If we exclude the 10 known fake votes in the poll of self-reported PATMA scores, 145 people have thus far obtained the following scores:
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,4,4,3
If you copy and paste this data into this wonderful standard deviation calculator, you get a mean of 7.9 and an SD of 1.4
This distribution forms a gorgeous bell curve though it’s truncated because the test is too easy for about the top tenth of my readership:
On a scale where Nothern American whites average 100 with an standard deviation of 15, my readers are known to average about 126 with an SD around 16. Given this info, there are two ways to convert PATMA scores to IQ.
Method 1: Assign each PATMA score its normalized Z score based on its percentile rank among blog readers and multiply said Z score by 16 and add 126.
Method 2: Calculate the actual Z score of each PATMA score (among blog readers) using the observed mean and SD of PATMA scores (7.9 and 1.4 respectively) and multiply said Z score by 16 and add 126.
| PATMA score | frequency among PP readers | percentile rank among PP readers | IQ (method 1) | IQ (method 2) |
| 10 | 19 | 93.45 | 150 | 150 |
| 9 | 34 | 75.17 | 137 | 139 |
| 8 | 37 | 50.69 | 126 | 127 |
| 7 | 33 | 26.6 | 116 | 116 |
| 6 | 16 | 9.66 | 105 | 104 |
| 5 | 3 | 3.08 | 96 | 93 |
| 4 | 2 | 1.38 | 91 | 81 |
| 3 | 1 | 0.69 | 87 | 70 |
| 2 | 0 | 59 | ||
| 1 | 0 | 47 | ||
| 0 | 0 | 36 |
Method 1 is clearly better. Are any of my readers intelligent enough to understand why?
Pumpkin Person 
I would say this :
You ll get [0-5] only if you have less than 100 IQ and only 5% of your readers are in this category.
So it’s a worse idea to use this small group of 5% of your readers actual scores to scale Patma than to do it the other way around.
That’s why with method 2 you get artificially low IQ for
3-4 because you force a meaningless flat curve Into a perfect symmetrical Gaussian you re test wasn’t able to measure.
If you transform the first 2 easy questions into 2 very difficult questions (One level or two above the last one) the two methods may be equivalent with a 96-156 range with an average of 126.
You may have 3 perfect 12 scorers, 2 at 11 and 5 at 10. It’s always a bit more crowded at the roof than just one step under in most clever tests. Like in Math Olympiad there are always 2/3 perfect 42 scores but less in the 39-40-41 scores. The same for perfect SAT compared to 1580-1590.
Would you explain to me how to do the last two questions? No one seems willing
I mean, the first eight are things I would expect any stem major worth his salt to do nite or less instantaneously. The last two I still don’t understand. I must be missing something.
The last 2 might be unfair to non-readers of this blog. I’m not sure if anyone who doesn’t regularly read my blog was able to solve them. My blog might be an example of what Jensen called “teaching to the test”.
I solved them without reading your blog regularly, have no relevant training in statistics, and don’t really understand the logic in a formal sense. I still got them right by reasoning out various approaches and choosing the one I thought was most sensible.
I didn’t read this blog regularly before taking the PATMA, have no relevant statistical knowledge, and still am not certain of the mathematical underpinning of the questions. I nonetheless found the intended, and hopefully correct, answers to questions 9 and 10 by reasoning out various approaches and choosing the ones I thought were most sensible.
Interesting. I’d be curious to see your reasoning.
Am I allowed to post it in the comments, or do I need to e-mail it to you?
you can post in the comments. just put a warning so that people who may still want to take the PATMA can delay reading your explanations.
Alright, then. WARNING for commenters: I’m going to explain my solutions to PATMA problems 9 and 10.
.
.
.
.
.
.
.
.
.
.
.
PATMA 9: “If the tallest kid in class in class is six inches taller and 25 pounds heavier than average, and the heaviest kid in class is 50 pounds heavier than average, how many inches taller than average should we expect him to be?”
