Today’s post was supposed to be about Ann Coulter, but I thought I’d write a quick post about a commenter who is currently using the pseudoname “Jesse Watters” who claims to have obtained some freakishly high scores on the WAIS-IV.

Keep in mind, I’m not a professional, but I do know a bit about psychometrics.

The WAIS-IV is an IQ test that actually consists of 15 mini IQ tests (subtests), however to differentiate the subtest scores from overall IQ scores, the subtest scores are expressed as scaled scores. Unlike the overall IQ scores, which have a mean of 100 and a standard deviation of 15 in the U.S. population, the scaled scores have a mean of 10 and an SD of 3, and as commenter Animekitty noted, can be converted to IQ equivalents by multiplying by 5 and then adding 50.

So commenter “Jesse Watters” claims to have obtained the following scaled scores on the 15 WAIS-IV subtests:

Similarities: 19

Vocabulary: 17

Information: 19

(Comprehension: 19)

Block Design: 19

Matrix Reasoning; 18

Visual Puzzles: 19

(Figure Weights: 19)

(Picture Completion: 19)

Digit Span: 19

Arithmetic Reasoning: 19

(Letter-Number Sequencing: 19)

Symbol Search: 19

Coding: 18

(Cancellation: 19)

Now the subtests in brackets are supplementary tests, which are not supposed to be used to calculate the full-scale IQ unless one of the other subtests gets “spoiled” or is deemed inappropriate for that subject a priori, however since he took all 15 subtests, I am going to sum them all, and then prorate to estimate his sum of scaled score if only the 10 core subtests were given. The prorated sum is 187.3, remarkably close to the 186 he actually obtained on the 10 core subtests.

Prorating works!

Unfortunately, the WAIS-IV assigns all sum of scaled scores of 181 or higher, an IQ of 160. however we can estimate, from the roughly linear relationship between sum of scaled scores and IQ, that he is above 160.

For example:

sum of scaled scores IQ

10 40

33 55

55 70

79 85

100 100

122 115

141 130

162 145

182 160

From here we can deduce that full-scale IQ = 0.697057(sum of scaled scores) + 31.533486.

Plugging in “Jesse Watters’s” prorated sum of scaled scores of 187.3 into this formula gives a full-scale IQ of 162, however even this might be an underestimate, because look at his scaled scores, when listed from lowest to highest:

17,18,18,19,19,19,19,19,19,19,19,19,19,19,19

Notice how his lowest scaled scored (17) is below his median scaled score (19), but his highest scaled score (19) is equal to his median scaled score (19). That’s not a symmetrical distribution of scaled scores, but one that is truncated by the fact that the WAIS-IV does not give scaled scores beyond 19. Now if I knew “Jesse Watters’s” raw scores and age, I might be able to extrapolate some of his scaled scores beyond 19, but without that information, all I can do is calculate that a scaled score of 17 is at the 7th percentile of Jesse’s distribution of scaled scores (normalized Z = -1.5) , and that a scaled score of 18 is at the 20th percentile of his distribution (normalized Z = -0.87). **[NOTE: these Z scores are with reference to Jesse’s other scaled scores, not with reference to other people]**

Assuming his distribution of scaled scores would have been Gaussian had the artificial ceiling of 19 not been imposed on each subtest, we can extrapolate linearly from those two Z scores to guess that a Z score of 0 in his distribution of scores (the median score) would have been 19.385. Since the median score (50 percentile) is the average score in a normal distribution, and since the sum of scaled scores is just the average scaled score multiplied by the number of scaled scores, we can guess that if not for the artificial ceiling, Jesse’s sum of 10 scaled scores (actually he has 15, but we will prorate) would be:

Sum of scaled scores = (Median scaled score)(10)

Sum of scaled scores = (19.385)(10)

Sum of scaled scores = 194

Now converting sum of scaled scores to full-scale IQ using the formula I suggested above:

full-scale IQ = 0.697057(sum of scaled scores) + 31.533486

full-scale IQ = 0.697057(194) + 31.533486

full-scale IQ = 167 (U.S. norms)

If his self-reported scores are true, that would make him almost certainly the smartest person to ever post on this blog, or any other blog you frequently visit. Because only one in 251,515, Americans have a deviation IQ of 167+.

An IQ of 167 is 4.47 standard deviations above the U.S. mean. To put that in perspective, the average American young adult (men and women combined) is about 5’7″ with a standard deviation of about 4 inches. Thus being 4.47 standard deviations above average in height (the vertical equivalent of a 167 IQ) would be a height of 7’1″!

