ElMaestro ★★★ Denmark, 20091003 19:05 (4214 d 12:36 ago) (edited by ElMaestro on 20091003 20:52) Posting: # 4291 Views: 30,500 

Dear all, In a previous thread I asked what the power in a 2,2,2BE trial is at N=6, CV=65% and T/R=95%. The things is, Fartssie comes up with a negative reply. HS's implementation in R of the equations given by Julious (Statistics in Medicine, 2004 vol. 23, 19211986) also evaluates to a negative figure. A central role here is played by the noncentral t distribution. My guess was that we were torturing the algorithm, and I think this was HS's point as well (quote "I think we are pushing software to the limits, i.e., running into troubles of getting a reasonable value of the noncentral tdistribution (...)"). This I wanted to look a little into using R as my reference. Wikipedia tells us what the distribution's density function looks like. I made an independent implementation of this expression, plus an implementation of the integrated density function from t and downwards, which is basically the same as the function pt in R which is based on ASA243 according to the documentation. The values from pt can be easily reproduced, it turns out. But I cannot "improve" them, although I have all the time in the world to integrate with ridiculously small stepsizes and tweak and fiddle. As it turns out in the concrete example, we are asking for probabilities from the noncentral t dist in a region of tvalues plusminus 2.13 and noncentrality parameters 0.50 and 0.80. These are not at all extreme values. I think it sounds reasonable that "prob1" and "prob2" (using HS's terminology) are around 0.89 and 0.17 [try and plot the densities as function of t, eyeball the relative amount of curve left of the indicated values]. For this reason I am becoming a sceptic now. Either I am not able to make a better implementation than ASA243, or ...please forgive me... the equations given by Julious (and others) are not exact in certain situations (for example: I only see the issue when t2 < nc2), or something entirely else is in play. Can anyone shed light on this? Let me add: If the problem lies in ASA243 then I'd love to write one that gets it right, of course.) Many thanks for any input and best regards, EM. 
Helmut ★★★ Vienna, Austria, 20091003 21:45 (4214 d 09:56 ago) @ ElMaestro Posting: # 4292 Views: 27,875 

Hi ElMaestro, very interesting question! I'm too short in time to read Owen's paper again (and likely too stupid to understand it as well). nQuery Advisor 7 (ASA184, I guess) comes up with The computed power was too low for the approximation to be considered reliable. Use a larger sample size. The lowest sample size without an error message was 40 (power 5.871678%, more than 10times the value R comes up with)... Have you considered contacting Russell Lenth (author of ASA243 and the VBAroutines in FARTSSIE)? He writes: Accuracy
— Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
ElMaestro ★★★ Denmark, 20091004 21:51 (4213 d 09:50 ago) @ Helmut Posting: # 4293 Views: 27,723 

Dear HS, » Have you considered contacting Russell Lenth (author of ASA243 and the VBAroutines in FARTSSIE)? Might be the way to go. One could hope that the author of Fartssie reads these discussions and looks into it. It is of course true, depending on how we look at this there is a lot of numerical integration and/or summation going on, and a lot of 'small' errors would indeed sooner or later amount to a 'large' error. To be honest I am just a little sceptical here, because we are not really involving extreme values of t or the noncentality parameters, so I am not at this point fully convinced that this is no more than just a numerical precision issue. Must read some more papers, I guess. Or implement some C library which works with 117 decimals or something obscene and try anew. If anyone has any insight into how Al Gore Rhythms can be validated when true results at the test conditions are not known then I'd be happy to learn it. Or even better, how to determine under which conditions ASA243 is accurate to 3 decimals or something like that. EM. 
Helmut ★★★ Vienna, Austria, 20091004 23:58 (4213 d 07:43 ago) @ ElMaestro Posting: # 4294 Views: 27,766 

