Conscientiousness & Online Education

Technology-driven shift in demand for Conscientiousness, not intelligence
psychology, sociology, meta-analysis, anime, Python, R, survey, IQ, bibliography, order-statistics
2012-07-202016-01-20 in progress certainty: possible importance: 8


like has been hailed as a ma­jor in­no­va­tion which will rev­o­lu­tion­ize higher & lower ed­u­ca­tion, ed­u­cate stu­dents bet­ter, and cut costs. They’re an in­ter­est­ing idea and worth try­ing though over­all, I take a fairly skep­ti­cal at­ti­tude to­wards MOOCs: they seem like a clear ex­am­ple of Ama­ra’s Law (“We tend to over­es­ti­mate the effect of a tech­nol­ogy in the short run and un­der­es­ti­mate the effect in the long run.”), and in gen­eral are not do­ing a good job of ex­ploit­ing the pos­si­bil­i­ties of the Web (no MOOC I’ve seen pro­vides a learn­ing tool even a tenth as good as Bret Vic­tor’s “Up and Down the Lad­der of Ab­strac­tion”).

One of the ques­tions that in­ter­ests me is the pos­si­ble long-term effects. In gen­er­al, changes do not pre­serve all rel­a­tive po­si­tions or ra­tios—­some­one ben­e­fits dis­pro­por­tion­ate­ly, some­one ben­e­fits only a lit­tle. It seems highly un­likely to me that on­line ed­u­ca­tion will re­duce all costs equal­ly, or ed­u­cate all stu­dents bet­ter by the same de­gree.

So what differ­en­tials can we ex­pect from on­line ed­u­ca­tion? Hoary ar­ti­cles from the ‘90s about the’’ might make one pre­dict that it will ben­e­fit mid­dle and up­per-class whites; but on the other hand, pro­po­nents love to talk about fa­vored mi­nori­ties (eg a for­eign black fe­male, like a girl in an African vil­lage) who can now ac­cess on­line ed­u­ca­tion through cheap cell­phones, so one might pre­dict in­stead that on­line ed­u­ca­tion will in­stead help level play­ing fields. No longer will there be a big gap be­tween re­ceiv­ing es­sen­tially no ed­u­ca­tion and re­ceiv­ing a real ed­u­ca­tion, a gap that per­pet­u­ates cy­cles of pover­ty. As In­ter­net ac­cess be­comes more com­mon than ac­cess to qual­ity schools, qual­ity school de­liv­ered through the In­ter­net will lead to an equal­iz­ing effect (the elites will be no bet­ter off than be­fore, and the non-elites now have the chance to ob­tain a pre­req­ui­site to be­com­ing an elite).

Success factors

It may help to ask what causes suc­cess in ed­u­ca­tion and see how on­line ed­u­ca­tion affects it. To a first ap­prox­i­ma­tion, ig­nor­ing en­vi­ron­ment, one earns ed­u­ca­tional suc­cess through:

  1. /g

    IQ ob­vi­ously pre­dicts a huge chunk of ed­u­ca­tional suc­cess (lead­ing to the ironic ac­cu­sa­tion that IQ tests are only aca­d­e­mic ques­tions) since the smarter one is, the eas­ier learn­ing any­thing is, much less one’s school­work.

  2. Con­sci­en­tious­ness (a per­son­al­ity trait in the ; of the hard work, grit, effort)

    If one is not smart enough that one can sim­ply in­hale lessons and pass tests, one still has the op­tion of work­ing hard: do­ing ex­tra prac­tice prob­lems, ask­ing for help, etc. Suc­cess will not come easy, but it will still come. These 2 fac­tors to­gether will cor­re­late some­where like 0.7 with ed­u­ca­tional suc­cess: some­one who is smart and hard-work­ing will go to the top, and some­one who is stu­pid and lazy will not.

  3. Mis­cel­la­neous

    The rest of the cor­re­la­tion is made up of so­cioe­co­nomic sta­tus, cul­ture (eg. East Asian?) and ran­dom other things: ran­dom life events or hard-to-mea­sure en­vi­ron­men­tal fac­tors like an ex­tra-in­spir­ing teacher, etc.

(One fac­tor that does not mat­ter much is qual­ity of school build­ings, text­books, etc. These do not sub­stan­tially pre­dict grades or de­grees ex­cept as prox­ies for SES or stu­dent body qual­ity or sim­i­lar things, which is why in­creas­ing fund­ing typ­i­cally makes no differ­ence and nat­ural ex­per­i­ments in­di­cate ex­tremely small re­turns. In­deed, it’s some­what ab­surd to sug­gest that ac­cess is an is­sue in the In­ter­net age where we are drown­ing in dig­i­tized text­books & pa­pers, used books, and one can­not give away a 5 year old com­put­er; we are a long way in­deed from the world of Ra­manu­jan where the most in­tel­li­gent & mo­ti­vated au­to­di­dact could have se­ri­ous trou­ble lay­ing hands on im­por­tant re­sources.)

Conscientiousness

IQ is well stud­ied, with a thor­ough lit­er­a­ture go­ing back nearly a cen­tu­ry; it cor­re­lates with . But Con­sci­en­tious­ness is more ob­scure, so it’s worth giv­ing back­ground on why we might men­tion it in the same breath as IQ.

A fa­mous & much-cited 1991 meta-analy­sis, Mount & Bar­rick’s “The Big Five Per­son­al­ity Di­men­sions and Job Per­for­mance: A Meta-Analy­sis” found that Con­sci­en­tious­ness cor­re­lated (~0.2; pos­si­bly ~0.31) with var­i­ous job per­for­mance mea­sure­ments even after con­trol­ling for all the ob­vi­ous thing like IQ & ed­u­ca­tion, as did a fol­lowup sur­vey in 1996. Con­sci­en­tious­ness cor­re­lates weakly with IQ in the first place (but maybe not); cor­re­lates with suc­cess in med­ical school or as a teacher or in spelling bees along with all the cor­re­la­tions with ed­u­ca­tional suc­cess (Noftle & Robins 2007; Poropat 2009; ; Chamor­ro-Pre­muzic & Furn­ham 2008; Grigsby 2015) and in par­tic­u­lar may de­ter­mine one’s suc­cess in on­line ed­u­ca­tion (Elvers et al 2003); cor­re­lates with ed­u­ca­tional cre­den­tials after men­tal abil­ity has been con­trolled; cor­re­lates with not hav­ing been in jail and pre­dicts later crim­i­nal records; cor­re­lates more strongly (sum­mary) than IQ with so­cioe­co­nomic sta­tus (SES) and , and al­most as strongly as IQ with oc­cu­pa­tional sta­tus (and pre­dicts em­ploy­ment); like IQ, Con­sci­en­tious­ness cor­re­lates with be­ing thin­ner, re­duced men­tal & phys­i­cal dis­ease, and longevity (both as chil­dren and adults; see also Bogg & Roberts 2004, , ); cor­re­lates (0.4) with ‘over­all qual­ity of life’ and (0.25) ‘hap­pi­ness’ (S­teel et al 2008, “Re­fin­ing the re­la­tion­ship be­tween per­son­al­ity and sub­jec­tive well-be­ing”). show cor­re­la­tions to di­vorce rates, SES, and longevi­ty; or sim­ply on nearly every be­hav­ior rel­e­vant to longevity (see Roberts & Bogg 2004). of the (sim­i­lar to SMPY re­sults), found that for these bright-to-bril­liant kids, Con­sci­en­tious­ness affects life­time earn­ings (usu­ally $2-3 mil­lion) even more than IQ (although only a bit more than ); this is not due solely to it in­creas­ing how much ed­u­ca­tion the par­tic­i­pants got. Eye­balling the graphed cor­re­la­tions on page 45, it seems that go­ing from the 10th per­centile of Con­sci­en­tious­ness to the 90th was worth ~$800,000. (It’s worth not­ing that there is a which is to Con­sci­en­tious­ness with longer-term per­spec­tive and less feed­back, but which seems to cor­re­late bet­ter with GPA, mil­i­tary acad­emy grad­u­a­tion, and spelling bee per­for­mance.) Along with , Con­sci­en­tious­ness is one of the main cor­re­la­tions with cre­ative sci­en­tists (stronger than In­tro­ver­sion!).