Honestly, I can’t provide a coherent explanation of my reasoning for this question, not even an intuitive one lacking mathematical formalism. The most I can say is that I felt my instincts from algebra kick in, but backwards: double one side of the equation, and halve the other to balance it out.
PATMA 10: “If the tallest kid in class is 12 inches taller than the shortest kid in class, and if height, practice, speed and coordination are all equally important in basketball, how many inches taller should we expect the best basketball player in class to be compared to the worst?”
This was the only PATMA problem where I hesitated on my answer. I probably spent more time on this problem than I did on the previous nine combined.
My intuitive reasoning went roughly as follows:
If the tallest kid is 12 inches taller than the shortest kid, there are 12 inches of spread for basketball players’ height to vary, assuming that they all play basketball, which I figured was implicit to the context of the question.
If height, practice, speed and coordination are all equally important in basketball, then they should each account for 25% of the variance within that spread.
We don’t know anything about how practice, speed, and coordination, which collectively account for 75% of the variance in basketball skill, correlate with height, so we’ll assume that those four factors are perfectly orthogonal to each other. Therefore, the expect value of height will be exactly at the midpoint of its range, implying a “baseline” height of [(12-0)]/2 = 6 inches above the shortest kid in the class. (This is the step I was least confident about.)
Combining the previous two paragraphs, we expect that the worst basketball player would have -(12 * 0.25) = -3 inches of height relative to the baseline of 6 inches, and the best basketball player would have +(12 * 0.25) = +3 inches relative to the baseline. +3 – (-3) = 3 + 3 = 6, so we expect the best basketball player to be 6 inches taller than the shortest.
I hope that explanation makes sense. It makes sense to ME, but I recall that XKCD comic about communication being a one-party activity…
Fascinating how you solved those with no statistical knowledge! Extremely impressive!
expected* value
Thanks, I guess, but I feel compelled to object to calling a score “impressive.” A psychometric test is only supposed to give an objective result, not a value judgment. To paraphrase Paul Cooijmans: Imagine if you said to low scorers, “This score is terrible, you idiot!” That’s a two-way street, in my view.
Son when I give a complement, smart people take it.
All (x-90) degrees of it.
My approach was basically the same as Ganzir’s for question 10, which means I must have gotten number 9 wrong.
yeah, mine was pretty much Ganzir’s approach (but I got it after I submitted the first run through). Pumpkin, what was the logic you had in mind? The answer just felt intuitive, I can’t scope out the logic behind it.
I wonder if Mugabe realizes that tesla is more than just a car company??
I’ll see the cucks and boomers on r/wallstreetbets thinking tesla is overvalued but they don’t realize it’s a fucking tech company.
Look im not the dude who just dickrides musk, in fact I hate him and his whole fake libertarian persona, but he DOES provide.
The past week I’ve made 50,000 dollars on tesla calls alone. Imagine if I had just went YOLO.
But I’m smarter than that.
https://www.reuters.com/article/us-usa-stocks-tesla/teslas-market-value-zooms-past-that-of-gm-and-ford-combined-idUSKBN1Z72MU
Gestalt 121
PATMA 104
what is my IQ now pumpkin?
Gestalt 121
PATMA 105 (using method 1)
Composite IQ 116
Puppys IQ tests are horrible
You still stand by that distribution for your readers? You think its plausible 12% of your readers or whatever have the same IQ or better than Richard Feynman. [redacted by pp, aug 26, 2020]
yeah I do. If you look just at the 10 most prolific commenters we have Mug of Pee (who claims to have scored 1560 on the old SAT and scored perfect on all three sections of the GRE) and Bruno who scored over 160 on some Mensa verbal test. Blogs about IQ are going to attract a lot of high IQ people. If I blogged about height, 12% of my readers might be over 6’7″. If I blogged about anorexia, 12% of my readers might be under 100 lbs.