Hi ElMaestro! » Might be the way to go. One could hope that the author of Fartssie reads these discussions and looks into it. Hhm, David logged in the last time in midMarch. But he has activated his email in the forum and I had some nice conversations in the past. » […] To be honest I am just a little sceptical here, because we are not really involving extreme values of t or the noncentality parameters, so I am not at this point fully convinced that this is no more than just a numerical precision issue. » Must read some more papers, I guess. Or implement some C library which works with 117 decimals or something obscene and try anew. Sorry I'm of no big help now (still a lot of slides to prepare for a twoday workshop next week), but I think the algo uses a Taylorexpansion which is truncated after the first (?) term. One thing coming into my mind is the possibility that when we run into numerical issues, they may be resolved by going 'deeper' into the Taylor series? » If anyone has any insight [...] Sancta simplicitas, non! — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20091005 12:58 (4212 d 18:43 ago) @ ElMaestro Posting: # 4296 Views: 27,960 

Dear ElMaestro, don't waste your time in attempting to improve Al Gore's rhythms. The inventors of them for the noncentral t distri had already made every effort for its accuracy and reliability, I think. Your time is better invested for NLYW (blonde downstairs) or for the Seven seas . The formula given in Julious is definitely approximate, albeit a good one for the usual power range ≥70% as the sample size calculations with that formula show. The exact algo for the power of the equivalence test (two one sided tests aka TOST) in a 2x2 crossover is ([1],[2]): Power=Prob(t_{1}≥t_{1alpha,(n2)} and t_{2}≤t_{1alpha,(n2)}bioequivalence) The t_{1} and t_{2} values are the tvariates of the two onesided ttests of bioequivalence. (t1, t2) have according to Owen a bivariate noncentral tdistribution and the power can be calculated as the difference of two definite integrals (Owen's Q functions dependent on df=degrees of freedom and with four arguments) Power=Q_{df}(t_{1alpha,(n2)},d_{2},0,R)Q_{df}(t_{1alpha,(n2)},d_{1},0,R) See [1] and [2] for that and for the formulas for d_{1}, d_{2} and R. So you need not a better algo for the noncentral t but rather an algo for Owen's Qfunctions . My SAS beast has these functions implemented (but not documented!). » In a previous thread I asked what the power in a 2,2,2BE trial is at N=6, CV=65% and T/R=95%. And my sasophylistic answer to the your ElMaestrophylistic question "what the power in a 2,2,2BE trial is at N=38, CV=65% and T/R=95%." given here, power=4.5%, is based on these Qfunctions. Implementing the Julious formulas (according to Helmut's Rcode) in "The power to know" results in power=0.027799235, same as Fartssie! [1] Diletti, E., Hauschke, D., and Steinijans, V.W. (1991), — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20091005 14:53 (4212 d 16:48 ago) @ d_labes Posting: # 4297 Views: 27,766 

Dear D Labes, » Implementing the Julious formulas (according to Helmut's Rcode) in "The power to know" results in power=0.027799235, same as Fartssie! Funny! My Rcode was just ported from Patterson's/Jones' SAScode. Tweaking the code to calculate power (haha) at n=38: options(digits=8) I get 0.027799235, which is either an Ouroboros or another strong hint that SAS and R follow the same algorithm. — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20091006 14:31 (4211 d 17:10 ago) @ Helmut Posting: # 4301 Views: 27,651 

Dear Helmut, » [...] which is either an Ouroboros or [...] It is always a pleasure for me to learn from you. Thanks for that nice dragon I'm not aware of until now. Seems to me as an allegory of some/many things I/we do in my/our daily work. (delete as applicable) Regarding the translation SAS>R>SAS I must notice that we are in great luck to have the same results after that cycle. Others are not if I think about f.i. english>german>english translations. Although such back and forth translations are seen as QA measure in doing translations of study documents, f.i. volunteers informed consent which must be in the language of the country a study is performed in. To try out what happens with automatically translations visit Lost in translation. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20091006 14:42 (4211 d 16:59 ago) @ d_labes Posting: # 4302 Views: 27,667 