And there is one key differ­ence be­tween IQ and Con­sci­en­tious­ness: in­creas­ing IQ is a tricky and often im­pos­si­ble task, but there is weak ev­i­dence that Con­sci­en­tious­ness can be im­proved by try­ing harder tasks. (There is an irony here—it’s hard te­dious work to de­velop the abil­ity to do hard te­dious work, so how does one start?) In­ter­est­ing­ly, Con­sci­en­tious­ness in­creases steadily over a life­time (in con­tradis­tinc­tion to IQ’s steady fall), which is a hope­ful ob­ser­va­tion. I like how put it in :

…Now for the mat­ter of dri­ve. You ob­serve that most great sci­en­tists have tremen­dous dri­ve. I worked for ten years with John Tukey at Bell Labs. He had tremen­dous dri­ve. One day about three or four years after I joined, I dis­cov­ered that John Tukey was slightly younger than I was. John was a ge­nius and I clearly was not. Well I went storm­ing into Bode’s office and said, “How can any­body my age know as much as John Tukey does?” He leaned back in his chair, put his hands be­hind his head, grinned slight­ly, and said, “You would be sur­prised Ham­ming, how much you would know if you worked as hard as he did that many years.” I sim­ply slunk out of the office!

What Bode was say­ing was this: “Knowl­edge and pro­duc­tiv­ity are like com­pound in­ter­est.” Given two peo­ple of ap­prox­i­mately the same abil­ity and one per­son who works 10% more than the oth­er, the lat­ter will more than twice out­pro­duce the for­mer. The more you know, the more you learn; the more you learn, the more you can do; the more you can do, the more the op­por­tu­ni­ty—it is very much like com­pound in­ter­est. I don’t want to give you a rate, but it is a very high rate. Given two peo­ple with ex­actly the same abil­i­ty, the one per­son who man­ages day in and day out to get in one more hour of think­ing will be tremen­dously more pro­duc­tive over a life­time. I took Bode’s re­mark to heart; I spent a good deal more of my time for some years try­ing to work a bit harder and I found, in fact, I could get more work done. I don’t like to say it in front of my wife, but I did sort of ne­glect her some­times; I needed to study. You have to ne­glect things if you in­tend to get what you want done. There’s no ques­tion about this.

Or to quote some Harry Pot­ter fan­fic­tion in­stead:

[Har­ry:] “Where would I go, if not Raven­claw?”

[Sort­ing Hat:] “Ahem. ‘Smart kids in Raven­claw, evil kids in Slyther­in, wannabe he­roes in Gryffind­or, and every­one who does the ac­tual work in Hufflepuff.’ This in­di­cates a cer­tain amount of re­spect. You are well aware that Con­sci­en­tious­ness is just about as im­por­tant as raw in­tel­li­gence in de­ter­min­ing life out­comes, you think you will be ex­tremely loyal to your friends if you ever have some, you are not fright­ened by the ex­pec­ta­tion that your cho­sen sci­en­tific prob­lems may take decades to solve…”

Online education’s factors

How does on­line ed­u­ca­tion affect them—re­duc­ing the need for that fac­tor to reach a cer­tain level of at­tain­ment, leav­ing it alone, or in­creas­ing the need for that fac­tor?

  1. IQ seems like it could go any way:

    • Any effects could roughly can­cel out, per­haps in some sort of com­pen­sat­ing mech­a­nism where stu­dents only aim at par­tic­u­lar lev­els of mas­tery or per­for­mance and bet­ter or worse meth­ods only change how much time they need to in­vest be­fore they go off to play video games.

    • It could in­crease the need for IQ, be­cause now all the ex­tra­ne­ous time-wast­ing ‘gunk’ like sharp­en­ing pen­cils or do­ing rol­l-call can be cleared away by the tech­ni­cal so­lu­tions, leav­ing more time for pure learn­ing. By elim­i­nat­ing all the en­vi­ron­men­tal hin­drances and vari­a­tion, the only vari­a­tion left will come from the stu­den­t’s in­nate in­tel­lec­tual abil­i­ties: IQ. Stu­dents will race through courses un­til they hit their nat­ural lim­its; even Sal Khan’s videos can’t make a dim bulb cal­cu­late so­lu­tions to Schro­ding­er’s equa­tion.

      It has been noted in the psy­cho­me­t­ric lit­er­a­ture that suc­cess­ful at­tempts to elim­i­nate so­cio-e­co­nomic penal­ties and pro­vide qual­ity en­vi­ron­ments for all chil­dren would nec­es­sar­ily in­crease the ap­par­ent con­tri­bu­tion of hered­i­ty: if every child is in an en­vi­ron­ment that lets them de­velop and flour­ish to their fullest ex­tent, then any re­main­ing differ­ences in their de­vel­op­ment will be due to hered­i­tary fac­tors! If vari­a­tions in IQ are the joint prod­uct of vari­a­tions in hered­ity and en­vi­ron­ment, then elim­i­nat­ing all vari­a­tion in en­vi­ron­ment, set­ting en­vi­ron­ment to 0, means the re­main­ing vari­a­tion will be just the vari­a­tion in hered­i­ty.

    • It could re­duce the need for IQ, since on­line ed­u­ca­tion will lead to a mar­ket­place of lessons where only the clear­est, most in­sight­ful, eas­ily un­der­stood lessons sur­vive. In or­di­nary class­rooms staffed by or­di­nary teach­ers, ex­tem­po­ra­ne­ous lec­tures or ex­pla­na­tions are nec­es­sar­ily more opaque and low­er-qual­ity com­pared to a lec­ture that the world-class pre­sen­ter has spent months or years hon­ing.

      But it is a utopian thought that per­haps every­one will be suc­cess­ful at ed­u­ca­tion; so the ques­tion be­comes, what trait or en­vi­ron­men­tal fac­tor would then be­come the best pre­dic­tor of at­tain­ment? If you re­duce the need for brains, then per­haps you still need mo­ti­va­tion and ap­petite for work, which in con­junc­tion with the pre­vi­ous point about joint prod­ucts leads us to the next ob­ser­va­tions…

  2. Con­sci­en­tious­ness is the jok­er. There is one clear pos­si­ble change: on­line ed­u­ca­tion will in­crease de­mand for Con­sci­en­tious­ness com­pared to offline ed­u­ca­tion.

    This has been sug­gested on more than one oc­ca­sion & con­nected to discipline/time-management prob­lems12. This tal­lies with my per­sonal ex­pe­ri­ence with on­line courses and classes with on­line as­sign­ment com­po­nents like com­puter sci­ence classes (where class at­ten­dance may be op­tional and pro­gram­ming projects or home­work are sub­mit­ted re­mote­ly). I had a good deal of trou­ble just sit­ting down to do the course or as­sign­ment, even though it was not nec­es­sar­ily that diffi­cult. The dis­trac­tions on my lap­top beck­oned: I would go use crufty old So­laris boxes in the com­puter labs just to avoid the dis­trac­tions and get some­thing done. Other ex­pe­ri­ences were more dra­mat­ic: one CS exam was done on com­put­ers, with a built-in test suite you could run to get your ex­act grade, so one could spend hours work­ing on it un­til one had a per­fect 100 (which was­n’t ter­ri­bly hard), which of course I did—so I was shocked when the teacher showed us the grade dis­tri­b­u­tion and it looked like a nor­mal CS exam dis­tri­b­u­tion, with plenty of <100 scores and out­right fail­ures!

  3. Mis­cel­la­neous is too var­ied and het­ero­ge­neous to be pre­dictable, so we won’t dis­cuss it fur­ther.

It’s also worth not­ing that due to so­cioe­co­nomic eco­nomic sta­tus be­ing de­ter­mined in large part due to IQ & Con­sci­en­tious­ness, and both be­ing highly her­i­ta­ble, we might pre­dict in ad­vance that on­line ed­u­ca­tion will not be a lev­el­ing force as far as other traits go; claims that on­line ed­u­ca­tion or MOOCs will re­duce in­come in­equal­ity seem to be based on a stan­dard so­cial sci­ence model world­view in which there are no cog­ni­tive differ­ences be­tween in­di­vid­u­als since every­one is equally intelligent/patient/hard-working/curious and that any ob­served in­equal­ity of out­comes must be due to pre-ex­ist­ing differ­ences of en­vi­ron­ment or dis­crim­i­na­tion, that ac­cess to ed­u­ca­tional ma­te­r­ial is the bot­tle­neck, and that in­creas­ing ac­cess will per­force re­duce in­equal­i­ty. None of which is true, and so we would not be too sur­prised to find that MOOCs are dom­i­nated by the al­ready well-e­d­u­cated or high SES (Hansen & Re­ich 2015), who are in­tel­li­gent & mo­ti­vated enough to seek out fur­ther ed­u­ca­tion

Existing research

The gen­eral back­ground of on­line ed­u­ca­tion demon­strated in a large DoE 2009 meta-analy­sis is that a lot of stud­ies are poor or not ran­dom­ized con­trolled tri­als (un­sur­pris­ing­ly) but in the qual­ity stud­ies, on­line learn­ing slightly out­per­forms reg­u­lar classes and mixed classes out­per­form both on­line & offline classes3 (see also the sim­i­lar re­sults & Bowen et al 2012). The age of stu­dents does­n’t seem to mat­ter much al­though the meta-analy­sis seemed to see a shrink­ing effect go­ing from un­der­grad­u­ate col­lege stu­dents to pro­fes­sion­als or post­grad­u­ates4. This meta-an­a­lytic re­sult is broadly con­sis­tent with the pic­ture pre­vi­ously paint­ed: if we ac­cept that on­line ed­u­ca­tion should be bet­ter then a small in­crease in av­er­age scores is con­sis­tent with some stu­dents ben­e­fit­ing much more and some los­ing a lit­tle; the mixed class­es, with their face-to-face el­e­ments, com­pen­sate for lacks in Con­sci­en­tious­ness, giv­ing more stu­dents the best of both worlds; and in­de­pen­dent study hurts re­sults for the same rea­son. At­tri­tion-wise, on­line courses may per­form worse: MOOCs have low suc­cess rates but com­par­ing them to tra­di­tional col­leges (with some­thing like a 60% de­gree com­ple­tion rate) is ap­ples and or­anges; some stud­ies sug­gest proper on­line courses still lose some more stu­dents (eg Xu et al 2011), and Pat­ter­son 2014 re­ports that, in line with re­search on s to de­feat , use of the Res­cue­Time in a Stan­ford MOOC re­sulted made par­tic­i­pants “spend 24% more time work­ing on the course, re­ceive course grades that are 0.29 stan­dard de­vi­a­tions high­er, and are 40% more likely to com­plete the course”.

