[R] Help documentation of "The Studentized range Distribution"

[peter dalgaard]

Well, it is clear enough that the problem is in interpreting the documentation. However, when you claim you tested something, and found it inconsistent with tables, it would be advisable to back it up with examples!

The description in the help files and in the sources is admittedly confusing. The original paper has this, rather more clear, description in the abstract:

"We consider the probability distribution of the maximum of r statistics each distributed as the Studentized range of means calculated from c random samples of size n from normal populations. The rc samples are assumed to be mutually independent and a common pooled—within—samplevariance is used throughout."

So the connection is nranges == r, and nmeans == c. (n never actually factors in because sqrt(n) is part of the standardization)

For the typical application, r is 1 for the usual studentized range distribution. E.g. for two large groups:

> qtukey(.95,2,df=Inf)
[1] 2.771808

As there is only one difference to consider, this should be distributed like the absolute value of the difference between two standard normals, and yes: We get our old friend 1.96 from

> qtukey(.95,2,df=Inf)/sqrt(2)
[1] 1.959964

It is less than fortunate that the help file speaks of "sample size for range". It is marginally defensible, because it is about the standardized range of a sample _of means_, but it is likely to confuse the actual reader into believing that it has to do with the sample size for each mean.

-pd

> On 10 Jul 2017, at 05:04 , Jeff Newmiller <jdnewmil at dcn.davis.ca.us> wrote:
> 
> We cannot help you understand what you are doing if you do not show us what you are doing.  Here are some discussions about how to communicate questions about R [1][2][3].
> 
> [1] http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example
> 
> [2] http://adv-r.had.co.nz/Reproducibility.html
> 
> [3] https://cran.r-project.org/web/packages/reprex/index.html
> -- 
> Sent from my phone. Please excuse my brevity.
> 
> On July 6, 2017 11:36:47 AM PDT, Ursula Garczarek <Ursula.Garczarek at cytel.com> wrote:
>> Dear all,
>> I wanted to compare Bonferroni vs TukeyHSD correction over a range of
>> groups and group sizes, and wanted to use the function qtukey.
>> 
>> In the help documentation it says
>> 
>> qtukey(p, nmeans, df, nranges = 1, lower.tail = TRUE, log.p = FALSE)
>> Arguments
>> q
>> 
>> vector of quantiles.
>> 
>> p
>> 
>> vector of probabilities.
>> 
>> nmeans
>> 
>> sample size for range (same for each group).
>> 
>> df
>> 
>> degrees of freedom for s (see below).
>> 
>> nranges
>> 
>> number of groups whose maximum range is considered.
>> 
>> log.p
>> 
>> logical; if TRUE, probabilities p are given as log(p).
>> 
>> lower.tail
>> 
>> logical; if TRUE (default), probabilities are P[X � x], otherwise, P[X
>>> x].
>> 
>> 
>> But when I test it, "nmeans" actually should be the number of groups,
>> and not "nrange" to fit with tables of the studentized range
>> distribution.
>> 
>> Can that be - it should be a rather old procedure, so I wonder whether
>> I get something completely wrong...
>> 
>> Regards,
>> Ursula
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> This email and any attachments are confidential and may
>> ...{{dropped:8}}
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com