What does it all ‘mean’?

I was listening to an interview with Charles Murray recently.  For those of you who aren’t familiar with him, he is the person who wrote, what became a controversial book, The Bell Curve.  Through some careful research he showed that white people had a higher IQ than black people, and had a lower IQ than Asians.  He was labeled a nazi and a racist, and many other things for this research.  Now I don’t want to get into this debate, I think that as a scholar his methodology was sound, but what his book doesn’t answer the reason for such differences.  Is it genetic?  Is it environmental?  I am sure it is more often the latter.  The more important question is, what is the value of such research?  Is it really doing any good, or does it just feed the bias of a racist, while angering others?  If you’d like to listen to the interview, I think you will find him cordial, but it’s not really the main thing I want to talk about, although what I do want to talk about is mentioned several times throughout out the interview, and that is what differences really mean.  How should perceive differences in IQ or any quality for that matter?  There are certain issues that have become very taboo in our society, and things become emotionally charged quickly when one tries to talk about them.  These includes talk about differences between people of different races, different religions, different genders, and different sexual orientation.  A discussion about any statistical differences between different populations along those lines usually doesn’t end well for the person trying to bring them up.  And it’s possible that there is little value in discussing these differences, but I thought a short post to really visualize things from a statistical perspective is important, because I think people often don’t view the statistics properly when these issues come up.  And it’s true not only for these “hot button” issues, but a lot of issues in which scientists discuss differences between populations.

For many studies, particularly in the social sciences and biological sciences you will find data is distributed.  For any two variables that you are trying to find a relationship with, you will find the outcomes range across a particular set of values.  For instance, if we were trying to determine how depression influences someone’s eating habits, even in a perfect experiment we would likely find that most people eat more to comfort themselves.  Perhaps a large majority would say take in 50% more calories than they normally would.  But a small minority would take less calories, perhaps -20%, and another small minority would take in twice as many calories.  This is called a frequency distribution.  We plot the range of outcomes versus the amount of time those outcomes occur.  There are several types of distributions.  There are skewed distributions, bimodal distributions, and then there is the normal distribution.  This is generally the most common one and the easiest to say something about statistically.  As our sample size increases, a relationship between two variables that are related to each other should get closer to a normal distribution.  I realize that I am simplifying here, but my goal is not to get deep into statistical theory, but simply to illustrate why differences between populations might be more or less meaningful.

In a normal distribution the most common occurrence (the mode of the distribution) is the mean, and it is the value you get at the middle and tallest part of the curve.  First let’s ask how useful is this to begin with?  By definition of the mean is the middle value, half of the people lie above and half of the people lie below.  So when we look at the means of two different populations we might see an overlap as illustrated here:

Despite the different averages we can see that much of the populations span the same range of values.  The source for this graph discusses the meaning of overlapping means in more detail. A more specific example is here:

This graph comes from an interesting discussion about differences between populations of men and women.  In this example we can see that the average height of women and men are different, but of course no one would say that any given man will be taller than any given woman. What this means is that if we are talking about people there is very little we can assume a priori meeting any individual member of a group.  We can only say this is how things are on average and we can decide if anything should be done about it or anything can be done about it if we desire those averages to be the same.

Averages are talked about far more than perhaps they should.  While it is a good summary of data, frequently the devil is in the details and we can say little concrete on averages alone.  Rarely do researchers themselves so narrowly focus on the statistical analysis they do, but I think much gets lost when a journalist tries to report on the findings.  The average, being the easiest to understand, is thus the easiest to report on and that’s when people start making assumptions about what the data are actually saying.  Read an actual paper and you will find all sorts of other statistics discussed.  Averages are all too common though.  We get them in school, they are reported in sports statistics, the news.  But one has to be put it in context of the entire set of data.  Let’s not define people by an average.  What is equally relevant is the variance among the population as well.

People are often easily fooled by statistics because they don’t understand them adequately.  Statistics also deals with probabilities.  Something we are terrible at from an intuitive level.  If you are interested in having a better understanding of basic statistics, I found this website to be quite helpful.   I believe that by having a better understanding of statistics we can have more meaningful reactions to the findings of data analysis, and thus have more meaningful discussions about what we can really conclude from those data.


