Adjusted (shrunken) R**2 can be negative. Cheers, Karl W. -----Original Message----- From: Rick Froman [mailto:[email protected]] Sent: Wednesday, April 21, 2010 8:47 AM To: Teaching in the Psychological Sciences (TIPS) Subject: RE: Re:[tips] Biserial r.
OK, I know that some correlational techniques occasionally produce r greater than 1 or less than -1 but I think I am on firm footing when I say that I am not going to see a negative r-squared in the set of real numbers used in statistical calculations (although it may occur with complex numbers http://mathforum.org/library/drmath/view/52613.html). Rick Dr. Rick Froman, Chair Division of Humanities and Social Sciences John Brown University Siloam Springs, AR 72761 [email protected] ________________________________________ From: Mike Palij [[email protected]] If one comes across a biserial r that is greater than +1.00 or less than -1.00, then I think one should treat it the same way one might treat a negative Cronbach's alpha or a negative R-squareed: it's an indication that something is seriously wrong and you need to review the validity of your assumptions, the nature of your data, and the suitability of your analysis for the situation. -Mike Palij New York University [email protected] On Tue, 20 Apr 2010 23:31:30 -0500, Jim Clark wrote: > Hi > Following SPSS simulation generates 1000 samples of 100 x y pairs with known > population rho (#r = .9 here), then dichotomizes x to create categorical > predictor c, which is then used to calculate rb, the biserial r (I had to > track down various algorithms for this, but it seems correct ... mean rb, for > example, is very close to rho). Anyway, it illustrates that for extreme > values of rho, rb can in fact exceed 1 (presumably same at other tail). 12 > of 1000 rbs were > 1 in one simulation I ran. Perhaps there are other > factors that also influence likelihood of getting values beyond normal range > for rs (e.g., size of categories). > > input program. > comp #r = .9. > loop samp = 1 to 1000. > leave samp. > loop obs = 1 to 100. > comp x = rv.norm(0,1). > comp y = rv.norm(0,1)*SQRT(1-#r**2) + x*#r. > end case. > end loop. > end loop. > end file. > end input program. > comp c = 0. > if x > -.2 c = 1. > if c = 0 y0 = y. > if c = 1 y1 = y. > > aggre /outfile = * /presort /break = samp > /m0 = mean(y0) /m1 = mean(y1) /p = fgt(c, 0) /q = flt(c, 1) /sy = > sd(y). > > compute z = idf.normal(q, 0, 1). > compute ord = .3989*2.71828**-((z**2)/2). > compute rb = (m1 - m0)*((p*q/ord)/sy). > freq rb /forma = notable /hist. > comp rbx = (rb<-1) or (rb>+1). > freq rbx. > > It is perhaps worth noting that there are other widely used statistics that > produce "impossible" values. The Bonferroni test, for example, can produce > ps > 1 if one computes LSD p x # comparisons (as reported in SPSS, for > example). SPSS rounds these to 1. Perhaps similar convention is adopted for > rb? > > I'm hard-pressed to decide whether to thank Karl for raising this interesting > question, or berate him for taking me away from my marking to do this > exercise! Or perhaps the latter should be a thanks as well? > > Take care > Jim --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13039.37a56d458b5e856d05bcfb3322db5f8a&n=T&l=tips&o=2128 or send a blank email to leave-2128-13039.37a56d458b5e856d05bcfb3322db5...@fsulist.frostburg.edu --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13060.c78b93d4d09ef6235e9d494b3534420e&n=T&l=tips&o=2130 or send a blank email to leave-2130-13060.c78b93d4d09ef6235e9d494b35344...@fsulist.frostburg.edu --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=2138 or send a blank email to leave-2138-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