There is also some aca­d­e­mic re­search di­rectly ex­am­in­ing per­son­al­ity fac­tors, which com­pare on­line and offline per­for­mance and also col­lect per­son­al­ity data5; I cur­rently know of these rel­e­vant stud­ies:

  1. “Pro­cras­ti­na­tion in On­line Cours­es: Per­for­mance and At­ti­tu­di­nal Differ­ences”, Elvers et al 2003; re­sult:

    There were no re­li­able differ­ences be­tween the 2 sec­tions of the class on the mea­sures of pro­cras­ti­na­tion, exam per­for­mance, or at­ti­tudes to­ward the class. Yet, pro­cras­ti­na­tion was neg­a­tively re­lated with exam scores and with at­ti­tudes to­ward the class for the on­line stu­dents, but not for the lec­ture stu­dents. This differ­ence may par­tially ex­plain why on­line courses de­signed to in­crease the ed­u­ca­tional effi­cacy of a course often show no differ­ence in per­for­mance when com­pared to lec­ture class­es.

    Back­ground:

    If pro­cras­ti­na­tion is a prob­lem in on­line class­es, it would be de­sir­able to know which stu­dents are most at risk for pro­cras­ti­na­tion. In­struc­tors could then offer the at-risk stu­dents in­ter­ven­tions de­signed to re­duce dila­tory be­hav­iors. Wat­son (2001) and Schouwen­burg and Lay (1995) cor­re­lated self­-re­ported pro­cras­ti­na­tion with five fac­tors of per­son­al­i­ty. Both found a re­li­able re­la­tion be­tween self­-re­ported pro­cras­ti­na­tion and low con­sci­en­tious­ness. Wat­son found a re­li­able re­la­tion be­tween pro­cras­ti­na­tion and neu­roti­cism. Schouwen­burg and Lay also found some, but not all, facets of neu­roti­cism to be re­lated to pro­cras­ti­na­tion.

    What did the stu­dents say and what differ­ence was found in their scores?

    One ques­tion asked in the end-of-se­mes­ter ques­tion­naire was whether the stu­dent dis­liked the class be­cause it was easy to get be­hind in the class. In the on­line class, 19 of 21 stu­dents re­ported that they dis­liked the class be­cause it was easy to get be­hind. Only 13 of 23 stu­dents in the lec­ture class re­ported that they dis­liked the class be­cause it was easy to get be­hind…How­ev­er, the mag­ni­tude of the re­la­tion be­tween pro­cras­ti­na­tion and class per­for­mance and at­ti­tudes seemed to be larger for the on­line class than for the tra­di­tional class. Pro­cras­ti­na­tion was a good pre­dic­tor of per­for­mance for each of the five tests in the class for the on­line stu­dents, but not a good pre­dic­tor of per­for­mance for any of the five tests for the lec­ture stu­dents.

    Fi­nal­ly, the quote that re­ally sums it all up:

    Ped­a­gogy sug­gests that ac­tiv­i­ties such as on­line dis­cus­sions, group writ­ing pro­jects, and im­me­di­ate feed­back on per­for­mance should lead to bet­ter per­for­mance. Thus, stu­dents in on­line class­es, which often con­tain these ac­tiv­i­ties, should have bet­ter per­for­mance in the class com­pared to tra­di­tional lec­ture class­es, which often lack these ac­tiv­i­ties. How­ev­er, this is rarely the case. Rus­sell (1999) cited more than 300 stud­ies that failed to find any re­li­able differ­ence in per­for­mance be­tween tra­di­tional classes and classes at a dis­tance (in­clud­ing cor­re­spon­dence cours­es, on­line cours­es, and tele­cours­es). The ob­ser­va­tion that the mag­ni­tude of the re­la­tion be­tween pro­cras­ti­na­tion and exam scores was larger in this on­line class than in the lec­ture class could be a pos­si­ble ex­pla­na­tion for these null re­sults. The ad­di­tional ac­tiv­i­ties in on­line classes that should in­crease per­for­mance may do just that. How­ev­er, the decre­ments as­so­ci­ated with dila­tory be­hav­iors in on­line classes may at­ten­u­ate the in­cre­ments as­so­ci­ated with the ad­di­tional ac­tiv­i­ties. By re­duc­ing dila­tory be­hav­iors, the ben­e­fits of on­line classes may be­come more ap­par­ent.

  2. Irani et al 2004, “Per­son­al­ity type and its re­la­tion­ship to dis­tance ed­u­ca­tion stu­dents’ course per­cep­tions and per­for­mance”: non-ran­dom­ized case study us­ing MBTI

  3. Kim & Schnieder­jans 2004, “The role of per­son­al­ity char­ac­ter­is­tics in we­b-based dis­tance ed­u­ca­tion courses”: in its sam­ple of 140 stu­dents, on­line ed­u­ca­tion worked best for those high on the Won­der­lic PCI Suc­cess Scales for ‘Com­mit­ment to Work’ (“The ten­dency to re­main on a job for a long time, and not be un­de­pend­able, ir­re­spon­si­ble, im­pul­sive, dis­or­ga­nized, or lack per­sis­tence.”) and ‘Learn­ing Ori­en­ta­tion’ (“The ten­dency of an in­di­vid­ual to be will­ing to en­gage in ac­tiv­i­ties to ac­quire knowl­edge, skills, and be­hav­iors and to learn new meth­ods and pro­ce­dures to im­prove job effec­tive­ness, how in­ter­ested they are in de­vel­op­ing them­selves, seek op­por­tu­ni­ties to learn new and differ­ent ways of do­ing things, and en­rolled in train­ing pro­grams that they are likely to be ac­tive and fully en­gaged par­tic­i­pants.”) Un­for­tu­nate­ly, these are not ex­actly equiv­a­lent to Con­sci­en­tious­ness.

  4. Schnieder­jans & Kim 2005, “Re­la­tion­ship of Stu­dent Un­der­grad­u­ate Achieve­ment and Per­son­al­ity Char­ac­ter­is­tics in a To­tal We­b-Based En­vi­ron­ment: An Em­pir­i­cal Study”; sim­i­lar to Kim & Schnieder­jans 2004, 260 stu­dents. It found Con­sci­en­tious­ness sta­tis­ti­cal­ly-sig­nifi­cant, but also 3 oth­ers (Open­ness, Neu­roti­cism, and Open­ness) and not Ex­tra­ver­sion. (Nei­ther seems to in­clude any effect size or whether Con­sci­en­tious­ness out­-pre­dicts the other fac­tors; this may be due to my in­abil­ity to in­ter­pret some of the pro­vided sta­tis­tic­s.)

  5. Bassili 2006, mea­sured only Neu­roti­cism and Open­ness, so can­not tell us any­thing about Con­sci­en­tious­ness.

  6. Bish­op-Clark et al 2007, “The effects of per­son­al­ity type on we­b-based dis­tance learn­ing”; MBTI, un­for­tu­nately

  7. Beren­son et al 2008, “Emo­tional In­tel­li­gence as a Pre­dic­tor for Suc­cess in On­line Learn­ing”; cor­re­la­tional study, col­lapses Con­sci­en­tious­ness with other items into a “per­sua­sive­ness” item which does cor­re­late with higher on­line grades.

  8. Bol­liger & Avgeri­nou 2009, “Stu­dent Sat­is­fac­tion with On­line Courses Based on Per­son­al­ity Type”; just an ab­stract (and MBTI). More im­por­tant­ly, it’s not clear we can learn any­thing from sur­veys of sat­is­fac­tion or hap­pi­ness or en­joy­ment: Ne­manich et al 2009, a qua­si­-ex­per­i­ment, found that in class­rooms, higher en­joy­ment = higher scores, but that cor­re­la­tion was much weaker in their on­line set­ting

  9. Avgeri­nou 2010, “Teacher vs. stu­dent sat­is­fac­tion with on­line learn­ing ex­pe­ri­ences based on per­son­al­ity type”: MBTI, does not re­port de­tailed in­for­ma­tion.

