q-distribution? (studentized range distribution)

[RenoFilla]

Hi, I am doing a within-subjects ANOVA and now want to do post hoc analysis with the Tukey's Range Test. For this I need the q-distributions, also called "studentized range distribution", which I cannot find in MathCad 14 - or am I looking in the wrong place?

http://en.wikipedia.org/wiki/Tukey's_range_test

This value of q is the basis of the critical value of q, based on three factors:

1. α (the Type I error rate, or the probability of rejecting a true null hypothesis)
   
2. n (the number of degrees of freedom in the first sample (the one from which range was calculated))
   
3. v (the number of degrees of freedom in the second sample (the one from which s was calculated))
   

Any idea where to look for this? I can find the tables on the net, though:

http://academic.udayton.edu/gregelvers/psy216/tables/qtab.htm

http://cse.niaes.affrc.go.jp/miwa/probcalc/s-range/

/Reno

[Fred_Kohlhepp]

Mathcad has Student's "t" distribution. What additional steps you might need to do for Tukey is not obvious to me. Good luck!

[RenoFilla]

Thanks, it would be quite bad indeed if MathCad would not feature the t-distribution...

I found this: http://davidmlane.com/hyperstat/A47912.html

Hmm, does that mean that I can somehow can use the good ol' t-distribution and modify it to get the studentized range distribution?

(My brain hurts...)

[PhilipOakley]

Reno Filla wrote:

does that mean that I can somehow can use the good ol' t-distribution and modify it to get the studentized range distribution?

In general: yes.

MathCAD doesn't attempt to be a full up, fancy, stats package, rather it provides all the basics so that you can create all the special variants you need.

The multiple hypothesis testing issue is nicely written up in "Everything is Dangerous: A Controversy" by S.Stanley Young, [multiple google hits, e.g. http://nisla05.niss.org/talks/Young_Safety_June_2008.pdf]. The issue being that the medics think the factor is 1.0 and so create the many and various false medical worries we see, e.g. BPA in USA.

The multiple hypothesis factor is simply a multiplier, as per Wikipedia. All the many other distribution functions can also be created in MathCad, as and when required 😉

In a lecture of 100 people, the lecturer demonstrates that tossing 8 heads in a row is rare - She tries 10 times, rarely getting past the first toss, then asks the students to repeat the test and, whoaa, someone calls out they have managed it, in just 2 goes, how rare was that...? So yes the factor needs to be included, and it has to be the proper one (the lecture theatre example is tricky because people don't toss all 8 tries before restarting, so it's a slightly different statistic). All good fun.

Philip

[RenoFilla]

Philip Oakley wrote:

Reno Filla wrote:

does that mean that I can somehow can use the good ol' t-distribution and modify it to get the studentized range distribution?

In general: yes.

Good, but how? I really need concrete help with this.

[PhilipOakley · Accepted solution]

I think you got us a little confused in the original question....

If the question is "how to calculate your studentised values"?, then the answer is fairly simple (It's hidden in the wiki pages)

for each category, calculate the difference between the minimum and the maximum in that category (i.e. the category's range), then divide by the standard deviation. This value is the "studentised range" requested in the question.

You can then look up the tables, or use mathcad's t-tables.

http://en.wikipedia.org/wiki/Multiple_comparisons has various options for the corrections (if you want to apply them for multiple hypotheses). some corrections go for correcting false positives, some for false negatives, and some attempt a balance (and no-one agrees on the right one...). e.g. http://en.wikipedia.org/wiki/Bonferroni_correction

Philip