33 thoughts on “What does it all ‘mean’?

  1. The IQ is misunderstood. It really measures learning, not really intelligence. Plus, it is renormalized frequently. If you go back decades, you will find that the average (normed to a score of 100) actually has gotten much better. A person scoring 100 70-80 years ago would be scoring closer to 90 now. People are become more educated!

    The real problem is not identifying these differences but interpreting them! We rarely get past “See, I told you they were different.” We flavor any “difference” identified as being “better” or “poorer” by means closer to prejudice than science.

    Did you know that kid’s shoes size correlates well with their IQs. Those kids with big feet must be real smart! (Actually, as children grow, their shoe size and IQ’s go up as they age. They are not otherwise linked.

    We seem not to be able to discuss anything seriously to be able to reach a conclusion. I had hopes that education would foment rational decision making, but that hope has been dashed (in my mind).

    Liked by 5 people

    1. Thanks Steve. I agree that IQ does only measure a certain kind of “intelligence”, and certainly doesn’t measure a lot of other things we value in society. Murray’s research does take the IQ changes into account, and there is quite a lot of research on IQ being a successful measure of prediction to one’s standard of living. That being said, I would argue we measure success in a somewhat superficial way in a consumer driven society. Perhaps success should be measured differently.

      And you are absolutely correct that the key is to the interpretation, but I think that we also have to not cast people down to the pits of hell for putting out results and think about the problem to have meaningful dialogue. In some ways if we see racial differences in IQ this might be cause for alarm, or at least re-evaluation of educational practices, or how we might be serving the needs of racial minorities in a particular country.

      Liked by 2 people

      1. I wasn’t commenting on his research, but the ordinary perception people have about what IQ stands for and their understanding of it. Historically, researchers have to take into account the renormalization as otherwise, some strangenesses will be created.

        If there were no racial differences in IQ, I would be shocked. The problem lies, as always, as how one defines race because biologically the concept is bankrupt. Race is social construct that has real consequences. I often want to ask those who think being Black is a real boon because of all of the social programs that support the, if they would like to be Black. I would ask this just to view the look of horror on their faces.

        Liked by 5 people

  2. There are physiological differences. There’s a reason why black men/women sweep the competitive track and field events, and why you’d be hardpressed finding a black man/woman anywhere near the highest levels of competitive swimming. Our pelvis’s (if I remember correctly) are shaped differently; one assisting a person to run faster, the other more favourable to swimming techniques. After that, and excluding individual gene differences, I think it’s mostly all environment, and that makes stats a useful tool, but by no means gospel.

    Liked by 4 people

    1. Well said. Yeah I’ve read some articles talking about how they feel like they’ve taken environment into account when studying intelligence, but I honestly don’t see how that’s possible. In the U.S. being poor and white still for the most part leads to a different kind of life than being poor and black in terms of how you are treated and the opportunities you have. Given that there is no intelligence gene, it would make sense that there would be genetic difference in intelligence, but it also makes sense that the combination of genes that would activate in any particular environment might also be different. People understand statistics so poorly on average as well, that even if it were gospel, people can easily be manipulated into believing all sorts of things, instead of it being a critical thinking tool.

      Liked by 4 people

  3. I have Dyscalculia, and a very poor recall rate when under the pressure of say a ‘test’. When observed over the period of a year during my education I was Queen of the Universe (I’d say princess, but I have never been a princess) so far as top marks go in any filed that doesn’t involve numbers. Out goes Physics, Chemistry, some biology and more subjects that I can’t recall because I have poor recall when in the moment (or hour, or month hahahaha). Having this longstanding problem with numbers also means I can’t understand the graphs and statistics when they’re described in their usual terms. I clicked through to the ‘understand statistics’ link, as soon as ‘half this, and half that’ appeared I was lost.

    My point is that whilst I can see that figures and averages are useful to some extent, the amount that is missed out involving individuals for hundreds of reasons is so large a factor it should be taken into account far more often. People use statistics as black and white facts (absolutely no slight meant there bearing in mind the original graph!), and if you don’t fit, then you are labelled according to the numbers collected. I’m a sharp cookie even though I say so myself, but I have never tried to find out my IQ as it would show me as being the local village idiot I’m sure hahahahaha! *shrugs*.

