No Such Thing As An Opinion!

My Ability 



This section was originally entitled "My IQ".   But I'm not a big fan of using that term, and I think many others aren't also.  "Capability" seems like a better choice.

Let me explain why I've even created a section explaining my capability.

It was not done with the intention to brag or seem superior to others.  Far from it, I'm one of the most down to earth people you'd ever meet.  (And I've also had more than my share of stumbling blocks). 

My site had originally mentioned that I placed 74th in the world on a measure of intelligence.  I didn't make the claim in order to brag, I made the claim as a marketing tool.  I felt that many readers would be curious to know the beliefs of someone with my ability!

There are hundreds of thousands of news sites out there, and I felt I needed a way to differentiate my site from others, in order to grab readers' attention.  Sure, my writing itself demonstrates my capability, but what good is that if the reader doesn't ever get to read my articles?  That's where the "74th place" marketing tool comes in.  It can motivate someone, who otherwise wouldn't have, to read my articles.

Furthermore, there are many writers who can claim to be capable, but fewer who can provide the test results.

The idea is that the claim will help attract the readers, and my writing will help retain the readers :)

I realize that some people are initially turned off by my mention of my 74th place ranking.  That's fair.  (Some of those people might be turned off enough to visit the site, to try to outsmart me!)  However, I would hope that they would be understanding after having read this explanation.

It all comes down to this:  Do the benefits of mentioning my capability outweigh the costs?  I definitely think they do.

After I initially mentioned my capability (then described as my IQ), some readers questioned the validity of my test results.  In order to respond to them, and in order to provide some interesting analysis in the meantime, I created this section.

So, here's the explanation of my capability:



These are the results from a widely taken test that appeared on Facebook.  (Please note that the test no longer appears on Facebook).  Notice that "World" and "Monthly" are highlighted.  This means these were the top scores in the world during the month previous (among the entire Facebook sample that had taken the test).

The score I earned while playing that day was 3,575, placing me 74th in the world (I've deleted the pictures, and my own name, for privacy reasons).


The top half of my screen is my overall profile to date. 3,692 is my highest score ever (this would have ranked me even higher than 74th had I earned that score that day).


When the test was available, if you logged into the test on Facebook, you can verify that only users have access to their own profiles-I wouldn't be able to access someone else's profile, making it more difficult for me to falsify this.


RELIABILITY OF MY SCORE


A few readers have claimed that my having placed 74th in the world on Facebook's test is not reliable. I will address this below.

First, I bet they didn't take a look at the test itself.


It is not one of those Facebook quizzes that asks you 10 questions and gives you a score between, say, 75 and 150.


The test has twelve subtests, four of which are used to compute your score (you can select the four or let the computer randomly choose the four).


This is what's on the test:


Each subtest has a 60 second time limit. Just like better known tests, it has a time limit, and the answers progress in difficulty. The more questions you answer correctly within the time limit, the higher your score.  You get points for a right answer, but also get points deducted for a wrong answer.  The tests are designed to measure answer accuracy and mental speed.


Recent research found that
mental speed is linked to intelligence.

Therefore, it reasons: The higher my score on the Facebook subtests, the faster my mental speed is likely to be.  And the faster my mental speed, the more capable I'm likely to be.


Therefore, even when looking at mental speed
alone (apart from simply measuring the accuracy of my answers), the twelve Facebook subtests are very likely to be an excellent measure of capability.

These are the twelve subtests:


1) A visual spatial test.  Each question shows a scale that holds different items on either side.  The scale tips to one side, and you have to choose, from a selection, which item is heavier based on how the scale tips.


This becomes difficult as the questions quickly progress to showing two to four scales at once, with varying numbers and types of items on it.  One needs to figure out relations like: first, is the pear heavier than the apple based on their relation to several items and each other on the scales? And then, is the pear heavier than the orange?
Two apples may weigh more than one pear, but does one apple weigh more than one pear?  There will be several types of items, about four to six, all piled up in different quantities on each scale end of four scales, and you need to figure out which single item weighs the most. You select the item from a multiple choice answer that presents several items.

2) A visual spatial counting test.  Blocks are dropped from the sky into a pile.  You need to count how
many there are. When you answer a question correctly, the next question will display a greater (or equal) number of blocks.  The blocks are piled in piles of different heights-some are one high, some piles are two high, some are five high. Some are partially hidden.

3) A visual spatial test.  A question has, for example, two cars entering a maze, and two possible exits from the maze.  The maze of roads includes about 20-50 turns.


The rule is that as a car drives forward, when it hits an intersection in the road the car must turn that way.  But it is complicated because there are so many turns, and some turns are only millimetres away from other turns, meaning it’s not visually easy to quickly get the right answer.