I refuse to believe that the distribution for your commenters, despite their frequent conspicuous illiteracy and pervasive lack of understanding, is centered at something like the 95th percentile of the general population. The average person can’t really be that dumb, can they? Can they? How would we have ever crawled out of the caves?
Well that’s probably because the ability at taking IQ tests isn’t equivalent to intelligence.
An interesting aspect is that if the model is OK, you would have just 1/3 of your readers with higher IQ than you and 2/3 under. It could be something true for most writers.
Meaning a 90 IQ would have 1/3 above 90 IQ and the average IQ of readers would be 83IQ, meaning the author would recruit in the bottom fourth.
A 150 IQ person would have an average readership of 143IQ, meaning he would recruit into the 0,5% if he writes for himself (things at the maximum level of his/her understanding and intestests).
In a country of 320M people, if you can satisfy yourself with even 1M public target to get 50K readers, 150 IQ would be the absolute maximum iQ in wich a professional writer could throw himself heart and soul and still get some meaningful wide readership …
So you would put money on 12% of your readers winning the noble prize?
Philo you are oblivious of the fact that a necessary condition is not a sufficient condition (by far).
I believe it too. Compare the comments here to the comments on Twitter—or even the editors’ comments on Wikipedia. They’re in a completely different league.
Sailer still has the smartest commenters though.
The comments on science forums I sometimes lurk in are miles ahead of these.
Miles ahead in specialized science knowledge but probably not much ahead in intelligence
I’m not making that observation based on whatever science they’re knowledgeable in.
It’s based on their ability to reason in general, which I notice is very sharp. Most people on this blog make ignorant statements on blind intuition and outright refuse to consider alternate hypotheses.
To me, those are unintelligent habits.
I’d actually be surprised if anyone other than Mugabe, Me, and LOADED have high general knowledge.
the guy is fucking superman.
but he’s OLD.
Intelligent enough to understand why, you say? I don’t even understand why the answers to the last to PATMA questions are what they are, and I still got them right! Trust your gut indeed.
You sound demented. You think youre brighter than the commenters on here when you cant even spell “two” properly?
No thats just a ridiculous thing to make fun of but my point stands…some of our commenters here are highly successful irl and have done absolutely amazing things on tests valid measurements of intellectual achievements if you take it at face value! Can you say you emulate any of this behavior or performance?
Have you accomplished any of that? Just one 10 on the PATMA aint gunna save you Ganzir.
Also for curiosity purposes where are you from? Your name sounds Persian, who are exceptionally bright in mathematics but nothing else lol. Though i digress from that since it is a broad generalization. The point I wanna make is that theyre extremely nationalistic or ethnocentric (more ethnocentric like all middle easterners) and will always believe they create the smartest individuals.
Something to keep in mind….
Yes, okay, I hit the wrong button on my keyboard. Tu quoque enters into full force here, if you think that “youre” free from the occasional fatfinger yourself.
I’m from Florida and have no Middle Eastern descent as far as I know.
Just looked up what Ganzir means its the ancient Mesopotamian underworld. Neat. But still doesnt mean you can criticize anybodys intellectual accomplishments on here even if you this is a judgment of sorts for all of us.
I named myself after the Global Occult Coalition fortress in SCP-5000.
Method 1 is clearly better. Are any of my readers intelligent enough to understand why?</em?
Is it because method 1 uses equipercentile equating, which is more accurate than assuming a perfect correlation bw PATMA z-scores and IQ?
In both methods there’s a perfect correlation assuming perfect correlation means identical rank ordering of scores
Curve is censored, not truncated.
Also, is method 1 better since standard deviations for PATMAS distribution don’t correspond to correct percentiles (because curve has funny shape)? So being 1 SD above average, for instance, doesn’t actually imply having a score higher than ~84% of people.
But why might the curve have a funny shape?
