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 James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax [email protected] >>> "Wuensch, Karl L" <[email protected]> 20-Apr-10 4:03:26 PM >>> See: The Theory of Correlation Between Two Continuous Variables when One is Dichotomized Author(s): Robert F. Tate Source: Biometrika, Vol. 42, No. 1/2 (Jun., 1955), pp. 205-216 Cheers, Karl W. ________________________________ From: Paul Bernhardt [mailto:[email protected]] Sent: Tuesday, April 20, 2010 3:43 PM To: Teaching in the Psychological Sciences (TIPS) Subject: Re: [tips] Top 10 challenging concepts I am skeptical that the Biserial correlation can exceed an absolute value of 1. Can you provide an example in which it does that? Paul Bernhardt Dept of Psychology Frostburg State University pcbernhardt _at_ frostburg _dot_ edu On Apr 20, 2010, at 8:44 AM, Wuensch, Karl L wrote: Actually, there are some correlation coefficients that can exceed one (the biserial, for example). Tell your students to square r before comparing one with another. Give them a set of data and the plot and the accompanying negative r. Then invert or reflect one of the variables and present the plot and positive r. They should get the message then. Try a criminal courtroom analogy. Assume innocence. Type I = convict an innocent defendant. Type II = let a criminal get off. Cheers, Karl W. From: [email protected]<mailto:[email protected]> [mailto:[email protected]] Sent: Monday, April 19, 2010 8:43 AM To: Teaching in the Psychological Sciences (TIPS) Subject: Re: [tips] Top 10 challenging concepts A couple of editorial comments (unwanted I am sure but I don't care): differentiating between the phallic and genital stage Since there is very little validity or empirical support for Freud's theoretical constructs of development and personality, I would say that there is no need to waste precious class time on this distinction m- It helps the modern scientific psychologist not at all... Let the English, Philosophy or History prof deal with it. > -why a -7.0 correlation coefficient is more significant than a +5.0 There > are no such things as a -7.0 correlation coefficient or a 5.0 one. All "r"s range between -1.00 and +1.00 Nancy Melucci Long Beach City College Long Beach CA -----Original Message----- From: Mike Palij <[email protected]<mailto:[email protected]>> To: Teaching in the Psychological Sciences (TIPS) <[email protected]<mailto:[email protected]>> Cc: Mike Palij <[email protected]<mailto:[email protected]>> Sent: Sun, Apr 18, 2010 10:19 pm Subject: re: [tips] Top 10 challenging concepts On Sun, 18 Apr 2010 16:06:30 -0700, Michael Sylvester wrote: >I am attempting to compile a list of the top 10 challenging concepts >to explain to students.So far I have come up with the following from >my courses: > -Type 1 and type 2 error > - differentiating between the phallic and genital stage > -negative reinforcement > -positive punishment > -why a -7.0 correlation coefficient is more significant than a +5.0 > - assimilation and accomodation in Piagetian theory > - diathesis stress theory of schizophrenia Why do fools fall in love? -Mike Palij New York University [email protected]<mailto:[email protected]> P.S. 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