I have an extremely high score on this test.  One analysis suggested (but didn’t prove) that my score on this test was ranked tied for 3rd all time in the country! (It’s not conclusive because I looked only at the top 100 overall scores garnered from the total of all
four subtests.  It’s possible, but less likely, that someone with an overall score outside the top 100 also had a score higher than I and the top two earned on the car test.

4) A math test where you type in the answer.  Early questions are easier (like 14+1), and progress to harder questions, like (15*18)-(14*2)=.  The questions don’t progress to ones that are
extremely difficult; it’s partly a test of mental speed, resulting from the time limit.

5) A math test with questions of the same difficulty level as above, but with one difference.  They give you the answer, you need to fill in the missing signs.  Eg   (12*2) * (8  2)=48.  You then choose your answer: either +, -, * or /.


6) A math test.  This time, the "answer" is already provided.  But the "question's" equation is not given.  You are given a bunch of numbers to choose from, as well as two to three signs to choose from, in order to complete the equation. Eg:  Answer is 12.  You are given a 5, 9, 4, 8, 3 *, -, +.


You select from the bunch to get the equation. In this case, it’s 5*4-8=12


7) A memory test.  The face of several cards at once are displayed for about one to two seconds. Then they turn over.  You need to remember where the matching pairs of cards are and select them in pairs.


This progresses in difficulty until about more cards appears, with about 16 cards showing at once at one point.


It also becomes more difficult because each time you match a pair, the location of two other cards switch places on the screen, making it more difficult to keep track of where the matching pairs are.


8) A memory test.  For about one to two seconds, up to six items are shown on the screen.  Once they disappear, you need to recreate the exact order of the items.  If you get the order of just one item incorrect, you don’t progress.


For example, it might show something like this:  pear, apple, apple, dog, fries, hat.


9) A memory test.  Have you ever played the game at the carnival where you see things pop up quickly and you have to hit them with a hammer? Well, imagine if you had to recreate the order in which they appear.


One question shows about eight eggs. A chick pops up quickly (appears for about ¼ of a second) out of one egg. A chick then pops out of the seven other eggs.  You have to click on each egg in the order the chick appeared.


10) A visual spatial and memory and math test.  About eight circles appear on the screen. They are all moving at one time, and spinning in circles.  Each circle has a number in it.  You have to click on them in order of smallest number to largest number.


This involves spatial ability by testing your ability to recognize the numbers that are spinning and moving.  It involves memory by testing your ability to remember what number you just glanced at on the other side of the screen. (The more you remember, the quicker you can move).


For example, the circles might show:  -43, -41, -4, 10, 11, 35. They would all be spinning and moving, and you’d have to click them in the sequence I listed them.  Sometimes they use letters, such as G, X, V, F, N, B.


11) A spatial puzzle.  A largely completely puzzle is shown with several pieces missing.  You have to select the fitting pieces from a list, and place them in the right spot of the puzzle.  This is not easy, because there are many similar looking pieces to choose from, and the pieces you choose from are rotated left or right so that you can’t easily see if they fit.


12) A spatial puzzle.  A group of about 16 different items will be shown adjacent together, similar to cells in a bees nest.   Then you’ll be provided with a sequence of three items in certain order.  You need to find those three items in the bees nest and highlight them with the mouse in the order they appear.  This involves skill, because you might find the first two items but then find that a third, adjacent, item doesn’t connect to them. So you have to begin elsewhere in the nest.  This tests your mental speed and spatial ability.


Overall, this test measures spatial ability, memory and mental speed.  These are all aspects of capability that are measured on traditional, well known intelligence tests.


So, is the test a
complete test of capability? No.

But it definitely measures capability, just not
every aspect of capability.

And if one was to leave one measure out of a capability test, I'd argue that verbal testing is what you’d want to leave out. Why? Well, many of its questions are subjective, and hence are flawed, because extremely capable people can provide a correct answer that is actually marked as incorrect. This is explained
here.

Also, verbal scores are more affected by education (reading) than other types of capability, which are more hard wired in the brain (math, memory, spatial etc).


Also, don’t think that my score is so high because I scored high
only on the four tests I selected. (I feel I need to be thorough in explaining this, because haters will attack any opening you give them!)

My scores are high on
all twelve subtests. The test provides “trophies” if you achieve certain scores. I have all 18 trophies (3 other trophies are related to challenging other players and playing on a mobile phone, and I didn’t bother doing any of that;  I would've achieved them easily).

