinds of people: those who can count, and those who can't.

Title: Re: Quartiles.
Post by Grimbal on Sep 3^rd, 2005, 2:40pm

on 09/01/05 at 10:57:13, JocK wrote:

Obviously, there is three kinds of people: those who can count, and those who can't.

One half is always equal to the other half, maybe half of the people know that, but then it is a very small half.

Title: Re: Quartiles.
Post by Sir Col on Sep 9^th, 2005, 5:09pm

I could be wrong, but they may be basing it on a similar measure to IQ testing, in which a score of 100 represents the population average. If this boundary is labelled C, then taking 25% of the population above and below 100, based on historical data, finds the B and D boundary score respectively. Similarly, 25% above and below the B and D boundary we find the A and E boundary score.

Anyone scoring above 100 but below the boundary for B is classified C. In the same way, a student is labelled according to the boundary they do not exceed.

As we are dealing with an historical data model a candidate could score above the 100th percentile and find themselves as being labelled A (exceptional performance). A candidate scoring below the E boundary has failed to meet any standard, which in itself is quite an exceptional performance.

Of course, what is more likely is that they meant quintiles and did not realise the significance of the prefix quart- (from Latin: quartus=fourth). Interestingly I couldn't find the statistical terms tercile (tertius=third, hence tertiile->tercile) or sextile in any online dictionaries.

Another demonstration of general misuse today is usage of the terminology with reference to percentiles. Most people think that any score found below the 25th percentile is a lower, or first, quartile value. They fail to realise that first quartile is synonymous with 25th percentile, and as such it refers to the boundary, not the interval. It may well be convenient to talk about a "3rd quartile score" to mean a score between the 50th and 75th percentile, but the phrase means they scored a value equal to the 75th percentile. As the second quartile (=50th percentile) is the same as the median, how would they define a median score?