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 . 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.
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  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

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