The trophies are:


For each of the twelve subtests, a trophy is given if you achieve a score of at least 650. I earned them all. My lowest score was 680, the rest were all 704 or over. Four of my scores are 1001 and over!


Another trophy is called the “All-rounder”. It’s given to someone who gets a score of at least 500 on
all twelve tests.  I earned that.

Another trophy is called “Mr. Right”. It’s given to someone who earns a score of 2,600 with zero mistakes.  I earned that.

The last trophy is called the “Masterful Score Trophy”. It’s given when you score 1,000 points on
one of the twelve tests.  This, of course, suggests that 1,000 points is rarely achieved. Not only did I earn it, I earned it on four of the twelve tests, with scores of: 1001, 1026, 1078, 1352.

Three other trophies were less meaningful: one for beating all of my friends, and two for the number of games played.


So, I’ve established that the test measures many aspects of capability.


Now, was it impressive that I placed 74th in the world on the monthly rankings? Of course! (But intelligence isn
t everything in life, my friends.  I guarantee you that). 

Facebook has 500 million members! But how many of them was I being compared to?

Facebook said I placed at the 99.9th percentile. However, they don
t display the percentile results to two decimal places (and they don't round up or down, for reasons explained below).  Therefore, my ranking could be as low as 99.90 or as high as 99.999999.  There is a massive difference between the two, in terms of probability!

So, how should I estimate what the sample size was?


Well, about 10% of my Facebook friends have taken the test at some time.  However, not all of them take it monthly.  And perhaps the test isn’t provided in countries that don’t speak English.  However, I think it's safe to assume that people that score very highly are more likely to retake the test because they are happy with the results and want to increase their ranking.


I think that it would be incorrect to say that I was being compared to 10% of Facebook members.  I believe that a reasonably fair number would be about 0.1% to 1.0% of Facebook.


That’s 500,000 to 5,000,000 members. For me to beat all but 73 of them, that’s impressive.


For my calculations, let’s assume the low end of the range, to be conservative.


With a sample size of 500,000, what ranking would I need to achieve to achieve the 99.90th percentile (which was the minimum percentile ranking that Facebook said I earned, since they don’t expand to two decimal places)? 500.


I can tell you that before I achieved the ranking of 74th in the world, a previous best score was several hundred points lower. I was probably ranked lower than 500th in the world (the reason why my best score increased significantly at one point was because I became aware that I was able to use the keyboard, and not just the mouse, to answer some, but not all, questions.  Given that the tests are only 60 seconds, the extra speed I had when answering some questions made a significant difference).


When I ranked 501 or lower, if the sample size was only 500,000, my percentile ranking would have been 99.80 or lower (because a rank of 501 out of 500,000 is the 99.8998th percentile. When a percentile is ranked to one decimal place, anything equal to or above 99.8 and below 99.9 falls in the 99.8th percentile. They can't round it up to 99.9 because you didn't actually beat all 99.9%.  Similarly, when someone has a rank of 99.96, it’s not rounded up to 100.00, because that would mean you beat 100% of the scores, and are the smartest person in the world. Well, that’s not the case with 99.96).


But at the time that my score was significantly lower (probably ranked 501 or below), my Facebook profile still ranked me at the 99.9th percentile, not the 99.8th percentile that you'd
expect with a rank of 501 out of 500,000! The only way my 99.90 percentile could occur in this context is if the sample size was much LARGER than 500,000, meaning I beat at least 99.90% of the people.

So, let's try to estimate a revised sample size, to account for the findings in the previous paragraph.  Let’s assume my earlier, lower ranking was 1000 (It's very difficult to be precise, but 1000th place is reasonable given that the score was several hundred points lower than when I ranked 74th).

 
When I ranked 1000th, was I at the low end of the range (99.90) or closer to the high end of the range (99.99999)?  I assume I was at the lower end of the range, since my score was several hundred points lower than when I ranked 74th at the 99.90th percentile.

Let me estimate that my percentile ranking when I ranked 1000th was 99.92, near the low end of the range.


To rank 1000th with a percentile of 99.92, the sample size must be 1,250,000.


So far my assumptions are that 0.1% of Facebook members took the test, that my earlier lower score ranked me in 1,000th place, and that the 1000th place score ranked me at the 99.92 percentile. The facts are that my earlier lower score placed me at a minimum percentile ranking of 99.90+, one would need to rank below 500 to earn a percentile rank of 99.80 with a sample size of 500,000, and my best score ranked me 74th.


FINAL ESTIMATE OF FACEBOOK SAMPLE SIZE


These data lead to the calculation that I placed 74th out of a sample size that was at least 1,250,000! This is a percentile rank of at least 99.99408.