I imagine some readers might object to me calculating his sum of scaled scores on a theoretically ceiling-less WAIS-IV and then applying a formula that equates summed scaled scores to IQ on the actual WAIS-IV (which does have subtest ceilings), however because that formula is based on a linear relationship across the full range of WAIS-IV scores (the vast majority of which are unaffected by ceiling bumping) it’s unlikely to make much if any difference.

But I’m just an amateur so don’t take my calculations too seriously!

And “Jesse Watters” is just a pseudonymous commenter. His scores have not been verified.

It should also be noted that although the Wechsler scales are probably the most accurate IQ tests in existence, not even they correlate perfectly with the putative general mental ability (the famous g factor) or mental ability in general, so anyone who scores this freakishly high, likely got a bit lucky, either in not making mistakes, or in the selection of talents the test sampled. He should not be surprised if he regresses to the mean on other standardized tests, especially low quality ones.

**[Update March 5, 2016: The WAIS-IV was normed in 2006, a decade ago, so depending on how recently “Jesse Watters” was tested, he might have to deduct as much as 3 IQ points from his full-scale IQ since old norms inflate IQs at a rate of 0.3 points per year. Of course we don’t know if the Flynn effect has still be in full force in the last decade, and because the WAIS-IV expresses IQs in U.S. norms, instead of U.S. white norms, as the original Wechsler scales did, it’s even possible that environmental gains in IQ, have been negated by demographic shifts]**

**[Update March 16, 2020: I am grateful to commenter A Very Purple & Skeptical Entity for pointing out a couple math errors that I have just now corrected] **

Deeru

said:Do each of the four categories (verbal, perceptual etc.) also have ceilings with legroom? If someone had all 19s in one category, but not in the rest, what can be done, if anything, to estimate the full iq more precisely?

pumpkinperson

said:I would just take all the subtests, line them up from lowest to highest and find the median. If the median subtest is lower than the mean subtest, it implies that the mean is being supressed by ceiling bumping (that is the 19s could actually be higher than 19 if the test was harder)

If the mean is supressed by ceiling bumping, I would determine the sum of scaled scores by multiplying the median by 10 to get the sum of scaled scores, instead of the actual sum of 10 scaled scores (which is equivalent to the mean scaled score multiplied by 10)

I couldn’t do this simple method in Jesse Watters’s case, because he had so many 19s that even the median was hitting the ceiling

Jesse Watters

said:Thanks for the analysis, Pumpkin. If I remember correctly from a particular Quora answer, the WAIS IV norms were last updated in 2012. In addition, I’ve read studies stating that the Flynn effect is non-negligible in the high-IQ threshold, which means that I wouldn’t necessarily have to deduct points off of my FSIQ. I’m not sure how much of a difference these raw scores will make in my FSIQ calculation, but here are my raw scores for the subtests on which I hit the ceiling (for your reference, I’m 18 years old):

Similarities: 36

Information: 26

Comprehension: 36

Block Design: 66

Visual Puzzles: 26

Figure Weights: 27

Picture Completion: 24

Digit Span: 46

Arithmetic: 22

Letter-Number Sequencing: 30

Symbol Search: 56

Cancellation: 72

Most of these subtests were very easy for me; if the subtests had higher ceilings, I would’ve definitely achieved higher subscores, particularly on the working memory and perceptual reasoning subtests. I felt I had to put in more mental effort for the verbal and processing speed tasks, so I am dubious as to whether I would’ve scored higher on those subtests.

ruhkukah

said:Those scores are incredible! You’ve really been blessed by the WAIS gods!!

Assuming these scores are true, I hope you’re putting your intellect to good use. Are you a researcher in any important fields? Any published works? I know you’re only 18, but I can only foresee you doing important things.

Jesse Watters

said:From a previous post:

“I won’t give too many specific details, but I’m currently pursuing a B.S./M.S. in mathematics through an accelerated program. My interests among many others, include politics/government, mathematics, HBD, psychology, post-WWII American history, astronomy/space exploration, sports (basketball, baseball, track and field), philosophy, crime, and cinematography. Most of the time, my interests hold my attention captive in lieu of my studies, though I don’t have trouble getting respectable grades in my classes. Once I graduate, I plan to pursue a J.D. at a prestigious university, and after that, I’ll probably apply for a position at a prominent think tank.”

pumpkinperson

said:It looks like you not only hit the scaled score ceiling, but the raw score ceiling too. I will check to see if I can squeeze a bit more ceiling out of those tests.

