[R] Whiskers on the default boxplot {graphics}

[Robert Baer]

And try this (which seems to leave us with type=2) and is listed in 
?quantile as "Discontinuous sample quantile types 1, 2, and 3"
> quantile(1:101, c(1,3)/4, type=2)
25% 75%
 26  76

> David,
>
> try this:
>
> fivenum(1:101)
> quantile(1:101, c(1,3)/4, type=5)
>
>  -Peter
>
> On 2010-05-13 8:55, David Winsemius wrote:
>>
>> On May 13, 2010, at 10:25 AM, Robert Baer wrote:
>>
>>>> Hi Peter,
>>>>
>>>> You're absolutely correct! The description for 'range' in 'boxplot'
>>>> help file is a little bit confusing by using the words "interquartile
>>>> range". I think it should be changed to the "length of the box" to be
>>>> exact and consistent with those in the help file for "boxplot.stats".
>>>
>>> The issue is probably that there are multiple ways (9 to be exact) of
>>> defining quantiles in R. See 'type= ' arguement for ?quantile. The
>>> quantile function uses type=7 by default which matches the quantile
>>> definition used by S-Plus(?), but differs from that used by SPSS.
>>> Doesn't fivenum essentially use the equivalent of a different "type= "
>>> arguement (maybe 2 or 5) in constructing the hinges?
>>>
>>> It seems perfectly reasonable to talk about 'length of box' (or 'box
>>> height' depending how you display the boxplot), but aren't the hinges
>>> simply Q1 and Q3 defined by one of the possible quartile definitions
>>> (as Peter points out the one used by fivenum)? The box height does not
>>> necesarily match the distance produced by IQR() which also seems to
>>> use the equivalent of quantile(..., type=7), but it is still an IQR,
>>> is it not?
>>>
>>> Quantiles apparantly can be defined in more than one "acceptable" way
>>> (sort of like dealing with ties in rank statistics). The OP seemed to
>>> want an "exact" explanation of the wiskers, and I think Peter has
>>> pointed us at the definition of quartiles used by fivenum, as opposed
>>> to the default used with quantile(..., "type=7").
>>
>> Yes, and experimentation leads me to the conclusion that the only
>> possible candidate for matching up the results of fivenum[c(2,4] with
>> quantile(y, c(1,3)/4, type=i) is for type=5. I'm not able to prove that
>> to myself from mathematical arguments. since I do not quite understand
>> the formalism in the quantile page. If the match is not exact, this
>> would be a tenth definition of IQR.
>>
>>  > set.seed(123)
>>  > y <- rexp(300, .02)
>>  > fivenum(y)
>> [1] 0.2183685 15.8740466 42.1147820 74.0362517 360.5503788
>>  > for (i in 4:9) {print(quantile(y, c(1,3)/4, type=i) ) }
>> 25% 75%
>> 15.82506 73.93080
>> 25% 75%
>> 15.87405 74.03625
>> 25% 75%
>> 15.84955 74.08898
>> 25% 75%
>> 15.89854 73.98352
>> 25% 75%
>> 15.86588 74.05383
>> 25% 75%
>> 15.86792 74.04943
>>
>
> -- 
> Peter Ehlers
> University of Calgary
>