  10. Abzug 2010, “E-con­sci­en­tious­ness and e-per­for­mance in on­line un­der­grad­u­ate man­age­ment ed­u­ca­tion”; did not mea­sure Con­sci­en­tious­ness via stan­dard ques­tion­naire but via ac­tiv­ity in the on­line course (a per­for­mance mea­sure sim­i­lar to that of Heden­gren & Strat­mann 2012’s item non-re­sponse way of mea­sur­ing Con­sci­en­tious­ness)

  11. Chahino 2011, “An ex­plo­ration of per­son­al­ity type suc­cess in on­line classes”; uses (not Big Five or MBTI), find­ing no cor­re­la­tion with DISC re­sults

  12. Mell­ish 2011; cor­re­la­tion­al, us­ing MBTI; 102 on­line stu­dents (83 fe­male) were equally dis­trib­uted among per­son­al­ity types (no offline control/comparison), no ob­vi­ous per­son­al­ity cor­re­la­tion with per­for­mance

  13. Varela et al 2012, “On­line learn­ing in man­age­ment ed­u­ca­tion: an em­pir­i­cal study of the role of per­son­al­ity traits”; qua­si­-ex­per­i­men­tal com­par­i­son of offline & on­line:

    In test­ing H2, learn­ing was re­gressed on con­sci­en­tious­ness. Re­sults sup­port the abil­ity of con­sci­en­tious­ness to ex­plain learn­ing vari­ance across groups (β=4.11, SE=1.41, p<.05). Then, learn­ing was re­gressed on con­sci­en­tious­ness, ini­tial­ly, in the face-to-face sam­ple and then, in the on­line group. While the re­gres­sor co­effi­cient was not sta­tis­ti­cal­ly-sig­nifi­cant for the face-to-face group (β=3.49, SE=2.01, p>.05), the re­gres­sion co­effi­cient ex­hibits a stronger and [s­ta­tis­ti­cal­ly-]sig­nifi­cant effect size for the on­line group (β=4.59; SE=1.96, p<.05). Con­sis­tent with the ex­pec­ta­tions in H2, re­sults cor­rob­o­rate that con­sci­en­tious­ness has a stronger abil­ity to ac­count for learn­ing vari­ance in on­line set­tings (R2=.079) than in face-to-face con­texts (R2=.040).

  14. El­lis & Howard 2012, “The Effects of Gen­der and Dom­i­nant Men­tal Processes on Hy­per­me­dia Learn­ing”: MBTI, no offline

  15. Yang et al 2012, “The im­pact of so­cial cap­i­tal and per­son­al­ity traits on stu­dents’ e-learn­ing ex­pe­ri­ence”; no ran­dom­iza­tion or com­par­i­son group, no­table mainly that in their on­line mar­ket­ing class, “Con­tra­dic­tory to this com­mon be­lief, our find­ings show that the con­sci­en­tious­ness trait does not in­flu­ence stu­dents’ e-learn­ing ex­pe­ri­ence. How­ev­er, the so­cial ori­en­ta­tion trait does. Fur­ther­more, this pos­i­tive in­flu­ence from the so­cial ori­en­ta­tion trait be­comes stronger when larger so­cial cap­i­tal ex­ists.”

  16. Pun­noose 2012, “De­ter­mi­nants of In­ten­tion to Use eLearn­ing Based on the Tech­nol­ogy Ac­cep­tance Model”; mas­ters de­gree Thai stu­dents, did not in­ves­ti­gate any cor­re­lates of achieve­ment but did find Con­sci­en­tious­ness had small cor­re­la­tions with at­ti­tudes to­wards the course.

  17. Keller & Ka­rau 2013, “The im­por­tance of per­son­al­ity in stu­dents’ per­cep­tions of the on­line learn­ing ex­pe­ri­ence”: “The cur­rent re­search ex­am­ined the re­la­tion­ship be­tween the Big Five per­son­al­ity di­men­sions and five spe­cific types of on­line course im­pres­sions (en­gage­ment, value to ca­reer, over­all eval­u­a­tion, anxiety/frustration, and pref­er­ence for on­line cours­es). Re­sults re­vealed that con­sci­en­tious­ness was the most con­sis­tent pre­dic­tor of an in­di­vid­u­al’s im­pres­sions of on­line cours­es.” They did not record any grades or exam scores.

  18. Fariba 2013, “Aca­d­e­mic Per­for­mance Of Vir­tual Stu­dents Based On Their Per­son­al­ity Traits, Learn­ing Styles And Psy­cho­log­i­cal Well Be­ing: A Pre­dic­tion”; sur­vey of self­-s­e­lected on­line stu­dents which found large neg­a­tive cor­re­la­tion be­tween grades & Neu­roti­cism, and smaller cor­re­la­tions with Conscientiousness/Extraversion/Openness.

  19. Shih et al 2013, “The Re­la­tion­ship Among Ter­tiary Level EFL Stu­dents’ Per­son­al­i­ty, On­line Learn­ing Mo­ti­va­tion And On­line Learn­ing Sat­is­fac­tion”: “ex­tra­ver­sion and con­sci­en­tious­ness were the two im­por­tant traits among the Big Five in pre­dict­ing mo­ti­va­tion and sat­is­fac­tion” (but no mea­sure of grades or online/offline ex­per­i­men­tal de­sign)

  20. San­to, S.A.: “Vir­tual learn­ing, per­son­al­i­ty, and learn­ing styles”. Dis­ser­ta­tion Ab­stracts In­ter­na­tional Sec­tion A, Hu­man­i­ties & So­cial Sci­ences, 62, pp. 137 (2001)

  21. Zob­de­h-Asadi, S.: “Differ­ences in per­son­al­ity fac­tors and learn­ers’ pref­er­ence for tra­di­tional ver­sus on­line ed­u­ca­tion”. Dis­ser­ta­tion Ab­stracts In­ter­na­tional Sec­tion A: Hu­man­i­ties & So­cial Sci­ences, 65(2-A), pp. 436 (2004)

  22. Ran­dler et al 2014, “The In­flu­ence of Per­son­al­ity and Chrono­type on Dis­tance Learn­ing Will­ing­ness and Anx­i­ety among Vo­ca­tional High School Stu­dents in Turkey”: sur­vey, no large re­la­tion­ship with any of the sur­vey in­stru­ments; no ques­tions were asked about grades or suc­cess

Factor changes

Now, we dis­carded #3 as be­ing im­pos­si­ble to gen­er­al­ize about, and #2 sug­gests that Con­sci­en­tious­ness will in­crease in its cor­re­la­tion with suc­cess, while to me the more plau­si­ble out­come for #1 is that it will re­duce the need. But to be con­ser­v­a­tive, let’s as­sume the need for IQ re­mains un­changed. This sug­gests the fol­low­ing ar­gu­ment:

  1. Ma­te­r­ial pre­sented in an on­line ed­u­ca­tion for­mat: re­quires the same amount of IQ to un­der­stand6
  2. Ma­te­r­ial pre­sented in an on­line ed­u­ca­tion for­mat: also re­quires more Con­sci­en­tious­ness than the same ma­te­r­ial pre­sented in a class­room
  3. there are no other fac­tors; then
  4. less of the gen­eral pop­u­la­tion will be able to learn it.

To be­la­bor the ob­vi­ous and dress it up in math­e­mat­i­cal garb: for a par­tic­u­lar sta­tic set/population Z, the num­ber of Z mem­bers which sat­isfy the re­quire­ments , be­cause the frac­tion of the pop­u­la­tion with both the nec­es­sary IQ and the nec­es­sary Con­sci­en­tious­ness must be equal to or smaller than the frac­tion with just the nec­es­sary IQ; for any prop­er­ties . See also the con­junc­tion fal­lacy. When it comes to nor­mally dis­trib­uted traits like IQ, mod­est se­lec­tion pres­sure can drive down the frac­tion of el­i­gi­ble peo­ple to near-zero rates; for ex­am­ple, far less than 1% of the pop­u­la­tion will be 2 stan­dard de­vi­a­tions above the mean on both IQ and Con­sci­en­tious­ness and this holds true even if we as­sume that both traits are highly cor­re­lated with each other (they’re not), see the ap­pen­dix for for­mu­las & cal­cu­la­tions.