The WAIS-IV was published in 2008 and normed in 2006 according to James Flynn. I believe they only renorm the test when they are creating a new version (i.e. WAIS-V or when they are norming the test in another country) so what you recall reading on Quora doesn’t make sense to me, but perhaps I’m missing something. Or maybe the person on Quora was thinking about the Canadian norming of the WAIS-IV, which shouldn’t apply to you unless you were tested in Canada

There are conflicting reports about the Flynn effect at the high end.

Jesse Watters

said:See: https://www.quora.com/IQ-Testing/Is-there-any-calibration-over-time-for-standard-IQ-tests

pumpkinperson

said:It doesn’t seem to say or imply that the WAIS-IV was updated in 2012.

Thomega

said:I believe that a scaled score of 18 on the matrix reasoning subtest is the ceiling for those below a certain age (much older than 18). Also:

What are the vocabulary words that you flubbed? What type of think tank would you like to be a part of?

pumpkinperson

said:I believe that a scaled score of 18 on the matrix reasoning subtest is the ceiling for those below a certain age (much older than 18).Correct

Also:What are the vocabulary words that you flubbed?

I was wondering that too but hopefully he will not answer, because mentioning specific items on a public blog could compromise the test.

pumpkinperson

said:The most informative raw score is the 30 you obtained in letter-number sequencing. I will soon do a quick post discussing the implications.

JJJJ Smith

said:Can I ask you why you decided to use the name “Jesse waters”? Jesse waters is of course Bill O’reilly’s obnoxious sidekick who likes to ambush interview people.

Jesse Watters

said:BTW Pumpkin, I just found this; hopefully, it’ll be useful for you in the future:

I’d suspect that the raw score necessary for a FSIQ of 160 on the WAIS is less than that on the WISC, since most adults become specialized in specific fields, and thus correlations between different subtests become slightly lower.

pumpkinperson

said:BTW Pumpkin, I just found this; hopefully, it’ll be useful for you in the future:Thanks for the link!

I’d suspect that the raw score necessary for a FSIQ of 160 on the WAIS is less than that on the WISC, since most adults become specialized in specific fields, and thus correlations between different subtests become slightly lower.That’s a very interesting theoretical point. Ideally, these subtests are supposed to be measuring innate ability, uninfluenced by what you choose to specialize in, but if in fact the correlation decreases in adulthood, it would be a way of empirically showing the influence of training.

drew

said:What is your take on Jeremy Cahill’s IQ? He’s a UMass Linguistics major who claims to have hit the ceiling on each subtest of the WAIS, even though he took it when he had just turned 15 (still WISC age). He also got a 47/48 on the Titan Test. He did the reddit AMA as a mega society member a few years ago.

pumpkinperson

said:Depends what he means by “hit the ceiling”

RuralRuski

said:he was clear – WAIS III. Scale scores ceiling on each subtest

RuralRuski

said:The guy was anonymous doing AMA. How did you get his name?

asldasdjli sasdasd

said:It looks like you have the wrong name. The guy on reddit specifically said he not only majoring in a STEM field(I don’t linguistics is considered STEM) but that he was triple majoring,

JJJJ Smith

said:What do you make of Evangelos Katsioulis claiming he got the following score on the Wais

“On Weschler Adult Intelligence Scale — Revised (2002): raw 196/200. Full Scale score IQ 150+. Verbal and Performance Scores extrapolated to an IQ 180+, sd 16 (by Dr Xavier Jouve).”

https://m.facebook.com/Highest.IQ/about?expand_all=1

How does the above score compare to this alleged score from this Jesse Waters?

pumpkinperson

said:He took the WAIS-R in 2002? The norms by then were over two decades obsolete so I would need to deduct points for the Flynn effect, but more importantly, I would need to know approximately how old he was when he was tested because unlike its successors, the WAIS-R adjusted for age AFTER scaled scores were calculated, not before.