Data is censored, as mentioned. Probably there are other effects, but censoring is most noticeable.
There’s a more fundamental reason
Method 1 Is better because Method 2 assumes PATMA scores to have the same distribution as IQ scores (i.e. distribution to have the same shape, that being a normal distribution).
Are you asking why PATMA scores don’t have the same relative distribution?
Yes
Bad test-construction and lack of independence in correctly answering a question?
Should clarify that a simple correlation between answers wouldn’t be a problem (and is necessary for the test to be non-random), so problem is not lack of independence exactly. But more complicated relationship would still cause problems.
What I mean is that if correlation between IQ and PATMA was linear, PATMA, issue with censoring aside, would have approximately the same distribution, and method 2 would work. But this might not be the case.
To have an average of 126, you just have to let people auto-select themselves at 1 in 12. That’s not unbelievable if your blog has articles on intelligence.
Mensa is believed to be at 140 (Jensen comparing Mensa crowd to Berkeley students) on average despite having a threshold officially at 132 that in fact is around 125 because people can select their best score among a plurality. Mensa would be much higher than here despite people being probably less interested in intellectual matters.
I agree that NewYorker, Unz and TheEconomist readership must be at a slightly higher level than here. Probably by 5 to 10 points for average regular readers.
Although I’m arbitrarily seizing for myself an opportunity to inform the audience of this to the possible benefit of my reputation, since the topic of head size is occasionally discussed on this blog, I thought I should mention that my head circumference tops 25″. I’m a 5’11” white male, for reference.
Ok so youre a 5’11” white male who has head circumference over 25”…do you really think youre smarter than Mug in crystallized knowledge Bruno in math, Pill in analytical thought, Anime in curiosity, me in verbosity, MeLo in critical thought, and RR in attention to detail. Not to mention Pumpkin is a man who has all those abilities!
No I dont think you do so dont compared yourself on here to the best and brightest!
I don’t know who the majority of those people are, but I can confidently say “probably yes to at least 3/8.” Unilaterally, though, I won’t compared myself to them.
What is your head length and width?
I recently had the opportunity to re-measure my head with a more flexible tape measure than the one I previously used, and arrived at the following measurements:
Head circumference: 25.7″
Width: ~9″
Length: ~10″
Height: ~10.5″
I used the “approximately” marks in front of the Width/Length/Height measurements because I had difficulty handling the tape measure with the adeptness required for suitable precision. I might try again later with a measurement apparatus I can better manipulate.
The basic oval formula predicts a head circumference of 75.9 cm/29.88 inches with those values. And the formula actually under-predicts the average head circumference when average head length and width values are used as an input both in the case of the US Army records and a couple of recent-ish studies of Chinese heads.
For such a discrepancy to exist, either your head is extremely bumpy/ill filled or the measurements are wrong. Try and get someone to help you out like this: http://windrosearmoury.com/zencart/index.php?main_page=page&id=5
Calipers would be even better.
My head appears to be pretty much normally shaped, so the W/L/H measurements are probably faulty towards the high end. I’ll see what I can do to get better dimensional measurements.
Pumpkin, on this one study, it says the discrepancy between similarities and picture concepts for bilinguals is 5 points, does that seem accurate?
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5221650/
Pumpkin, by how much would a practice effect be increased on tests like the PATMA if you were to remember the questions?
Pumpkin, somehow I got 9 and 10 right- I didn’t understand the how the logic worked, but the logic just made sense, as in it felt right intuitively, but I still can’t explain why the logic works- if this is the case, is it fair to add the cube question to my total score?
It was also my first attempt after the initial attempt, so I didn’t just do trial and error, the first time I applied the logic it was correct. What does this mean?
So Pumpkin, since I got 3 of the questions afterwards, would by score be underestimated by around 5 points right?
I also did these 10 days after I took it the first time, I really didn’t think about the individual questions.