Dear D Labes! » » […] an Ouroboros » » Thanks for that nice dragon I'm not aware of until now. As a trained chemist I heard of Kekulé's daydream which lead him to the discovery of the unsaturated ring structure of benzene. That's why I know this beast. » Seems to me as an allegory of some/many things I/we do in my/our daily work. » (delete as applicable) Nothing to delete. — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20091006 15:14 (4211 d 16:27 ago) @ Helmut Posting: # 4303 Views: 27,573 

Dear Helmut! » As a trained chemist I heard of Kekulé's daydream Here comes the true Kekulé's daydream: Source: Berichte der durstigen Chemischen Gesellschaft Unerhörter Jahrgang, Nr. 20 zum 20.9.1886 Translated by babelfish: Reports of the thirsty chemical society outrageous class, No. 20 to 20.9.1886 Back to German Reports der unverschämten Kategorie der durstigen chemischen Gesellschaft, Nr. 20 bis 20.9.1886 To English again: Report of the impudent category of the thirsty chemical society, No. 20 to 20.9.1886 .... — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20091006 21:46 (4211 d 09:55 ago) @ d_labes Posting: # 4306 Views: 27,596 

Dear D Labes! Google translate:
— Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
ElMaestro ★★★ Denmark, 20091005 17:32 (4212 d 14:09 ago) @ d_labes Posting: # 4298 Views: 27,976 

Dear dlabes, » Your time is better invested for NLYW (blonde downstairs) or for the Seven seas . I agree. One of the options you mention would get higher priority then the other _{if I had a choice}. » The formula given in Julious is definitely approximate (...) Cool. It becomes more and more difficult to find out who to trust. » So you need not a better algo for the noncentral t but rather an algo for Owen's Qfunctions . Excellent input. The noncentral t dist is hereby dead and buried. Seems this is a good place to start, and this power document gives the Qv function. Must see if I can implement that. Thanks for the good post! EM. 
d_labes ★★★ Berlin, Germany, 20091006 16:45 (4211 d 14:56 ago) @ ElMaestro Posting: # 4304 Views: 27,903 

Dear ElMaestro! » Excellent input. The noncentral t dist is hereby dead and buried. Seems this is a good place to start, and this power document gives the Qv function. Must see if I can implement that. Once again: Your time is better invested for whatever you prefer . Also I confess that implementing it itself can be very satisfactory! ('Oh what a great guy I am which can solve such complicated definite integral!') Have a look at the R package MBESS. If I had seen it right there is a function power.equivalence.md that will give you some spare time. Could not test it by myself. No spare time at moment. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20091007 02:18 (4211 d 05:23 ago) @ d_labes Posting: # 4309 Views: 27,597 

Dear D Labes! » Have a look at the R package MBESS. If I had seen it right there is a function power.equivalence.md that will give you some spare time. Quick tests require(MBESS) In the text output power is the theoretical value 0.05 (=α) at the borders of the acceptance range. Now for ElMaestro's candidates: n < 6 Yet some other values for our collection. — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20091007 08:46 (4210 d 22:55 ago) (edited by d_labes on 20091007 09:07) @ Helmut Posting: # 4310 Views: 27,643 

Dear Helmut! » Quick tests Oh actually quick! But dirty . I assume that your 5th parameter is meant as CV. But the function requires sigma, I think. With that modification library(MBESS) The answer for n=38 seems to me very sasophylistic homebrewed magic and Qfunctionalistic . Not so astonishing if you look at the author of that pice of Rsoftware. PS: I have just seen that the documentation suggest that CV can be used in case of log. But this seems erroneous. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20091007 12:38 (4210 d 19:03 ago) @ d_labes Posting: # 4314 Views: 27,503 

Dear D Labes! » Oh actually quick! But dirty . I always thought of it as a nice combination. » The answer for n=38 seems to me very sasophylistic homebrewed magic and Qfunctionalistic . » Not so astonishing if you look at the author of that pice of Rsoftware. Ah, Kem Phillips! » PS: I have just seen that the documentation suggest that CV can be used in case of log. But this seems erroneous. Exactly. The example in the documentation drove me to my quickshot. — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20091007 11:32 (4210 d 20:09 ago) @ d_labes Posting: # 4312 Views: 27,604 