JJJJ Smith

said:Well he was born in born 19 January 1976,so he would have been about 26.

pumpkinperson

said:In the WAIS-R standardization sample, Americans aged 25-34 had a mean sum of scaled scores of 111.31 (SD = 25.27). So a sum of scaled scores of 196 would be +3.35 SD, or IQ 150 (U.S. norms). But because the WAIS-R was normed 24 years before 2002, I would deduct 7 points for the Flynn effect, which would reduce the score to 143 (U.S. norms) or 141 (white norms).

pumpkinperson

said:But in fairness, scores that close to the ceiling are pretty meaningless. It might be possible to extrapolate a higher sum of scaled scores if I knew the individual subtest scores, but the sum of subtest scores taken at face value equates to an IQ in the lower 140s.

JJJJ Smith

said:HMMM. I wonder how Dr Xavier Jouve “extrapolated to an IQ 180” then?

JJJJ Smith

said:” , AMERICANS aged 25-34 had a mean sum of scaled scores of 111.31 (SD = 25.27).”

Oh that might explains the question of how Dr Xavier Jouve “extrapolated to an IQ 180”. Evangelos Katsioulis is Greek not AN American so those Norms wouldn’t have been used with him right? But it doesn’t seem like Greek norms would be much different than American and certainly not that be of a difference.

JS

said:In regards to cognitive reasoning among Europeans, Middle Easterners and South Asians, and how Caucasoids do better than East Asians on reasoning tests, I believe part of it or perhaps most of it, stems from East Asia being the most agricultural sound region in the world. It could also explain their lack of creativity, lower sociability with less extroversion. You are growing your crops, so you want to be left alone. Caucasians were nomadic longer than East Asians so they didn’t grow their own food, for longer periods, which requires higher verbal ability to depend on others for food in a bartering scheme, where you talk your way in trading your non perishable goods for other food. This is of course, would require reasoning skills, to avoid conflicts and close the deal successfully.

JS

said:Jews throughout their history were traders, bankers, mostly non-agricultural, and thus, they developed a high capacity in verbal skills.

Ylunov

said:I’m not sure the relationship between scaled scores and IQ is as facile as you present it here; my own scaled scores on the HAWIK-R, the WISC-R’s German version, administered to me in primary school a good two decades ago and using the same scoring system, were as follows:

Information: 13

Comprehension: 13

Arithmetic: 12

Similarities: 18

Vocabulary: 18

Coding: 9

Picture Completion: 9

Matrices: 12

Visual Puzzles: 8

Block Design: 9

Needless to say, a profile prodigiously slanted towards VIQ over PIQ. That merely as a side note, though; the score total (121) would translate, according to the table you present, translate to an IQ of just below 115. Yet this falls short of the IQ then assigned to me and which broadly tallies with the results of other tests I have taken over the years, which have produced ratings in the high 120s and low 130s. I suspect that adjustments are made to the scoring when there is a large gap between subscores (as in my case, amounting to no less than three σ between the highest and lowest scores), or that the divergence may arise out of considerations expressed in a few lines of regrettably largely illegible drawl the psychologist scribbled on the bottom of the evaluation form I have before me.

I have also been diagnosed with ADHD (before the differentiation of “primarily inattentive” and “primarily hyperactive” became prominent), so if the subtests are administered in the order in which they are presented on the evaluation form (verbal first, performance after), the consideration reflected in those lines may be that the scores of later tests would have been adversely affected by my declining attention.

In either case, it appears that the conversion is not linear. Nor, even, from what I have heard, do equal scores always result in the assignment of the same IQ, but this is a topic for another day and which I am only vaguely informed about.

illuminaticatblog

said:Similarities: 15

Vocabulary: 15

Information: 15

Block Design: 15

Matrix Reasoning; 15

Visual Puzzles: 15

Digit Span: 15

Arithmetic Reasoning: 15

Symbol Search: 15

Coding: 15

If all ten scaled scores were 15 (IQ 125) then:

136 = 0.697057(150) + 31.533486.

If all ten scaled scores were 13 (IQ 115) then:

122 = 0.697057(130) + 31.533486.

my raw score total is 120

115 = 0.697057(120) + 31.533486.