Pumpkin, on tests with low practice effects, would an average of all the attempts of the test work. So, if you took the Patma 3 times, anc you get scores 110, 120, and 130, could you average them, and your real score would be 120?
But if your scores keep going up then there’s obviously is some kind of learning effect in your case.
oh shit, did not think of that. but then, would everybody get the same learning effect. I got 6 of the answers the first time around, and then later on I figured out all 10 of em- what is the extent of learning effect vs actual ability in this case?
Also, if you have a much larger increase than the average, wouldn’t there have to be some amount of ability not shown the first time. Like, on the SAT, there’s still a ceiling score for people, as in no matter how many times you do the SAT, you won’t get past a certain score.
Pumpkin, even with a learning effect on the PATMA, since it is a logic test with low practice effects, wouldnt it make sense that an average of the scores would measure actual ability, especially since each question is like 10 points away from the last?
Dude, if you keep getting a higher score after each time, it’s obvious it’s got something to do with practice. You’re learning from your previous experiences on the test to solve the questions which is quite literally what practice is. You know what to expect from the questions and you know when you got something incorrect so you understand that you have to do something else.
I’d say the first score is the only valid one really. This goes for almost all IQ tests
Yeah, but it’s a logic test which is untimed. I’d assume that if your score increases highly on a logic test, your logic ability is higher than the first attempt. It’s not like you can just practice logic. I could be completely wrong though.
Yeah no offense or anything but I do think you’re wrong. If you’ve actually been getting higher scores from each around, it’s obvious it’s more of you learning from your past experiences than just pure intelligence. The practice effect kinda seems obvious to me at least
Yeah, I mean, you are kinda right. Once the word cube popped into my head, I realized that I screwed that question up. My point was just that if your practice effect on a test with very low practice effect is that high, there must be some ability behind it. Obviously most of it is practice effect, but if you can understand the logic I feel there has to be some sort of ability. I could be completely wrong (wouldn’t be surprised either), I have zero data to back myself up.
I took the http://free.ultimaiq.net/numerus_basic.htm again- I did this a couple times some 10 months ago and got a 120, now I got a 128. This time though, I got the easier patterns quicker, which let me think about the harder patterns for longer. Would this be a practice effect, or is this just ability better shown?
I got a perfect score on that test. Although, to be fair, that took me more than the requested 2 tries. I believe I scored like 148 under the “proper test taking procedure.”
I would assume the practice effect on this to be very low, which would mean a huge score increase reflects some level of ability.
Just so this test and did it in a train trip. I checked answered one by one because I didn’t have any pen and didn’t want to lose time, but only once – I didn’t correct when it was false, and got 18 out of 20. I think 152. So as I still have a second try it should improve to 20 I guess in testing conditions . One is very easy and there were several answers and I have just checked it so 19. I don’t know the IQ because if don’t want to write again the 18 right answers. And there is still one I didn’t find.
I didn’t find the test able to discriminate that high because questions are very tricky for the last 10 but not in a clever way. It’s more guessing what trick was in a clever guys mind than a brilliant understanding. So when you find it, you don’t really experience having solved something interesting.
For example
1 10 110 1101 ???? … 10110
123 354 897 ??? …. 171615
5 10 20 35 ??? …. 55
2 4 12 ??? 72 …. 24
1/2 3/2 5/6 ???…… 11/30 (this one is quite childish)
77 49 36 18 ??? …. 8
11 32 54 78 ??? …. 916
123 451 ??? 512 … 234
The last thee are more difficult. I haven’t find the one with a prime number. But I have an idea of where it could go.
how accurate do you think it is for the lower end? It would be interesting if pumpkin polled us on how we did on this.
I don’t know. When I did the first answers (i don’t remember like 6/7) he said below 120. And then it iincreased quite rapidly to 152 for 18. So maybe by 3 or 4 IQ points for each additional answer.
I think the test is too tricky for normal <130 IQ but at the same time, too « childish play » above 145.
