Bert, Thanks for replying. Actually, Chuck and Mark's suggestions already helped, especially regarding to the problem you call type III error.
Best, Jia On Thu, Jul 8, 2010 at 11:06 AM, Bert Gunter <gunter.ber...@gene.com> wrote: > Inline below. > > Bert Gunter > Genentech Nonclinical Statistics > >> -----Original Message----- >> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] >> On Behalf Of markle...@verizon.net >> Sent: Thursday, July 08, 2010 7:52 AM >> To: chen_1...@fisher.osu.edu >> Cc: r-help@r-project.org; cbe...@tajo.ucsd.edu >> Subject: Re: [R] How do I test against a simple null that tworegressions >> coefficients are equal? >> >> >> hi: no. it's not the same. if you read the paper that I referenced last >> night, that explains how to do the following test : >> Ho: R2 = R1 >> H1: R2 != R1 >> that's a different test from what you did but i think it's what you >> want. >> >> On Jul 8, 2010, chen jia <chen_1...@fisher.osu.edu> wrote: >> >> Thanks, Chuck. I am reading the references, which are helpful. >> Just to understand what I have done wrong here, >> I proposed an alternative testing strategy: >> I run regressions y = a3 + b1 * x + b2 * z + e3 and test alternative >> hypothesis b1 != b2 against the null hypothesis b1 = b2 in this >> equation. > > If this is what you want (see below) try this: > > w <- x + z > > anova(lm(y ~ w), lm(y ~ x + w)) > > > However, as you seem to be somewhat at sea in your basic statistical > knowledge, I suggest you consult a local statistician to make sure whether > you are asking sensible questions in the first place. You appear to be at > high risk for type III error (right answer to wrong question). > > -- Bert > > > > >> Is it this the same test as >> y = a1 + b1*x + e1 >> y = a2 + b2*x + e2 >> test alternative hypothesis b1 != b2 against null hypothesis b1 = b2. >> Best, >> Jia >> On Wed, Jul 7, 2010 at 11:12 PM, Charles C. Berry >> <cbe...@tajo.ucsd.edu> >> wrote: >> > On Wed, 7 Jul 2010, chen jia wrote: >> > >> >> Hi there, >> >> >> >> I run two regressions: >> >> >> >> y = a1 + b1 * x + e1 >> >> y = a2 + b2 * z + e2 >> >> >> >> I want to test against the null hypothesis: b1 = b2.  How do I >> design >> the >> >> test? >> >> >> > >> > You are testing a non-nested hypothesis, which requires special >> handling. >> > >> > The classical test is due to Hotelling, but see the references (and >> R >> code >> > snippets) in this posting: >> > >> >     http://markmail.org/message/egnowmdzpzjtahy7 >> > >> > (it is the merest coincidence that the above thread was initiated >> by >> Mark >> > Leeds and that the URL is 'markmail' :-) ) >> > >> > HTH, >> > >> > Chuck >> > >> > >> >> I think I can add two equations together and divide both sides by >> 2: >> >> y = 0.5*(a1+a2) + 0.5*b1 * x + 0.5*b2 * z + e3, where e3 = 0.5*(e1 >> + >> e2). >> >> or just y = a3 + 0.5*b1 * x + 0.5*b2 * z + e3 >> >> >> >> If I run this new regression, I can test against the null b1 = b2 >> in >> >> this regression.  Is it an equivalent test as the original one? >> If >> >> yes, how do I do that in R? >> >> >> >> Alternatively, I think I can just test against the null: >> >> correlation(y, x) = correlation(y, z), where correlation(. , .) is >> the >> >> correlation between two random variables. Is this equivalent too? >> If >> >> yes, how do I do it in R? >> >> >> >> Thanks. >> >> >> >> Best, >> >> Jia >> >> >> >> -- >> >>             Ohio State University - Finance >> >>                  248 Fisher Hall >> >>                  2100 Neil Ave. >> >>               Columbus, Ohio  43210 >> >>               Telephone: 614-292-2830 >> >>            >> http://www.fisher.osu.edu/~chen_1002/ >> >> >> >> ______________________________________________ >> >> R-help@r-project.org mailing list >> >> https://stat.ethz.ch/mailman/listinfo/r-help >> >> PLEASE do read the posting guide >> >> http://www.R-project.org/posting-guide.html >> >> and provide commented, minimal, self-contained, reproducible code. >> >> >> > >> > Charles C. Berry               (858) >> 534-2098 >> >                       >> Dept of >> Family/Preventive >> > Medicine >> > E mailto:cbe...@tajo.ucsd.edu        UC San Diego >> > http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego >> 92093-0901 >> > >> > >> > >> -- >> Ohio State University - Finance >> 248 Fisher Hall >> 2100 Neil Ave. >> Columbus, Ohio 43210 >> Telephone: 614-292-2830 >> http://www.fisher.osu.edu/~chen_1002/ >> ______________________________________________ >> r-h...@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting- >> guide.html >> and provide commented, minimal, self-contained, reproducible code. > > -- Ohio State University - Finance 248 Fisher Hall 2100 Neil Ave. Columbus, Ohio 43210 Telephone: 614-292-2830 http://www.fisher.osu.edu/~chen_1002/ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