    I think a new method needs to be devised.

    (ps – Dyscalculia is such a great name for a ondition to have, because you sound like a Vampyre!)

    – Esme sat on the village green looking happy and showing her long teeth, abacus in hand upon the Cloud

    Liked by 4 people

    1. It does sound like a vampire! lol

      But I’ve read a bit about this condition, and believe I have met at least a couple students with it. One person in our meteorology program said he had been diagnosed with it. I’m like okay, I accept that you have it, but that doesn’t change the fact that this is a quantitative field that is applied math and physics. It doesn’t mean your dumb, it just means you’d be best served doing a different profession. Really he just wanted to be a TV meteorologist, but there aren’t many stations that just hire TV meteorologists without a degree in meteorology even if they don’t have to use those skills very often. There are really bright and mathematically minded TV meteorologists though and they can be a huge boon in helping improve forecasts aside the National Weather Service as opposed to just passively accepting the forecast that is given to them.

      But yes, as I said to Steve, IQ measures only a certain type of intelligence at best, and even researchers who study IQ know that there are many people that would be outliers in the data set. You are such a person. And as I also mentioned to Steve, intelligence isn’t the only thing we value. IQ doesn’t test how compassionate you are, how moral or ethical you are. It doesn’t test how effective a communicator or negotiator you are. It doesn’t measure your humility, your courage, or your ability to take risks.

      You are a smart cookie indeed, and I think that IQ only has increased value in the type of “civilized society” we find ourselves in, but I think as many of us have seen the society we live in doesn’t seem to be serving a large majority of the people on this planet. So maybe it’s time we investigate new models to build a society around. I’d like to believe in such a society you would be a Queen. I’d happily be your jester. 🙂

      Honestly I’ve never taken an IQ test either. I think I’d probably do well though as I’ve never really had a problem with standardized tests, but my intelligence means little to me if I’m not trying to grow as an individual and try to make the world a better place.

      You are interesting though because I was just thinking that there are many people you can tell have a very poor intuition for probabilities and are swayed much more easily by statistics. You on the other handed are quite level headed when it comes to distinguishing between what’s meaningful and what’s not. It makes me wonder how different parts of the brain might be responsible for intuition in this area, and how emotional intelligence plays a role, because you clearly have a lot of that as well.

      Liked by 3 people

      1. I feel for that chap who wanted to be a meteorologist, and surprised he didn’t work it out beforehand, knowing what I know about number issues. I recall you introducing yourself to me as a professor of Clouds! And you are. It should be called that officially – *sees The Cloud nodding in agreement*.

        I’m incredibly logical but also have a huge capability for empathy, so I have an empath and a Vulcan living inside my brain; this makes me very good at understanding people and their behaviour, and I think a large chunk of that is very much linked to my brain being predominantly artistic in nature — I can therefore, somehow, write in such a way that readers (seem to) find an affinity within my words. I specialise in emotions, I want people to keep ‘feeling’ because when they stop terrible things happen, but would like to have a broader scope and be able to write in the same way about other subjects like ecology, politics and veganism, but I’m just not very good at debating as my empath gets over passionate and explodes into the aether and wombats go deaf.

        It’s awful.

        I envy people who can mix art with sciences, you can do that Swarn, you can write poetry and write articles like this and teach, – *throws an apple for the teacher at his head* – and I’m sure you are a whizz in person explaining things too. It’s not all fun and games being Queen of the Universe! I’ll have you higher than my jester I think though hahahahaha.

        – Esme feeling everything but not looking like Spock that much upon the Cloud

        Liked by 3 people

        1. Thank you for your kind words. I’m a natural lefty who was forced to use his right hand, so the creative part has taken some cajoling to get out. lol

          I think though also I have also been drawn to people with a strong creative abilities. My wife is one of those people while also a scientist, so it was the best of both worlds, but I’ve felt that just by watching and learning about such people this has helped a great deal. Maybe it’s not true for everybody, but I think a lot of the creative side is simply having the courage to try and express things that aren’t easily understood. As soon as you let your art be seen there is a vulnerability as well, and you have to have the courage to be vulnerable.

