Epsilon: Display US definition of quartiles in Statistics

[artaxxx]

As we want to avoid to add this in Settings, the best way should be to use the US definition of quartiles when the language is English and use the other definition for the rest.

[madhatter0]

Is it possible to understand the backstory here a little better? If there are different definitions of quartile and one is used in the US while another is used in the UK (I have no idea if this is true, which is why I'd like to understand the backstory better) then using the US one when the language is set to English is not helpful.

[adriweb]

I agree that in such cases, grouping together language and math definition is not the best idea at all. Indede, what if India, UK, Australia, and US schools aren't taught the same definitions? Despite students choosing English, they'd need to be able to choose whichever setting they need!

[artaxxx]

The problem in this case is that students cannot chose between different definitions because they do not know them. It's even hard for us to select our definition (I didn't know the existence of the US definition till last year...). I think we shouldn't allow the user to choose between several quartiles definitions.

I agree with you that it's a little weird to link language selection with math definitions but we can simply add an "English US" version to the language selection screen.
Does anyone know if the use of the US definition is limited to the US?

[adriweb]

Better idea, then: instead of letting the user choose the "US definition" or "French definition", just select by default something according to the current language, AND have a settings submenu where the user could choose a definition of things like quartile from a list of formulas (or whatever it is).
The user then wouldn't choose _"French definition"_, but _"Q1: <= 25%"_, etc. People wouldn't need to know which definition it is for which country. Much more visual and intuitive IMHO.

[ian-abbott]

Casio Prizm calculators have a "Q1Q3 Type" setting that lets you choose between two methods.

[madhatter0]

Artaxxx, it'd be helpful if you could briefly summarise how it's done in the US. Locals can then confirm whether or not it's done that way in other English-speaking countries.

[artaxxx]

Good suggestion @madhatter0 !

Let's do that with a simple set of data: {1,2,3,4,5}.

In the US, Q1=1.5 and Q3=4.5 (you set the median apart, which is 3 and then Q1=med{1,2} and Q3=med{4,5}).

In France, Q1=2 and Q3=4 (rounded up in a way)

[adriweb]

Well in France, it's just that the Q1 has to belong to the set, IIRC, and follow the definition: "Q1: <= 25%".
As long as there's a setting clearly explaining which one to choose (name/definition/example, even ?), it's all good. The more intuitive, the better.

[ian-abbott]

The English Wikipedia pages list 3 methods for calculating quartiles. Wolfram MathWorld lists 5 methods!

[madhatter0]

OK, I've checked with a friendly local A-level maths teacher. The textbook they sent me a snippet of notes that "_there are many different methods for calculating the quartiles, and they may give slightly different answers_". They then go on to say "_this book will use the following method_" and give both a method and an example which is the same as the French method. So UK students at least do expect there to be several methods of calculating the IQR, and don't always default to the US method.

Let me know if you'd like me to attach the scanned page of textbook (on a fair-use basis).

[dicorynia]

There are at least 9 ways to compute quartiles ; see (for R) :

> quantile(c(1,2,3,4,5), type = 1)
  0%  25%  50%  75% 100% 
   1    2    3    4    5 
> quantile(c(1,2,3,4,5), type = 2)
  0%  25%  50%  75% 100% 
   1    2    3    4    5 
> quantile(c(1,2,3,4,5), type = 3)
  0%  25%  50%  75% 100% 
   1    1    2    4    5 
> quantile(c(1,2,3,4,5), type = 4)
  0%  25%  50%  75% 100% 
1.00 1.25 2.50 3.75 5.00 
> quantile(c(1,2,3,4,5), type = 5)
  0%  25%  50%  75% 100% 
1.00 1.75 3.00 4.25 5.00 
> quantile(c(1,2,3,4,5), type = 6)
  0%  25%  50%  75% 100% 
 1.0  1.5  3.0  4.5  5.0 
> quantile(c(1,2,3,4,5), type = 7)
  0%  25%  50%  75% 100% 
   1    2    3    4    5 
> quantile(c(1,2,3,4,5), type = 8)
      0%      25%      50%      75%     100% 
1.000000 1.666667 3.000000 4.333333 5.000000 
> quantile(c(1,2,3,4,5), type = 9)
    0%    25%    50%    75%   100% 
1.0000 1.6875 3.0000 4.3125 5.0000 

References :
https://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html
https://www.amherst.edu/media/view/129116/original/Sample+Quantiles.pdf

[ian-abbott]

Those 9 methods supported by R's quantile function are from Hyndman and Fan's 1996 paper "Sample Quantiles in Statistical Packages". It's easy enough to find online, but I won't link to it here because you're supposed to pay for it. Microsoft Excel's QUARTILE.INC and QUARTILE functions correspond to R's type 7, and Excel's QUARTILE.EXC function corresponds to type 6 (ref. Why Excel has Multiple Quartile Functions and How to Replicate the Quartiles from R and Other Statistical Packages).

[abhobe]

When will the quartile update be released?

[nsajko]

@abhobe Look at the discussion above: there are more than 9 mutually incompatible definitions in use, so somebody first needs to propose how to present the choice of which one to use to the user, so the Numworks people could decide what to do.

For example, the Numworks people could decide that Epsilon should provide definitions: 1, 2, 3, 5, 7, 8.

Do you know which of the 9 definitions (from the PDF a little bit above, same as in R) do you want?

[abhobe]

@nsajko I am looking for type 6. (US Version)

[artaxxx]

Fixed in 15.0.0