Dear All! Back from the date with the Blonde downstairs an having some spare time , Seems ElMaestro's question is able to put the power to the limits. Here results of power.equivalence.md around N=6: R code: library(MBESS) Result:
n power I would expect power is increasing with increasing n. Or miss I here something? BTW: My SAS code shows the same effect. All this is hairsplitting of course. Edit: Added two lines above to allow copypasting of code to Rconsole. BTW, change the sample size vector to n<c(4,6,8,10,12,14,16,38,40,152,154,344,346) and watch (the gammafunction needs the faculty, which runs out of steam  at least on 32bit operating systems). [Helmut]— Regards, Detlew 
d_labes ★★★ Berlin, Germany, 20091007 15:15 (4210 d 16:26 ago) (edited by d_labes on 20091007 15:30) @ d_labes Posting: # 4316 Views: 27,420 

Dear All! Must post to myself because Helmut has posted an important finding in the edit line of the post of mine. » » [...] BTW, change the sample size vector to n<c(4,6,8,10,12,14,16,38,40,152,154,344,346) and watch (the gammafunction needs the faculty, which runs out of steam  at least on 32bit operating systems). [Helmut]Seems there is an implementation flaw in the code. And to add insult to injury it runs without error. But power is zero for n=346! After inspecting the code at the Rconsole > power.density.equivalence.md you can see where it is. So roll your own power.density.equivalence.md and change the line with red marker to power_const < (nu/2  1) * log(2)  lgamma(nu/2)  log(a) Now we have: n power This is one example of why open source is so beautiful . — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20091007 22:36 (4210 d 09:05 ago) @ d_labes Posting: # 4319 Views: 27,488 

Dear D Labes! » This is one example of why open source is so beautiful. Have you considered contacting Kem Phillips ( kemphillipscomcast.net) – also about the ambiguities in the documentation? — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20091015 14:57 (4202 d 16:44 ago) (edited by d_labes on 20091015 15:20) @ Helmut Posting: # 4366 Views: 27,249 

Dear Helmut! Dear all R adepts! Helmut, as you suggested I have contacted Kem Phillips. He has confirmed that sigma in case of logscale=TRUE is sqrt(log(1+CV^2)). He has also confirmed the error if n>344 and will change the code in MBESS accordingly. With respect to the power curiosity in my post "The Power at limits" above we are still in an ongoing discussion. Kem's first supposition was numerical problems. But considering the results I will present below he is thoughtful. Because PASS2008 gives the same results I have confronted Jerry Hinze with that curiosity. Here his answer: "This is surprising to me, but since it occurs in a range that is of little interest, I don't see the need to investigate it further. It could be due to a number of numerical problems that occur when dealing with such a small sample size. However, since as you say, it matches SAS Analyst, I would conjecture that it is probably due to the definition of the equivalence testthat is, the definition probably leads to this result." For me I had seen the need to investigate it further. I performed an "insilico" experiment to obtain an empirical power estimate. I have simulated data sets for 2x2 crossover with equal subjects in the two sequences using my beasty number cruncher SAS, performed the TOST and recorded the incidences of stating bioequivalence. Here my results: ratio0=0.95, CV=0.65, BE limits 0.8 ... 1.25 BTW: ElMaestro, can you tell me how Apfelstrudel has found his way to Gent/Belgium ? As you can see, all results from the different implementations have the same behavior. So Jerry Hinze's presumption seems true that this behavior is inherent to the test definition. BTW: The empirical power in that region badly converges to a stationary value. One has to use huge number of simulated datasets to obtain a reliable value to some degree. 50.000 is obviously yet to low. Greetings to all other pettifoggers (Hair splitting needs sharp tools and haven't got anything better to do ). — Regards, Detlew 
ElMaestro ★★★ Denmark, 20091017 12:26 (4200 d 19:15 ago) (edited by ElMaestro on 20091017 12:43) @ d_labes Posting: # 4370 Views: 27,193 