          Unfortunately that student didn’t get diagnosed until he started the program, but I suspect the problems were there a lot earlier. Too often kids slip by here without their learning difficulties being diagnosed.

          I would say though if I often haven’t given myself enough credit on the artistic side, perhaps you haven’t on the scientific side. While there certainly is a quantitative component to science, ultimately it is only a tool to help explain concepts and give them the weight the explanation deserve. Any time we have had a discussion like this on my blog you come as thoughtful, critical, and logical. As well as a muse extraordinaire who has wonderful wordcraft and can lead hearts around like the pied piper, you also come off as an engaging conversationalist who likely has valuable points of view on many topics. I shall not cajole you away from blogging what you feel most comfortable or enjoy putting out there…I’m only saying if you did choose to talk about so sticking marshmallows on her pointed ears so that if people start talking about her and her ears burn they will be something on the more serious side, you would be extremely worth listening to.

          * Professor of clouds sticks a couple of marshmallows on her pointed ears so that if someone starts talking about her and her ears burn they will be roasted to perfection.

          Liked by 2 people

          1. “As well as a muse extraordinaire who has wonderful wordcraft and can lead hearts around like the pied piper, you also come off as an engaging conversationalist who likely has valuable points of view on many topics. ” – Well you can stay for lunch, tea and supper with that kind of talk!

            Seriously though, thank you. Can you edit my ‘chunk’ line to be correct as Hariod seems to find it absolutely hilarious amidst my claims of greatness? Thank you in advance.

            – Esme scowling at Hariod whilst pouring some Earl Grey for Swarn upon the Cloud

            Liked by 1 person

            1. Fixed. It is good that you have a guardian angel who is intent on making you appear as the pinnacle of perfection everywhere you go. I suppose at least 25% of my compliments towards you now should go to Hariod? I’ll do better in the future! lol

              Liked by 1 person

  4. Swarn,

    It is sort of ironic that this post touches on some exact subjects I’m covering in my current blog-series, particularly Part III I am drafting now! For example, from Nobel Prize winner Roger W. Sperry on the human elements of genetics vs. environment and ontological constraints contributing to ignorance:

    “A psychobiologist considers the implications of ongoing evolution:  it “keeps complicating the universe by adding new phenomena that have new properties and new forces.” […] But the most daunting for these scientists is any phenomenon that is conditioned by human action and intention.”

    Nevertheless, the value of statistical analysis can never be overstated when dealing with knowledge and ignorance!

    Great post Swarn! Bravo Sir! ❤

    Liked by 3 people

    1. Is it ironic or coincidental? lol

      Thanks Professor. The disentangling of nurture and nature is difficult indeed, which is why most studies that try to do so need to be read with a skeptical eye. 🙂

      Liked by 2 people

      1. A skeptical or scrutinizing or the necessary patience to suspend judgment until enough data is collected. And I whole-heartedly agree about such “studies” — i.e. those who purport absolute certainty for sure! A prime example would be the O. J. Simpson trial, eh? 😛 😉

        Liked by 3 people

  5. There are findings that show children who are introduced to music at an early age are better students and better at a whole host of other things.

    Charlie Parker, Oscar Peterson, Dizzy Gillespie, Miles Davies, Count Basie , Sarah Vaughn, Jimi Hendrix, Herbie Hancock, Billy Cobham, Stanley Clarke, Tony Williams, etc, etc

    Liked by 3 people

        1. Agreed…I’ve read similar things. We’ve been working on making sure he has a 2nd language for now, but he certainly enjoys music, I hope he gains some interesting in actually wanting to learn how to play something. From what we can tell right now he wants to be a comedian of some sort. lol

          Liked by 2 people

  6. Every couple weeks there’s a news story about the cost of housing, as reported by CREA (Canadian Real Estate Association). The prices never make any sense, so I contacted CREA and asked them how they report average prices. It turns out, they report the mean (as opposed to the median) when they report on house prices. You can image a situation (which I think is not far from reality) where you have 10 houses. 2 sell for $50K, 7 sell for $100K, and 1 sells for $1M. CREA will tell you that the average house price is $180K when the average person buys a house for $100K. I believe this has the effect of driving up house prices because you might think that you’re being frugal if you buy a house for $150K, but really you aren’t. It’s a complete misrepresentation of the statistics when what people want to know is what is the price of the average house, not what is average price of all houses.