(A ma­jor caveat here is that the premises re­ally do need ab­solute val­ues of IQ and Con­sci­en­tious­ness. If you only have cor­re­la­tions, I be­lieve it is pos­si­ble for IQ’s cor­re­la­tion for ed­u­ca­tional suc­cess re­main the same and Con­sci­en­tious­ness’s cor­re­la­tion go up while the frac­tion of the gen­eral pop­u­la­tion suc­ceed­ing goes up also. For ex­am­ple, if on­line ed­u­ca­tion re­duced the need for Con­sci­en­tious­ness, but re­duced the need for IQ even more, more peo­ple will pass by the op­po­site of our con­junc­tive rea­son­ing, but any at­tempt to pre­dict suc­cess will ben­e­fit less from in­for­ma­tion about IQ than about Con­sci­en­tious­ness.)

Now, to dis­cuss claim #2 in more de­tail. The first study cited pre­vi­ously on on­line ed­u­ca­tion stress­ing Con­sci­en­tious­ness, Elvers 2003, is par­tic­u­larly in­ter­est­ing (see the quotes in the foot­note). Now, given the ev­i­dence from this study that on­line ed­u­ca­tion scores cor­re­late with Con­sci­en­tious­ness, it seems very likely that #2 is true. How­ev­er, the re­sult that the on­line stu­dents had the same av­er­age as the offline stu­dents in­di­cates that the con­clu­sion #4 is not true; the ob­vi­ous can­di­date to re­ject via modus tol­lens is as­sump­tion #1. As one would hope! But if #1 is not true, it could be true to a very large de­gree—as al­ready men­tioned, com­put­er­ized ed­u­ca­tion could make ed­u­ca­tion a lot less cor­re­lated with your raw IQ be­cause it’s pre­sented bet­ter or what­ever (to lis­ten to the most rap­tur­ous users of Khan Acad­e­my). How­ev­er, the equal­ity in scores be­tween the on­line and offline classes in­di­cates that what­ever the drop in IQ re­quire­ments, it was off­set by the in­crease in Con­sci­en­tious­ness re­quire­ments.

What does this trade­off be­tween load­ing on Con­sci­en­tious­ness and IQ sug­gest?

  1. First, it sug­gests that blended learn­ing will be in­ter­me­di­ate in re­sults: I’d ex­pect par­tial on­line ed­u­ca­tion to be ‘weaker’ than full on­line ed­u­ca­tion in load­ing on Con­sci­en­tious­ness.

    You have to force your­self to go to class, but then it’s still eas­ier to learn with­out bur­den­ing your willpower/Conscientiousness. (You can al­ways, say, not bring your lap­top to class—d­iffi­cult or im­pos­si­ble with on­line ed­u­ca­tion!) I’d ex­pect the effect of non-manda­tory to be in­ter­me­di­ate, much like I’d ex­pect fre­quent manda­tory dead­lines in on­line ed­u­ca­tion to help only a lit­tle.

  2. Sec­ond, if one lone course shows such a hit from lack of Con­sci­en­tious­ness, what hap­pens as ever more ma­te­r­ial goes on­line and stu­dents might be ex­pected to do en­tire se­mes­ters just on­line?

    Will we see the cor­re­la­tion go up, as stu­dents ex­pend all their willpower and run com­pletely dry (see eg. Baumeis­ter & Tier­ney 2010, Willpower)? (You may be able to lift 1 weight up to your head and do that 10 times in a row, but if given 10 weights si­mul­ta­ne­ously to lift, you’ll drop them al­l.) It seems that the trade­off might ex­tend well be­yond a sin­gle course to all cours­es.

Consequences

Is load­ing out­come more on Con­sci­en­tious­ness a bad thing? I think it is, for a few rea­sons, some of which fol­low di­rectly from the trade­off and some of which are spec­u­la­tion about fu­ture con­se­quences:

  1. there is no par­tic­u­lar rea­son to fa­vor Con­sci­en­tious­ness as an ad­di­tional re­ward for ‘good’ peo­ple. Whether we should fa­vor it over IQ de­pends on the con­se­quences such as what men­tal traits we need more of in our elites.

    Con­sci­en­tious­ness is not a ‘virtue’ in the sense that the (non-ex­is­tent) ho­muncu­lus in your brain is ‘good’ or ‘bad’ for choos­ing to be Con­sci­en­tious or not, any more than it is morally laud­able to be high IQ than low IQ. De­spite folk psy­chol­ogy & mor­al­iz­ing, the Big Five per­son­al­ity traits are sta­ble over life­times like IQ, are turn­ing out to be in­flu­enced by hered­ity like IQ, and progress is be­ing made on trac­ing the traits to the un­der­ly­ing neu­ro­log­i­cal fac­tors like IQ. You can no more ‘try hard to be able to try hard’ (how cir­cu­lar) than you can try hard to be more in­tel­li­gent.

    Even if we find that Con­sci­en­tious­ness is not affected or Con­sci­en­tious­ness does not cor­re­late with any prob­lem­atic traits like psy­chopa­thy, that does­n’t ex­clude other per­son­al­ity traits: Varela et al 2012 finds that on­line per­for­mance was also cor­re­lated with be­ing low on “gre­gar­i­ous­ness”, a sub­fac­tor of Ex­tra­ver­sion match­ing on “in­di­vid­u­als who con­fine them­selves from so­cial set­tings” (rather than just be­ing quiet and re­served in so­cial set­tings)—is this a good, bad, or neu­tral thing, moral­ly? Or prac­ti­cal­ly?

  2. As al­ready ob­served, the school sys­tem al­ready re­wards Con­sci­en­tious grinds, and op­presses cre­ativ­ity. Do we need to make the for­mer even more true? Think of how this will pe­nal­ize bright cre­ative po­ten­tial-fu­ture-great-sci­en­tists—but un­in­ter­ested in forc­ing them­selves to do man­dated drudge-work—n­erds. We have all heard sto­ries of ge­niuses like Ein­stein or Dar­win or Jung who de­spised lower or higher ed­u­ca­tion, or did their best to ig­nore it while ed­u­cat­ing them­selves—Si­mon­ton’s 1994 Great­ness: Who makes his­tory and why es­ti­mates that this is not a few anec­dotes but 60% of his sam­ple. (Con­sci­en­tious­ness is nec­es­sary for sci­en­tific great­ness, but not that much.)

    If we stand idly by and let Con­sci­en­tious­ness shifts hap­pen, say­ing that it must be a good thing since it is hap­pen­ing, I be­lieve we are guilty of . A use­ful thought here is Bostrom’s re­ver­sal test: why do we think that the cur­rent de­mands for Con­sci­en­tious­ness are op­ti­mal? Or the dou­ble-re­ver­sal test: sup­pose some alien or tech­nol­ogy sud­denly in­ter­vened in our ed­u­ca­tional sys­tem and made it load even more heav­ily on IQ but some­one came up with a sim­ple way to place bur­den back on Con­sci­en­tious­ness—­would we ac­cept their so­lu­tion? I sus­pect in both cas­es, we would be un­able to pro­duce any good an­swer to this im­por­tant is­sue.

    It’s worth not­ing that a lit­tle ap­pre­ci­ated prop­erty of the bell curve or nor­mal dis­tri­b­u­tion is that a very small shift in the av­er­age can have un­in­tu­itively large con­se­quences at the tails: a shift of 1 IQ point in the gen­eral pop­u­la­tion can re­sult in con­sid­er­able changes in the pop­u­la­tion all the way out at, say, 160+ IQs. We can grasp this by look­ing at the by stan­dard de­vi­a­tion: some­one at 2 de­vi­a­tions is 1 in 22, 3 de­vi­a­tions 1 in 370, 4 = 1 in 15,787 (42x fewer than 3), and 5 = 1 in 1,744,277 (110x fewer than 4). A com­mon stan­dard de­vi­a­tion for par­tic­u­lar IQ tests is 15 points, so 3 de­vi­a­tions out is ~145 IQ, which is around the ob­served min­i­mum for great No­bel-win­ning sci­en­tific or math­e­mat­i­cal work7. This is in­ter­est­ing be­cause some in­ter­ven­tions like can have in the worst-off en­vi­ron­ments—­such as an av­er­age in­crease of as much as 15 IQ points—which would sug­gest that if a hy­po­thet­i­cal in­ter­ven­tion moved a pop­u­la­tion a stan­dard de­vi­a­tion from 85 to 100 IQ, its sub­pop­u­la­tion at 145 goes from be­ing 4 de­vi­a­tions away to 3—which in­creases that sub­pop­u­la­tion’s ranks by 42x or 4200%!8 (One meta-analy­sis of io­dine effects, Scrimshaw 1998, ap­par­ently did find a shift of the over­all bell curve; and fur­ther, iodiza­tion ben­e­fits fe­males more than males, so there may have been non­triv­ial con­se­quences there…)

    The im­pli­ca­tions are ob­vi­ous for any aca­d­e­mic sys­tem that forced its mem­ber­ship’s av­er­age IQ down a few points in ex­change for re­searchers higher on Con­sci­en­tious­ness: it may have out­sized effect on how much of its mem­ber­ship are the very smartest re­searchers around.