Ahoy d_labes, » BTW: ElMaestro, can you tell me how Apfelstrudel has found his way to Gent/Belgium ? When I made port in Bremerhafen in 1953 I decided to give Apfelstrudel a try; it turned out to be a fully acceptable alternative to the famous Vlaamse Friet and with a pleasantly matching (lack of) nutritional value. Regarding only 50000 simulations: You can get the famous software EFG 2.01 from HS. It will do millions of sims in a few seconds. HS  put it up for download? Here's an update to give you more decimals, if you like: Apfelstrudel<function(t, df, ta, tb, ncp, ACCURACY) Best regards ElMaestro  sailor and simulant. Edit: BBCoded. [Helmut] 
Helmut ★★★ Vienna, Austria, 20091017 13:44 (4200 d 17:57 ago) @ ElMaestro Posting: # 4371 Views: 27,576 

¡Hola ElMaestro! » When I made port in Bremerhafen in 1953 I decided to give Apfelstrudel a try; it turned out to be […] a pleasantly matching (lack of) nutritional value. 'Apfelstrudel' in Bremerhafen where waitresses can't even pronounce the word correctly (I would except to hear something similar to Appelstrudel  whereas the correct pronounciation is Apflschdrudl)? Should give the real stuff (of course together with whipped cream) at try in Vienna. 400 kcal/serving are nourishing sailors well. » You can get the famous software EFG 2.01 from HS […] – put it up for download? OK. I bundeled the executable EFG 2.01 together with the manual of EFG 1.02. After download (MD5: 892f7df65887edc7e1e4a1817ff3d90c ) unzip to a folder of your choice. Should run on Windows (≥95); no installation required. Couldn’t test Win95, but WfW 3.11 with Win32extensions did not work. » It will do millions of sims in a few seconds. Well – a couple of seconds. Don’t get nervous – it never crashed my systems (Windows 2000 Pro SP4, XP/Pro SP3, and Vista/Pro SP2)*, but doesn’t give a clue about it’s progress. Don’t expect the infamous turning hourclass or a beep when the sim is finished. As software engineers use to say: ‘Quick and dirty – or clean and never.’ BTW, no other software I know can give you a sample size estimation for Denmark’s requirement (CI includes 100%) out of the box! ratio0=0.95, CV=0.65, BE limits 0.8 ... 1.25
— Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20091020 11:35 (4197 d 20:06 ago) @ ElMaestro Posting: # 4372 Views: 27,216 

Ahoy old simulant! » Regarding only 50000 simulations: » You can get the famous software EFG 2.01 from HS. It will do millions of sims in a few seconds. I have given EFG2.1 a try. Great . Thanks for that stress test for my CPU. But my SAS can better . What I'm a little bit curious of is that regardless how big the number of sims is, the power for low sample size does not converge to your 'normal' values (at least for CV=30%) . (This is the 'exact' power I think, using your 'Abbelssstrudel' ?). Here an example (power in %): CV=30%, ratio=0.95, BE limits= 0.8  1.25 (fixed in EFG?) My own simulations (but of course with lower number of sims because of CPU overheating) do not show this effect. I would expect a convergence to the 'exact' values because we simulate data with distributional characteristics that match those for which the exact power formula was derived. Do I miss somefink here? — Regards, Detlew 
ElMaestro ★★★ Denmark, 20091123 19:03 (4163 d 11:38 ago) @ d_labes Posting: # 4384 Views: 27,121 

» Ahoy old simulant! Ahoy, d_labes, perhaps I should get a contract in Hollywood? » What I'm a little bit curious of is that regardless how big the number of sims is, the power for low sample size does not converge to your 'normal' values (at least for CV=30%) . » (...) I would expect a convergence to the 'exact' values because we simulate data with distributional characteristics that match those for which the exact power formula was derived. I guess you are right, thanks for pointing it out. And yes absolutely, simulations of this type MUST converge towards the true value with increasing iterations. I will head down in the programming department and punish the perpetrator right away! Nuts. At any rate, I will post a little later a proposal on how to make the Brute Force parts of EFG 2.01 obsolete. Sorry I did not see your post before. Or should I say, I am sorry the forum admin screwed up, making it impossible to access the forum, thereby putting a halt to rapid progression of the science that works in the interest of the sick. EM. 
Helmut ★★★ Vienna, Austria, 20091123 19:17 (4163 d 11:24 ago) @ ElMaestro Posting: # 4386 Views: 27,016 