RuralRuski

said:using the method described here,

https://assessingpsyche.wordpress.com/2012/01/13/cant-decide-which-iq-is-best-make-a-composite-iq-score/

for all 15 subtests battery, having found first the average correlation btwn 10 subtests 0n the level 0f his performance, I have come to FSIQ 167.42… Very close…I just dont remember if I already posted it somewhere, sorry))

RuralRuski

said:It sould be a bit higher, because correlation between 15 subtests is a bit lower (very likely)

RuralRuski

said:Evangelos Katsioulis ( together with some French) toppedt t he ranking of Cerebrals High Iq society contest in 2009 (still available on their site as hight range IQ test) Somethingl latter the author published an article – see here. http://www.cerebrals.org/tests/cpic/pdf/2009_FSIQ.pdf

Since his raw score was 93 and his age was 33 (meaning no correction for age needed) , we can find the IQ score ( given in the table as confidence interval, exect number , according to what I know is, probably,164)

George

said:I scored 141 on the WAIS-IV back in 2015 when I was 20. I scored highest on Similarities (99th%) in the verbal tests, Block Design/Matrix Reasoning (98th%) on the perceptual tests, Digit Span (99.9th%) on the working memory tests, and Coding (99.6th%) on the processing speed tests.

This was very close to my score on the Test of General Reasoning Ability by Cecil Reynolds. This tests produces one score called the GRI or general reasoning index. It is similar to IQ. I scored 140 (99.6th%). My raw score was 58/60. 147 is the max for 22-year-olds.

I have ADHD, so it’s a marvel that my WAIS IV CPI (working memory + processing speed) is so high.

pumpkinperson

said:Yes, I know on my WISC-R results, digit span was described as a test of attention span, though I think it’s better thought of as a test of attentional capacity. I don’t know whether ADD is primarily a deficit in the former or the latter. I think of attention span as more of a personality trait, while attentional capacity (the amount of attention you have to pay) as a cognitive ability.

George

said:The distinction you make is one I’ve considered many times. The psychology doctoral student who evaluated me was stumped after I showed my WAIS-IV results and asked if it changes what she feels the diagnosis should be.

The ADHD traits that I display make me fear that I’ll end up wasting the potential that I have. Of course, I’m in school (and entering a top 25 grad school program) and have a decent work history through internships. But these accomplishments can be achieved with lower cognitive ability. There are times when I produce show-off-able intellectual output, but those come in spurts. I’m definitely not a 40-hour-per-week production facility.I do solve a lot of difficult puzzles (such as those displayed in online high-range IQ tests), however.

Recently, I had a professor come up to me and say that I show pretty high level of reasoning ability in class discussions and case study responses.She’s pulled me aside many times. She urges me to find something that I’m passionate about so that I can be motivated to extend. Maybe she’s a little concerned about my motivation because my attendance is unreliable.

Do you have any thoughts on what high-ability individuals should do? Or whether this is even a question to consider at all?

Teffec P.

said:I too took the WAIS-IV back in 2015 when I was 20 years old.

My scores:

Similarities, Vocabulary, information (99.9%)

Comprehension (99%)

Block Design, Picture Completion (99.9%)

Matrix Reasoning (98%)

Visual Puzzles (84%)

Arithmetic, Digit Span (99.9%)

Symbol Search (98%)

Coding (50%)

I have ADD also, and I was not on my meds when I took the test. That possibly contributed to my relatively low PSI.

Warren Dew

said:Just for your information, several recent studies have indicated that the Flynn effect has reversed in birth cohorts since about 1980, and is now proceeding in the opposite direction at about the same speed as before.

By your calculations, there are 1000 people in the US with an IQ over 168. I bet they disproportionately comment on blogs since they are more likely to have something to add. I would not be surprised to find one commenting here.

Also, height of men and women combined is not a normal distribution since the binary male/female variable has an outsize contribution. +4.5 SD on male height is probably closer to the typical NBA height of 6’8″ or so.

pumpkinperson

said:I have heard of Flynn effect reversals but not in the U.S., yet.

I’m doing private research showing the Flynn effect has been blown way out of proportion & was much smaller than everyone thinks.

Sex-combined distributions can be normally distributed if the sex difference is less than 2 SD.

Thinking Mouse

said:“I’m doing private research showing the Flynn effect has been blown way out of proportion & was much smaller than everyone thinks.”

Cool, i like the posts about things adjacent to flynn.

Rahul

said:@Thinking Mouse- Just to clear up the stuff happening in Robert Lindsay’s blog sometime ago, I was trying to say that you’re extremely intelligent, and that your writing played with abstractions brilliantly.

Thinking Mouse

said:Rahul,

Thats nice 🙂 Thanks

Yeah i forgot that aspect of the dunning kruger effect lol.