    Fortunately, the problem should correct itself when the housing market collapses and all the realtors are out of jobs. It’s unfortunate that the media perpetuates the problem by not holding CREA to account.

    Liked by 2 people

  7. Rarely do researchers themselves so narrowly focus on the statistical analysis they do, but I think much gets lost when a journalist tries to report on the findings. [snip] People are often easily fooled by statistics because they don’t understand them adequately.”

    Thanks for explaining this, Swarn. It’s difficult to make sense of these types of statistics and what they are actually saying when there’s so much disagreement among scientists regarding Murray’s research (and motivation). I think the problem lies in the fact that in his book he wrote some controversial “policy prescriptions”, as noted in the Scientific American article.


    After reading your post, I spent several hours yesterday digesting data, as well as the pros and cons from scientists regarding Murray’s research, and came to realize that it’s no wonder laypeople struggle to understand when even scientists are divided. But, the problem I see is that he wrote a book in 1994 (which became a best seller), knowing that most people are not educated in how to interpret the data, much less research methodologies. Here we are close to a quarter of a century later reading a blog post explaining to us what it all ‘means.’ That speaks volumes.

    Anyway, I appreciate your desire to educate (more than you may realize), and I do understand your motives, which are commendable.

    Seven days — wooohoooo!

    Liked by 2 people

    1. Thanks Victoria. I finally had time to read the the article you linked. I don’t doubt that there is room to criticize the book and as we discussed on the phone, such information can be easily used by those who are pushing a racist agenda for nefarious purpose. And as the author of this post says, this can largely be due to what they do not say. I would think if you were going to publish results like this you would want to spend a fair amount of time making clear that this data should not be used to push a racist agenda and why. While I didn’t get any impression that Charles Murray is racist, he does perhaps suffer from some privilege but so do many of us. What’s also interesting is that he wrote the book with someone else, who died very shortly after the book was published. As a result Murray has taken all the criticism and its not clear what differences of opinion both authors might have had over content they published. There is no question that there are holes in their scholarship, and I think criticism is certainly warranted. But the things that were said about him, and the fact that he is still not being allowed to speak is absolutely unwarranted. I honestly feel that if someone is making an honest scholarly attempt, gets published, even if that person isn’t as comprehensive as they should be, or even if they have bias, as we all do, they should get a seat at the table. Science, if it works at all, comes from scientists with various biases, but mostly good work sitting down and coming up with some sort of consensus.

      In regards to the statistics, I am sure many in 1995 could explain what I have very easily, but the internet certainly does make it easier to make such information available. It seems though many people think they understand what statistics are telling them and so don’t bother investigating what all these things mean at a deeper level. As with anything, people want to judge without understanding, because judging is the fun part apparently.

      And yes…one week! 🙂

      Liked by 1 person

      1. Indeed, but we didn’t have the internet and comprehensive search engines readily available at our fingertips. While there may have been many in 1995 who could explain, their outlets tended to be in academic settings.

        “and I think criticism is certainly warranted. But the things that were said about him, and the fact that he is still not being allowed to speak is absolutely unwarranted.”

        Given the volatile political environment, a resurgence of white nationalism \ white supremacy, and a lack of unity within the social science community regarding Murray’s book, I’m not surprised by the fallout.

        In this 2014 Q & A article, The Bell Curve 20 Years Later, Murray was asked:

        “Reflecting on the legacy of “The Bell Curve,” what stands out to you?