  3. The trade­off re­sult­ing in on­line ed­u­ca­tion fa­vor­ing Con­sci­en­tious­ness was nei­ther de­signed in nor re­al­ized by the de­sign­ers; it is purely ac­ci­den­tal and un­de­sired. Would­n’t it be ex­tra­or­di­nary if an ac­ci­den­tal trade­off turned out to be ex­actly op­ti­mal? How very con­ve­nient!

    This is a good time to ap­ply the sta­tus-quo re­ver­sal test: sup­pose on­line ed­u­ca­tion did not re­sult in any such trade­off but a Khan Acad­emy staffer uni­lat­er­ally made some changes meant solely to make KA scores re­flect Con­sci­en­tious­ness more (per­haps your progress would be deleted if you did not Con­sci­en­tiously log in every week and do a few prob­lem­s). Would you ap­prove of this change? Sup­pose fur­ther on­line ed­u­ca­tion ac­tu­ally re­duced the need for Con­sci­en­tious­ness (maybe be­cause the ser­vice pings your cell­phone with a quick prac­tice prob­lem every so often); would you ap­prove of the staffer’s change then? If you would not ap­prove in the lat­ter sce­nario where the shift along the trade­off curve is in­ten­tion­al, why would you ap­prove of a shift caused ac­ci­den­tal­ly?

  4. The cheap­ness of on­line ed­u­ca­tion may prove ir­re­sistible and a case of : the cost of hu­man teach­ers is non­triv­ial and may be in­creas­ing (whether this is due to back­loaded pen­sion com­pen­sa­tion, growth of the ed­u­ca­tion sec­tor & di­min­ish­ing re­turns, etc.), and this has prompted re­ac­tions like the death of uni­ver­sity tenure & whole­sale use of ad­juncts, at­tacks on unions, and in­ter­est in au­to­mated meth­ods of teach­ing… like on­line ed­u­ca­tion. Al­ready cuts have be­gun. Even if on­line ed­u­ca­tion is worse, there may be no choice about whether to use it or not—a sort of ed­u­ca­tional move­ment. This shift may or may not be eco­nom­i­cally effi­cient (if the pub­lic sec­tor is able to force the losses onto the pub­lic which is not or­ga­nized enough to avoid it, per­haps due to ide­o­log­i­cal di­vi­sion­s).

  5. Eco­nomic growth is in­creas­ingly cap­tured in the US by the most-e­d­u­cat­ed, with in­come growth go­ing mostly to grad­u­ate de­gree hold­ers. So any­thing which may lessen the ranks of the most highly ed­u­cated seems like it would ex­ac­er­bate the in­equal­ity of re­turns to ed­u­ca­tion. Is some gen­eral in­creases in the net wealth of the econ­omy worth it? Peo­ple do not eat ab­solute wealth in­creas­es, they eat rel­a­tive in­creas­es—­more egal­i­tar­ian economies are hap­pier pop­u­laces. (Note the same ques­tion can be asked of other ‘cheaper’ things like glob­al­iza­tion and out­sourcing, and the an­swer in those other cases is not triv­ial. does not mean every­one is bet­ter off, just that no one is worse off, and this as­sumes hu­mans do not care about their rank­ings or place—a patently false ap­prox­i­ma­tion.)

What other con­se­quences may there be?

This prodi­gious event is still on its way, still wan­der­ing; it has not yet reached the ears of men. Light­ning and thun­der re­quire time, the light of the stars re­quires time, deeds, though done, still re­quire time to be seen and heard. This deed is still more dis­tant from them than the most dis­tant stars—and yet they have done it them­selves.

Appendices

Selection on multiple normally distributed traits

Simple questions

Sup­pose an elite uni­ver­sity like Har­vard de­cided to set a new ad­mis­sions stan­dard: they will only ad­mit peo­ple who are 2 stan­dard de­vi­a­tions above the mean on both IQ and Con­sci­en­tious­ness. If the fil­ter is for 2 stan­dard de­vi­a­tions above the mean and the vari­ables are cor­re­lated with 1 (i­den­ti­cal), then 2.3% of the pop­u­la­tion will pass; if the vari­ables are un­cor­re­lated with 0, then 2.3% of 2.3% (or 0.000529%) of the pop­u­la­tion will pass.

Correlated

But what about in­ter­me­di­ate val­ues? For ex­am­ple, the psy­chol­ogy lit­er­a­ture has re­ported a cor­re­la­tion of -0.21 be­tween Con­sci­en­tious­ness & IQ, so we would ex­pect an even tinier frac­tion of the pop­u­la­tion to pass, but what if we were op­ti­mistic and thought there was a pos­i­tive cor­re­la­tion?

I con­sulted , but I did­n’t un­der­stand much of it. The clos­est I found was , but in this case what I want is closer to a min func­tion.

Simulation

I was able to work up a R sim­u­la­tion to see how that worked, and it seemed in line with my in­tu­itions:

# install.packages("fMultivar")
library ("fMultivar")

x <- rnorm2d(10000000, rho=0.5)

xgreater <- length(subset(x, x[,1] > mean(x[,1])+2*sd(x[,1])))
xandygreater <- length(subset(x, x[,1] > mean(x[,1])+2*sd(x[,1]) & x[,2] > mean(x[,2])+2*sd(x[,2])))

c(xgreater, xandygreater); c(xgreater / length(x), xandygreater / length(x), xgreater / xandygreater) * 100

## example results for different values of 'rho='
# 0.1
# [1] 454,664  17,570
# [1] 2.273e+00 8.785e-02 2.588e+03
#
# 0.2
# [1] 458,284  82,552
# [1]   2.2914   0.4128 555.1458
#
# 0.5
# [1] 454,484  80,872
# [1]   2.2724   0.4044 561.9794
#
# 0.9
# [1] 455,242 267,912
# [1]   2.276   1.340 169.922
#
# 0.95
# [1] 455,162 321,024
# [1]   2.276   1.605 141.784
#
# 0.99
# [1] 455,260 394,448
# [1]   2.276   1.972 115.417

Exact calculation

Bivariate min

I re­ally was hop­ing for more of a pre­cise an­a­lytic so­lu­tion, so some more search­ing even­tu­ally turned up a pa­per, “Ex­act Dis­tri­b­u­tion of the Max/Min of Two Gauss­ian Ran­dom Vari­ables”, which gives a de­fi­n­i­tion for the min of 2 cor­re­lated nor­mal vari­ables. This seems to be what I want; top of pg1, sec­ond column:

…where and are, re­spec­tive­ly, the pdf and the cu­mu­la­tive dis­tri­b­u­tion func­tion (cdf) of the stan­dard nor­mal dis­tri­b­u­tion. It is known that the of is , where

They give an R im­ple­men­ta­tion on pg6 (first colum­n); it seems to have a pnorm ty­po, but I fixed that. Once it was work­ing, I tried gen­er­at­ing a slightly (0.1) cor­re­lated bi­vari­ate dis­tri­b­u­tion, which look OK:

fmin <- function (y,mu1,mu2,sigma1,sigma2,rho)
     {t1<-dnorm(y,mean=mu1,sd=sigma1)
     tt<-rho*(y-mu1)/(sigma1*sqrt(1-rho*rho))
     tt<-tt-(y-mu2)/(sigma2*sqrt(1-rho*rho))
     t1<-t1*pnorm(tt)
     t2<-dnorm(y,mean=mu2,sd=sigma2)
     tt<-rho*(y-mu2)/(sigma2*sqrt(1-rho*rho))
     tt<-tt-(y-mu1)/(sigma1*sqrt(1-rho*rho))
     t2<-t2*pnorm(tt)
     return(t1+t2)}

fmin(c(1:200),100,100,15,15,0.1)
#  [1] 1.849e-11 2.864e-11 4.418e-11 6.784e-11 1.037e-10 1.578e-10 2.392e-10 3.608e-10 5.418e-10
#  ...

Now, I un­der­stand the PDF to be “a func­tion that de­scribes the rel­a­tive like­li­hood for this ran­dom vari­able to take on a given val­ue. The prob­a­bil­ity for the ran­dom vari­able to fall within a par­tic­u­lar re­gion is given by the in­te­gral of this vari­able’s den­sity over the re­gion”. So I sup­pose I should sum up every point in the pdf >130 (s­ince 130 is 2 stan­dard de­vi­a­tions up, by con­struc­tion when I spec­i­fied SD=15) and that’s my prob­a­bil­ity that a ran­dom de­vi­ate will be min(130,130). What’s the to­tal prob­a­bil­ity some­one will be over 130 on both vari­ables? I think that would be:

sum(fmin(c(1:200),100,100,15,15,0.1)[130:200])
[1] 0.001004

If I in­crease the r to 0.9, the re­sult is 0.01455 which is sat­is­fy­ingly larg­er.