I have noticed that an large issue with getting the correct mental stimulation now is not only my crystalized intelligence (especially in form of or my philosophical framework, or as Anon regular would say; my accepted models of “chaining together of bivalent causial statements”) but my time allocation and physical health. So to sustain an active intelectual life id have to increase either the complexity (change my environment) or brute prefrontal-cortex effort in life, one alternative being possibly inacessable. But often they complement eachoder to an certain degree, so fixing the environment is the only way i can see if ill preservere. Though maybe im just greedy and need to pick my priorities. I also think i should someday leave some time to study math only, the school curriculum is too slow for me. Id say my strong point is memorization and verbalizing formal stuff, since i remember details and especially the “propositional logic” in my language. Im also an big fan of math, its so pure :). Even though im not the most creative mathematical thinker. But ive also never excersized it to an large degree, so well see how good i really am, but for the moment it seems like im better at perceving proofs than thinking divergently to come to novell conclusions. The thing with the reading social sciences is that i never know when it will end, so i may very well leave in some years, as other obligations are being ignored in the moment and the opportunity cost looking ridicolous.

I kinda regrett writing those right-wing speculations as robert is easily agitated when it comes to politics (which i find fun). I could have spent that time talking about leftism like he did. The thing is that i never extrapolated.

What did you find impressive?

Where did your interrest in IQ begin?

Bubbabubba

said:Where can i find the WAIS-IV norms, i have raw scores how do i convert to scaled score?

Rahul

said:The formula: 2/3*(scaled score-100)+100

Rahul

said:My bad, that formula is for calculating IQ. Here’s where you get your raw to scaled conversions from- https://www.researchgate.net/publication/224707559_Variability_in_Wechsler_Adult_Intelligence_Scale-IV_Subtest_Performance_Across_Age

By the way, finding the correct scores is a pain in the ass.

pumpkinperson

said:Banned

A Very Purple & Skeptical Entity

said:I must say, pumpkinperson, watching you for several years and being taught statistics by reading your posts, I am disappointed. First of all, your proration is inflating his scores heavily, second of all, you’ve assigned the wrong rarities to his scores:

>17,18,18,19,19,19,19,19,19,19,19,19,19,19,19

>Notice how his lowest scaled scored (17) is below his median scaled score (19), but

>his highest scaled score (19) is equal to his median scaled score (19). That’s not a

>symmetrical distribution of scaled scores, but one that is truncated by the fact that the

>WAIS-IV does not give scaled scores beyond 19. Now if I knew “Jesse Watters’s” raw

>scores and age, I might be able to extrapolate some of his scaled scores beyond 19,

>but without that information, all I can do is calculate that a scaled score of 17 is at the

>3.33 percentile of Jesse’s distribution of scaled scores (normalized Z = -1.83) , and

>that a scaled score of 18 is at the 13.333 percentile of his distribution (normalized Z =

>-1.13). [NOTE: these Z scores are with reference to Jesse’s other scaled scores, not

>with reference to other people]

Oh, really? Because unless I’m as blind as I proclaim you are, even with your benevolently inflated “proration”, the scores frequency is 3/15 for 18 (17 counts too, because statistically, it belongs to the group of values 18 or lower) and 1/15 for 17. Which, if we do the maths, we get 20th percentile and 7th percentile respectively. If we translated that to a normalized Z score we’d then get -0.87 and -1.47. By subtracting the two from each other, we get that 1 point is .6 repeated of an SD of the variance within his score, meaning 1 SD is 1.5 points. Which, if we apply again to his lowered z-score, we get his mean is actually 19.3, definitely not as high as you suggested and definitely not what he’s getting anyways, because you inflated his z-score through the so called “proration”. I don’t doubt people as smart exist, I do however doubt that they know it about themselves and even if so, that they tell others. And if that is the case, there is still the case of their tremendous rarity. Only 13 000 people in the world score that high. I am highly skeptical of all scores beyond 150, let alone 160. Please, raise your standards!

pumpkinperson

said:I’m away from home but will double check your math within the next few days. Check back

pumpkinperson

said:17 = 1 out of 15 = 6.67 percentile = -1.5 SD

18 = 3 out of 15 = 20 percentile = -0.87 SD

Thus a difference of 1 = 0.63 SD, which means 1.59 = 1 SD.

So if 17 is 1.5 SD below the mean, the mean should be 17 + 1.5(1.59) = 19.385 (similar to what you get).

Thanks for discovering the error. When I get a chance I will correct the article and add a disclaimer noting the update.