Now, my entire analysis made some assumptions.  I'm fairly confident that two of my assumptions are very reasonable (1000th place and my choice of .9992 within the range of .9990 and 99.99999).


My third assumption assumed that 1,250,000 people took the test (0.1% of Facebook members adjusted by the two assumptions above).  Although 0.1% seems to me to be a reasonable assumption, it's very plausible that it's an underestimate. If only 0.2% of Facebook took the test that month, then it was reasonable to believe I was being compared against 2,500,000 people. And so on.


HOW WOULD I COMPARE AGAINST THE OVERALL POPULATION?


I
d like to think that the people I beat are probably more capable than the typical Facebook member. Why? Think about it.  Who do you think would be more likely to take the test and challenge themselves in the first place? Someone who is capable, or someone who is not very capable?  And once the test is taken, who do you think is more likely to keep retaking the test, someone with a high score, or someone with a low score?

Just the fact that somebody is on Facebook likely makes them slightly smarter than average (at least as of 2011!): it means they have a computer, likely have a bit more money than average, and income is linked to intelligence (As of this writing, although many people are on Facebook, thirteen out of every fourteen people worldwide are still not on it).


So, how should I adjust my estimated percentile ranking to take into account the fact that Facebook's members in general (and also the members who chose to take the test) are likely more capable than the average person? Well, this is a difficult question to answer precisely, because when you shift a "bell" curve to the right, it makes very large changes to the right tail of the bell curve.  (The actual curve in this situation may not actually be a bell, but as long as it slopes downward to the right, a shift would make a large change to the composition showing at the right tail)


If you shift the curve to reflect that the average (50th percentile) Facebook test taker places at, say, the 55th to 60th percentile of where the average person among the overall population would score, that results in a large change in the number of people appearing at the right tail.  The result would be that someone with my percentile ranking of 99.99408 would shift quite a bit to the right, perhaps to 99.999408 or more (99.999408 is associated with a sample size exactly 10 times greater than 99.99408).


Without computer software replicating this, I can't say how large the shift would be, but I think that a reasonable estimate would be that my percentile ranking on the Facebook test, if compared versus the overall world population, would be about 99.999408.


So, let me create a final range of what percentile ranking my score would place at if compared versus the entire population.


Using an assumption that 0.1% of Facebook's members took the test, ranking 74th would have placed me at the 99.999408th percentile among a sample equivalent to 12,500,000 (1,250,000 * 10) people from the overall population.


Using an assumption that 0.5% of Facebook's members took the test, 74th would have placed me at the percentile 99.9998816:  74th out of 62,500,000 (12,500,000 * .05/.01)


If you're curious what traditional IQ scores match with my percentile rankings,
here are the charts.

99.999408 is as rare as 1 in 168,919 people (166 IQ)

99.9998816 is as rare as 1 in 844,594 (171 IQ).

If anyone is able to provide me with information to update my assumptions, please do! The most useful figure I
d like to discover is: the total sample size that took the test within the month previous to my results!  I am also particularly interested in knowing just how much more capable the average Facebook member is relative to the average member of the overall population.

So I think I’ve proven that my score measures many aspects of capability.  That the sample size was huge.   I might not be 74th in the entire world, but 74th out of the equivalent of 12,500,000+ people is very flattering.


And think about this: even
if the test wasn’t a good measure of capability….whatever it did measure, I still placed 74th out of 1,250,000 Facebook people (equivalent to an estimated 12,500,000 people from the overall population)!

TRADITIONAL RESULTS


For those who want to know how I performed on more traditional tests  (yes, the ones that require studying).  Here are some results:

During university I placed first or second in the class on several university exams.  Such class sizes ranged from about 50 to 300 people. The university I went to is considered Ivy League by some (but not all) people, meaning the competition was tougher than most schools.  On one Finite Mathematics exam, I earned a grade of over 100% (a perfect score plus a bonus question). This meant I beat everyone who took that exam, about 600 to 1200 people (several classes took that course that year).  

Yet I also earned a D in a university Business course.

After university, I considered going back to school to take Information Technology.  I took a timed standard admission test, which was half logic (logic trees), and half mathematics. I was told that I received the highest score in their entire testing history.  I received a perfect score on the logic section of the test, answering every single question in the time provided.  I'm not sure, but I believe that every one of my math answers was correct.  (However, I remember that I didn't have enough time to answer every math question).

Ok.  I've finally exhausted my mind, expanding on every relevant tangent I can think of.  I'm not sure how many of you have gotten this far.  Perhaps it's mostly the haters who have gotten this far, hoping to bring me down a notch?

They'd be quite disappointed once they see that I'm just an everyday guy.

 


 

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