A san­ity check­—as the cor­re­la­tion goes to 1.0, there should be no de­crease. So we do the same ques­tion for a sin­gle nor­mal dis­tri­b­u­tion de­fined the same way:

sum(dnorm(c(1:200), 100, 15)[130:200])
# [1] 0.02459

## the function blows NaN chunks on 1.0, so we'll try a lot of 9s:
sum(fmin(c(1:200),100,100,15,15,0.9999999999)[130:200])
# [1] 0.02459
Bivariate double integral

An ac­quain­tance gave me a dou­ble-in­te­gral for­mu­la:

To cal­cu­late our 2-s­tan­dard de­vi­a­tion min­i­mum bi­vari­ate prob­lem with a r = 0.9 in R:

llim <- 2
ulim <- Inf
rho <- 0.9

f <- function(x,y) {
    (1 / (2 * pi * sqrt(1 - rho^2))) * exp(-(1 / (2 * (1 - rho^2))) * (x^2 + y^2 - 2 * rho * x * y))
}

# double-integration
integrate(function(y) {
   sapply(y, function(y) {
     integrate(function(x) f(x,y), llim, ulim)$value
   })
 }, llim, ulim)

# 0.01336 with absolute error < 1.6e-05

In Python us­ing :

from numpy import *;
from scipy.integrate import *;

from matplotlib.pyplot import *;

def func(x, y, rho):
        return 1.0/(2.0*pi*sqrt(1.0-rho**2.0)) * exp(-0.5/(1.0-rho**2.0) * (x**2.0 + y**2.0 - 2.0*rho*x*y))

def answer(rho):
        return dblquad(func, 2, 100, lambda x: 2, lambda x: 100, args=(rho,))[0]

x = arange(-0.99, 0.99, 0.1)
y = zeros(len(x))
for i in range(len(x)):
        y[i] = answer(x[i])
        print x[i], y[i]

plot(x, y)
show()
Monster

In­ci­den­tal­ly, we could also use this code for more friv­o­lous pur­pos­es; for ex­am­ple, the crit­i­cal­ly-re­garded manga cen­ters around two fra­ter­nal twins, one a psy­cho­pathic ge­nius, and one might won­der how fre­quently pairs of fra­ter­nal twins come as pairs of ge­niuses (~3 stan­dard de­vi­a­tions up) given that the fra­ter­nal cor­re­la­tions r=-0.7? We mod­ify the R pa­ra­me­ters:

llim <- 3
ulim <- Inf
rho <- 0.6
# ...
# 0.0001397 with absolute error < 3.4e-05

Twins in gen­eral make up 1-2% of the pop­u­la­tion, so one can tack an­other two ze­roes to get an es­ti­mate of ge­nius twins as be­ing 0.0001397% of the global pop­u­la­tion or ~9,779 (); this is a bit of an un­der­es­ti­mate since iden­ti­cal twins have much higher cor­re­la­tions like r = 0.86, but could also be an over­es­ti­mate since twins may have IQs lower by a third of a stan­dard de­vi­a­tion (although not all stud­ies are con­sis­tent) and this im­plic­itly as­sumes a global av­er­age IQ of 100 (ac­tual mean is more like 89). Fi­nal­ly, how many of those ~9,779 might we ex­pect to be ? The cor­re­la­tion be­tween IQ and psy­chopa­thy has to be weakly pos­i­tive, non-cor­re­lat­ed, or weakly neg­a­tive (once se­lec­tion effects like im­pris­on­ment are dealt with), for no ap­par­ent cor­re­la­tion; so we can sim­ply mul­ti­ply the 9,779 against the es­ti­mated pop­u­la­tion preva­lence of ~1% for a fi­nal es­ti­mate of 98 ge­nius psy­cho­pathic twins world­wide. (What frac­tion of those twins that might be raised in abu­sive or­phan­ages and go on to star in manga is im­pos­si­ble to es­ti­mate.)


  1. One might say it’s the ob­vi­ous chal­lenge for distance/online learn­ers, es­pe­cially to any­one who has tried. Eg. Coomb­s-Richard­son 2007:

    Per­son­al­ity types and learn­ing styles also may affect stu­dent per­for­mance in dis­tance learn­ing. Par­tic­i­pants with an ex­traverted per­son­al­ity type­-who en­joy the phys­i­cal in­ter­ac­tion of work­ing with oth­ers (Meis­geier and Richard­son 1996)-may feel iso­lated from the hu­man ex­pe­ri­ence and be­come dis­il­lu­sioned. Con­sid­er­ing learn­ing styles, Elkins et al. (2002) found in a two-year study of We­b-as­sisted courses that di­ver­gent learn­er­s-who seek broad elab­o­rate ideas prompted by a prob­lem or stim­u­lus-did not per­form nearly as well as con­ver­gent learn­er­s-who are able to bring ma­te­r­ial from a va­ri­ety of sources to solve a prob­lem…What does an on­line course de­mand that a face-to-face class does not? On­line learn­ing re­quires self­-dis­ci­pline and a greater amount of work than a face-to-face course. Stu­dents must demon­strate a high de­gree of au­ton­omy and mo­ti­va­tion (La­dyshewsky 2004).

    • Meis­geier, C., and R. C. Richard­son. 1996. “Per­son­al­ity types of in­terns in al­ter­na­tive teacher cer­ti­fi­ca­tion pro­grams”. The Ed­u­ca­tional Fo­rum 60(4): 350-60 TODO
    • Elkins, V., C. Rafter, R. Eckart, E. Rutz, and C. Malt­bie. 2002. “In­ves­ti­gat­ing learn­ing and tech­nol­ogy us­ing the MBTI and Kol­b’s LSI”. Pa­per pre­sented at the 2002 ASEE An­nual Con­fer­ence and Ex­po­si­tion, June 16-19, Mon­tre­al, Que­bec, Cana­da.
    • La­dyshewsky, R. 2004. “On­line learn­ing ver­sus face to face learn­ing: What is the differ­ence?” Pa­per pre­sented at the 2004 Teach­ing and Learn­ing Fo­rum, Feb­ru­ary 9-10, Mur­doch Uni­ver­si­ty, Mur­doch, West­ern Aus­tralia.

    See also Do­herty 2006, Win­ters et al 2008.↩︎

  2. Coomb­s-Richard­son 2007:

    …Suc­cess­ful dis­tance learn­ers share some dis­tinc­tive fea­tures in their mode of study (Lit­tle­field 2005):

    • They work in­de­pen­dent­ly, are self­-mo­ti­vated and per­sis­tent, and do bet­ter with­out peo­ple giv­ing them con­stant guid­ance.
    • They sel­dom pro­cras­ti­nate, re­al­iz­ing that time­lines are im­por­tant and that ne­glect­ing to turn in their work on sched­ule may end up de­lay­ing com­ple­tion of their stud­ies.
    • They demon­strate good read­ing and writ­ing skills, which are es­sen­tial for ac­quir­ing most of the course in­for­ma­tion. Though some dis­tance learn­ing courses offer video record­ings and au­dio clips, these are not suffi­cient to mas­ter the com­pe­ten­cies.
    • They are able to re­main on task in spite of re­lent­less dis­trac­tions, such as fre­quent in­ter­rup­tions while learn­ing at home.
    ↩︎
  3. In an in­ter­est­ing com­ment on the “pos­si­bil­i­ties” ar­gu­ment for on­line learn­ing (that such courses can add ma­te­r­ial and me­dia that offline courses can­not or will not), iden­tity of courses turns out to be an im­por­tant mod­er­a­tor:

    Stud­ies in which an­a­lysts judged the cur­ricu­lum and in­struc­tion to be iden­ti­cal or al­most iden­ti­cal in on­line and face-to-face con­di­tions had smaller effects than those stud­ies where the two con­di­tions var­ied in terms of mul­ti­ple as­pects of in­struc­tion (+0.13 com­pared with +0.40, re­spec­tive­ly)…In many of the stud­ies show­ing an ad­van­tage for blended learn­ing, the on­line and class­room con­di­tions differed in terms of time spent, cur­ricu­lum and ped­a­gogy. It was the com­bi­na­tion of el­e­ments in the treat­ment con­di­tions (which was likely to have in­cluded ad­di­tional learn­ing time and ma­te­ri­als as well as ad­di­tional op­por­tu­ni­ties for col­lab­o­ra­tion) that pro­duced the ob­served learn­ing ad­van­tages. At the same time, one should note that on­line learn­ing is much more con­ducive to the ex­pan­sion of learn­ing time than is face-to-face in­struc­tion.