Hi ElMaestro, nice to hear from you again! » […] Or should I say, I am sorry the forum admin screwed up, […] Don't dare! It was a hell of work to get the f**ing stuff up again. » […] thereby putting a halt to rapid progression of the science that works in the interest of the sick. Yeah, that's what it is all about in Big Pharma, isn't it? — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
yjlee168 ★★★ Kaohsiung, Taiwan, 20091007 00:08 (4211 d 07:33 ago) @ ElMaestro Posting: # 4307 Views: 27,546 

Dear all I got power = 0.0016 with PASS as the attached picture. Funny. » In a previous thread I asked what the power in a 2,2,2BE trial is » at N=6, CV=65% and T/R=95%. » The things is, Fartssie comes up with a negative reply. HS's » implementation in R of the equations given by Julious... — All the best,  Yungjin Lee bear v2.8.9: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
Helmut ★★★ Vienna, Austria, 20091007 01:16 (4211 d 06:25 ago) @ yjlee168 Posting: # 4308 Views: 28,039 

Dear Yungjin! » I got power = 0.0016 with PASS as the attached picture. Funny. Crazy. From the manual I guessed that PASS also uses AS 243 and would give results comparable with Patterson's/Jones' SAS code (also mine ported to R) and FARTSSIE. But from this post we know that PASS' result agrees with D Labes' magic SAShomebrew... That's another example supporting Jaime's advice: Never trust in any piece of software you haven't written yourself (and even then you should be cautious...) Was this the reason to write bear? — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
yjlee168 ★★★ Kaohsiung, Taiwan, 20091012 23:17 (4205 d 08:24 ago) @ Helmut Posting: # 4344 Views: 27,600 

Dear Helmut, » [..] you should be cautious...) Was this the reason to write bear? The reason to develop bear is to simply try to prove that R can do BE/BA too. We have a lot of funs from developing work. Lots to read and learn. That's been good enough for us. At least we have an open sourced package now for BE/BA community. — All the best,  Yungjin Lee bear v2.8.9: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
ElMaestro ★★★ Denmark, 20091009 11:32 (4208 d 20:09 ago) @ ElMaestro Posting: # 4332 Views: 27,541 

What comes out of lying sleepless at night: EatMyShorts < function (x, V, T, W) Increasing the integration steps (to some number higher than 500) may ímprove accuracy, as will e.g. a method like Simpson's formula. Can be played around with. Best regards EM. 
Ohlbe ★★★ France, 20091009 11:50 (4208 d 19:51 ago) @ ElMaestro Posting: # 4333 Views: 27,449 

Dear ElMAestro » What comes out of lying sleepless at night: » EatMyShorts < function (x, V, T, W) » Apfelstrudel<function(t, df, ta, tb, ncp) Regards Ohlbe — Regards Ohlbe 
d_labes ★★★ Berlin, Germany, 20091009 13:50 (4208 d 17:51 ago) @ ElMaestro Posting: # 4335 Views: 27,898 

Dear ElMaestro, dear All! Also suffering from senile "Bettflucht" (insomnia) here is my quick shoot with Owen's Q: (forgive me, I'm a very beginning adept of R) # The functions of normal, tdistributions and integrate() Some spare 'validation' results (Sample sizes from Diletti et. al. for target power 70%, 80%, 90%): CV=0.3, BE margins 0.81.25, Null ratio=0.95, alpha=0.05 n power(Q) Apfelstrudel PS: I think it's enough R power in this thread to have it in the R category now. Edit: Category changed. require(stats) not needed, because loaded by default. [Helmut]— Regards, Detlew 