        “I’m not going to try to give you a balanced answer to that question, but take it in the spirit you asked it—the thing that stands out in my own mind, even though it may not be the most important. I first expressed it in the Afterword I wrote for the softcover edition of “The Bell Curve.” It is this: The reaction to “The Bell Curve” exposed a profound corruption of the social sciences that has prevailed since the 1960s. “The Bell Curve” is a relentlessly moderate book — both in its use of evidence and in its tone — and yet it was excoriated in remarkably personal and vicious ways, sometimes by eminent academicians who knew very well they were lying. Why? Because the social sciences have been in the grip of a political orthodoxy that has had only the most tenuous connection with empirical reality, and too many social scientists think that threats to the orthodoxy should be suppressed by any means necessary. Corruption is the only word for it.

        Now that I’ve said that, I’m also thinking of all the other social scientists who have come up to me over the years and told me what a wonderful book “The Bell Curve” is. But they never said it publicly. So corruption is one thing that ails the social sciences. Cowardice is another.

        Liked by 2 people

        1. Interesting quote. I don’t think Murray is completely wrong. In his interview with Sam Harris it is clear that a number of people in the field that were guilty of some of the worst vitriol were being dishonest. I’ve read some articles that particularly talk about the liberal bias in the social sciences and I think there is cause for concern. The problem is of course that it’s one of those situations where it’s hard to disentangle that prejudice from the legitimate concerns and the legitimate science. In many if not all of these situations where students organize against a conservative speaker it is a faculty who is the rallying cry. Given the mentor, role model, somewhat parental like relationship students can feel with faculty it is not hard to bend some students into a fervor. In regards to a political bias this has certainly not always been the case historically, and one wonders how much of this change is organic and in some ways legitimate, because I don’t think, for the most part, that the situation we find ourselves in now is intentional.

          1. Given that the political spectrum has been pulled to the right in this country, how many faculty might still be more conservative, but find voting for Republican untenable, and find more appeal in a democratic party which is more right of center. This is academically the reality of the democratic party.

          2. Changes in hiring practices at university over the past 30 years have increased the number of females, homosexuals, and minorities, which tend to be democratic, simply because they have been oppressed and discriminated against and will naturally support a party that celebrates equality.

          In the end of course it is the quality of the scholarship that matters the most. And just like with the suppression of free speech for speakers we are better off letting them speak and challenging their ideas once presented. Similarly if there is a truly nefarious conservative social scientist out there he/she has to defend arguments scientifically. If they cannot, this is generally better for that particular field than not even letting certain research make it to the stage. In terms of hiring practice, the quality of the research should matter, not the political affiliation of the scholar.


          What’s also interesting is that Murray said in his interview with Harris that what was good about all the vitriol is that he was free from any sort of consequences of making his reputation worse. One can imagine that if he was a racist and producing this kind of research for nefarious means that the dishonesty he faced from other academics would potentially make the situation worse. You now have a person out there who is good with data who can no longer be damaged further in the public eye and he could become a much more productive bedfellow for racist groups. This is the part that’s frustrating because if we want to save our university institutions we need keep our eye on the bigger picture. Challenging ideas instead of being fearful of them. And believe me that’s the M.O. on the right, and well we know how well fear has worked out for them. 😉

          Liked by 1 person

          1. Well said. I may have mentioned this to you when we talked about this subject on the phone last week, but the way I got introduced to Murray’s book/research was during a discussion on a forum several years back. I have to admit, I was taken aback, and the person who introduced me to it believed that blacks were the cause of our educational institutions lowing their admittance standards and quality of education.

            I am reminded of when Charles Darwin believed women were inferior to men based on his research. In his book, “The Descent of Man, and Selection in Relation to Sex” he said that men attain “a higher eminence in whatever he takes up, than can women—whether requiring deep thought, reason, or imagination, or merely the use of the senses and hands.”

            My point being — if one is going to publish a controversial “scientific” book like these to the masses, they can’t be so naive as to assume that significant discrimination and harm won’t materialize. With this comes responsibility for the fallout.

            Liked by 2 people

            1. if one is going to publish a controversial “scientific” book like these to the masses, they can’t be so naive as to assume that significant discrimination and harm won’t materialize. With this comes responsibility for the fallout.

              Definitely a degree of irresponsibility at best in The Bell Curve. You definitely have to be cognitive of what impacts a book like this might have.


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