So I would say it’s a good test to know if you gifted with numbers (top 2%) or not but not able to evaluate much more .
But I am not an expert on test. Most test I got were from here 🙂
A good exercice would be trying to find the solution with the answer. That’s easier. And at the same time, it forces you to understand the numerical game.
thanks for answering man.
I heard some folks say it was accurate up to 130. It most definitely cannot discriminate in the high end. People get ridiculously high scores up there and it doesn’t match up. Even in the low end, it matches up more, but there isn’t much data.
So Bruno, what would me getting 126 on the Numerus Test mean? Does the test inflate my score or does it deflate it?
I’ll tell you the answers. I normally wouldn’t do this for a high-range test, but since it’s a free self-scored test, it shouldn’t be accepted for society admission anyway, so no real harm in it methinks.
SPOILER BLOCKING LINES BELOW…
.
.
.
.
.
.
.
AVERT YOUR EYES NOW IF YOU DON’T WANT TO SEE THE ANSWERS
.
.
.
.
.
.
.
.
.
.
.
18) 113 (just concatenating odd numbers)
19) 325 (I don’t even remember the logic for this one but I must have found it before because my browser suggested it for auto-complete)
20) 654 (concatenating the positive integer, except every odd-indexed group of three is backwards, so really it’s going: 123, 456, 789, 101112)
Hey Pumpkin, can you do a post about this test?
Ganzir,
altcucher has absurd hair, therefore he should be ignored.
“Dear Sir / Madam,
your raw score on Numerus Basic IQ test is 9/20.
Your estimated numerical IQ is 126, which is 1/24 rarity.”
I think it took me like 24 minutes to do this?
Don’t know if this is a good test or not but it falls in line with my results on the PATMA and other things.
It looks fine but I think some people would spend more time to get 2 or 3 more points. But maybe that’s part of the numerical IQ (Both crystallized Intelligence and mental engergy). For another try, spend more time and see if you go up …
126 here, 8/10 on the Patma which 8/10 gives a 126. For you they line up perfectly.
thanks to both commenters. Maybe I should have spent more time on it idk
Hey Ganzir, what did you think about this test?
Probably too easy, and norms at the high end are likely affected by people not doing their best since they have little motivation to score high.
I got an 8/10. I know I didn’t get the last one right but I don’t know the other one. The hose question was challenging for me personally so I think I got that wrong?
So I’m in the mid 120s? Interesting
Oh and I do believe that people on here are that smart like you said. This is a blog about IQ and I’m sure self-selection plays a very large role and affects the numbers quite a bit. Personally, I’d say 117-119 but yeah the people are intelligent (for the most part) and I’ve been following this blog for like 20 months…
Is 117-119 your assessment of the average for commenters on this blog? I could assess that to be accurate.
Where would you put me at just by reading my comments? Obviously it’s hard to gauge someone’s intelligence just from this one-dimensional process but I guess you can get a really good idea since youve consistently read this blog for 20 months, around the time I started commenting!
yeah I’d say the average IQ for the readers here is in the 117-119. I’ve seen some pretty interesting and thought-provoking stuff here posted by many of you guys. I also “use” Instagram, browse through Twitter sometimes and use other social media and I can safely say that we are far ahead of them. So yes, 117-119 is my assessment for the commenters/readers on this blog.
I’d say you’re in that ballpark too. You’ve got some interesting things to say. I have no background in psychology or anything though lol so I can’t really accurate estimate where you would stand intelligence-wise besides the fact that you are clearly above average in that department. 120 perhaps?
I agree with your analysis that people here are generally more thoughtful and intelligent than the general population. And I could see myself as being 120. I would say I am low 120s overall from a logical and verbal perspective but obviously have strengths and weaknesses in different things that skew subtests in different directions.
Anyways welcome to the commenting section! Good to have you!
Also, PP, please leave a link for the solutions to all of the questions that were on the PATMA test