    ↩︎
  4. This might be ev­i­dence again­st: since Con­sci­en­tious­ness in­creases mod­estly with age/experience, we would ex­pect older peo­ple (professional/post-grad) to ben­e­fit more than younger (un­der­grad­s). This may re­flect differ­ences in the kinds of sub­jects or the ma­te­ri­al—per­haps older peo­ple tak­ing train­ing are differ­ent from the stud­ied un­der­grads or per­haps their more advanced/specialized ma­te­r­ial has not been ped­a­gog­i­cally pol­ished as more com­mon un­der­grad ma­te­ri­al, etc.↩︎

  5. In stud­ies which don’t col­lect the nec­es­sary in­for­ma­tion on Con­sci­en­tious­ness, I be­lieve it may be pos­si­ble to ob­serve this effect by look­ing at stan­dard de­vi­a­tions in the scores: the on­line class should have a greater range, as the un-Con­sci­en­tious flunk out by do­ing less while the Con­sci­en­tious thrive on the op­ti­mized pre­sen­ta­tion. On the other hand, it could be that the on­line class has higher av­er­ages and sim­i­lar stan­dard de­vi­a­tions, and the un-Con­sci­en­tious just tend to make up the lower half of the test scores, so stan­dard de­vi­a­tions don’t seem like a re­li­able in­di­ca­tor. Un­for­tu­nate, since there are many more stud­ies sim­ply com­par­ing on­line and offline ed­u­ca­tion than com­par­ing them while also col­lect­ing per­son­al­ity data on sub­jects.↩︎

  6. One won­ders how much hope can we place in the fal­sity of #1. Just how much can ed­u­ca­tion’s IQ re­quire­ments be brought down? Ad­vo­cates seem op­ti­mistic, but is the cur­rent ma­te­r­ial all that bad? How dumb can you be be­fore even the best high­est-qual­ity of cal­cu­lus be­comes un­learn­able with fea­si­ble amounts of time and effort on your part? How close are ex­ist­ing on­line courses to this lower bound on IQ? At what point does #1 re­sume be­ing true?↩︎

  7. When this is men­tioned, some wit often tries to bring up sup­posed IQ score in the 130s; while this is ob­vi­ous bunk (a case of ), a closer look at the source of the anec­dote re­veals many rea­sons why the score is ei­ther false or un­re­li­able.↩︎

  8. , from the bell curve in re­al-world pop­u­la­tions at the ex­tremes (<70 and >140) points out the con­se­quence of shift­ing the means:

    Ex­am­i­na­tion of this nor­mal curve can be in­struc­tive if one notes the con­se­quences of shift­ing the to­tal dis­tri­b­u­tion up or down the IQ scale. The con­se­quences of a give shift be­come more ex­treme out to­ward the “tails” of the dis­tri­b­u­tion. For ex­am­ple, shift­ing the mean of the dis­tri­b­u­tion from 100 down to 90 would put 50% in­stead of only 25% of the pop­u­la­tion be­low IQ 90; and it would put 9% in­stead of 2% be­low IQ 70. And in the up­per tail of the dis­tri­b­u­tion, of course, the con­se­quences would be the re­verse; in­stead of 25% above IQ 110, there would be only 9%, and so on. The point is that rel­a­tively small shifts in the mean of the IQ dis­tri­b­u­tion can re­sult in very large differ­ences in the pro­por­tions of the pop­u­la­tion that fall into the very low or the very high ranges of in­tel­li­gence. A 10 point down­ward shift in the mean, for ex­am­ple, would more than triple the per­cent­age of men­tally re­tarded (IQs be­low 70) in the pop­u­la­tion and would re­duce the per­cent­age of the in­tel­lec­tu­ally “gifted” (IQs above 130) to less than one-sixth of their present num­ber. It is in these tails of the nor­mal dis­tri­b­u­tion that differ­ences be­come most con­spic­u­ous be­tween var­i­ous groups in the pop­u­la­tion that show mean IQ differ­ences, for what­ever rea­son, of only a few IQ points. From a knowl­edge of rel­a­tively slight mean differ­ences be­tween var­i­ous so­cial class and eth­nic groups, for ex­am­ple, one can es­ti­mate quite closely the rel­a­tively large differ­ences in their pro­por­tions in spe­cial classes for the ed­u­ca­tion­ally re­tarded and for the “gifted” and in the per­cent­ages of differ­ent groups re­ceiv­ing scholas­tic hon­ors at grad­u­a­tion. It is sim­ply a prop­erty of the nor­mal dis­tri­b­u­tion that the effects of group differ­ences in the mean are greatly mag­ni­fied in the differ­ent pro­por­tions of each group that we find as we move fur­ther out to­ward the up­per or lower ex­tremes of the dis­tri­b­u­tion.

    I in­di­cated pre­vi­ously that the dis­tri­b­u­tion of in­tel­li­gence is re­ally not quite “nor­mal,” but show cer­tain sys­tem­atic de­par­tures from “nor­mal­i­ty.” These de­par­tures from the nor­mal dis­tri­b­u­tion are shown in Fig­ure 2 in a slightly ex­ag­ger­ated form to make them clear. The shaded area is the nor­mal dis­tri­b­u­tion; the heavy line in­di­cates the ac­tual dis­tri­b­u­tion of IQs in the pop­u­la­tion. We note that there are more very low IQs than would be ex­pected in a truly nor­mal dis­tri­b­u­tion and also there is an ex­cess of IQs at the up­per end of the scale. Note, too, the slight ex­cess in the IQ range be­tween about 70 and 90.

    …The “ex­cess” of IQs at the high end of the scale is cer­tainly a sub­stan­tial phe­nom­e­non, but it has not yet been ad­e­quately ac­counted for. In his mul­ti­fac­to­r­ial the­ory of the in­her­i­tance of in­tel­li­gence, Burt (1958) has pos­tu­lated ma­jor gene effects that make for ex­cep­tional in­tel­lec­tual abil­i­ties rep­re­sented at the up­per end of the scale, just as other ma­jor gene effects make for the sub­nor­mal­ity found at the ex­treme lower end of the scale. One might also hy­poth­e­size that su­pe­rior geno­types for in­tel­lec­tual de­vel­op­ment are pushed to still greater su­pe­ri­or­ity in their phe­no­typic ex­pres­sion through in­ter­ac­tion with the en­vi­ron­ment. Every recog­ni­tion of su­pe­ri­or­ity leads to its greater cul­ti­va­tion and en­cour­age­ment by the in­di­vid­u­al’s so­cial en­vi­ron­ment. This in­flu­ence is keenly ev­i­dent in the de­vel­op­men­tal his­to­ries of per­sons who have achieved ex­cep­tional em­i­nence (Go­ertzel & Go­ertzel, 1962). Still an­other pos­si­ble ex­pla­na­tion of the up­per-end “ex­cess” lies in the effects of in the pop­u­la­tion, mean­ing the ten­dency for “like to marry like.” If the de­gree of re­sem­blance in in­tel­li­gence be­tween par­ents in the up­per half of the IQ dis­tri­b­u­tion were [sub­stan­tial­ly] greater than the de­gree of re­sem­blance of par­ents in the be­low av­er­age range, ge­netic the­ory would pre­dict the rel­a­tive elon­ga­tion of the up­per tail of the dis­tri­b­u­tion. This ex­pla­na­tion, how­ev­er, must re­main spec­u­la­tive un­til we have more defi­nite ev­i­dence of whether there is differ­en­tial as­sor­ta­tive mat­ing in differ­ent re­gions of the IQ dis­tri­b­u­tion.

    …The rea­son is sim­ply that as­sor­ta­tive mat­ing in­creases the ge­netic vari­ance in the pop­u­la­tion. By it­self this will not affect the mean of the trait in the pop­u­la­tion, but it will have a great effect on the pro­por­tion of the pop­u­la­tion falling in the up­per and lower tails of the dis­tri­b­u­tion. Un­der present con­di­tions, with an as­sor­ta­tive mat­ing co­effi­cient of about .60, the stan­dard de­vi­a­tion of IQs is 15 points. If as­sor­ta­tive mat­ing for in­tel­li­gence were re­duced to ze­ro, the stan­dard de­vi­a­tion of IQs would fall to 12.9. The con­se­quences of this re­duc­tion in the stan­dard de­vi­a­tion would be most ev­i­dent at the ex­tremes of the in­tel­li­gence dis­tri­b­u­tion. For ex­am­ple, as­sum­ing a nor­mal dis­tri­b­u­tion if IQs and the present stan­dard de­vi­a­tion of 15, the fre­quency (per mil­lion) of per­sons above IQ 130 is 22,750. With­out as­sor­ta­tive mat­ing the fre­quency of IQs over 130 would fall to 9,900, or only 43.5% of the present fre­quen­cy. For IQs above 145, the fre­quency (per mil­lion) is 1,350 and with no as­sor­ta­tive mat­ing would fall to 241, or 17.9% of the present fre­quen­cy. And there are now ap­prox­i­mately 20 times as many per­sons above an IQ of 160 as we would find if there were no as­sor­ta­tive mat­ing for in­tel­li­gence.3

    ↩︎