misuse and abuse of statistics
|Intelligence: misuse and abuse of statistics is one in a series of documents showing how to apply empiric reasoning to social and psychological problems..|
|Intelligence: misuse and abuse of statistics||drugs, smoking and addiction|
|establishment psycho-bunk||cause, chance and Bayesian statistics|
|on temperature and statistics||correlation - a little knowledge is dangerous|
|For related empiric reasoning documents, start with
Why Aristotelian logic does not work
Note:this document is non-linear, the position of text and boxes relative to other text and boxes is not particularly significant. Start wherever you like and expect to travel widely about this document as you read. Or start from the beginning and work your way through, if that gives you joy.
Statistical reasoning is among the most complex and difficult constructions
of the human mind. The interpretation of statistics takes considerable
subtlety. This document is to give you practice in recognising and avoiding
some common confusions. While I have widely used the ‘scientific’
arguments surrounding ‘IQ’ as a model in this document, the
critique is also intended for generalised application anywhere that statistical
methods are in use. Important in my purpose is to draw attention to the
The document laying the foundations
for sound education
It is currently claimed fatness is 70% inherited—it is strange to see so many fat people in the USA, yet so few in Afghanistan.
Crime has recently been rising in the UK, so has immigration, so have summer temperatures, so has the wealth of the country. I see many claims among unsophisticated people that increased immigration ‘causes’ the rises in crime. I see far fewer claims that the rise in crime is due to rising temperatures (ever noticed how the riots occur mostly in hot summer weather?).
That two items vary in a similar trend or direction says absolutely nothing about whether the items have any strong connection. This is expressed in the study of statistics as:
Correlation does not imply causation 
It is important to remember this.
Why do you think people in Afghanistan are generally slimmer than porky Americans? Do you think 70% of the difference can be attributed to genetics? Imagine that a ‘study’ were done to include half Americans and half Afghanis; do you think it would result in a similar 70% heredity figure?
Consider a statistical sum: I weigh one hundred 30-stone Americans, and I also weigh one hundred 10-stone Afghanis. The average weight will clearly come out at 20 stone. But the average weight for the Americans alone would be 30 stone, while the average Afghani weight would be 10 stone.
Now I do another ‘scientific study’ (that’s what academics and governments like to call these things, in order to get you to take them more seriously). This time I weigh 200 people who weigh 20 stone; note that I will get the ‘same’ average obtained in the first ‘study’: 20 stone. Note how the average tells you so very little of what is going down. The statistics might almost have been designed with the purpose of hiding real and useful facts.
Consider some potential daily slime headlines: AMERICANS ARE GROSS or AFGHANIS ARE LIGHTWEIGHTS or INTERNATIONAL AVERAGE WEIGHTS ARE 20 STONE. Often such pap will include rhetoric like “a scientific study found that”.
Most households have such a surfeit of access to food that any reasonably determined person can grow quite ginormous with a few years of effort. If you now weigh ten stone, and you put on just a pound a month; why in ten years time you’ll weigh a heart-stopping 19 stone – and your bikini won’t fit!
Consider another group: this time, ninety-nine 10-stone weaklings and one circus fat man weighing 40 stone. Again we take the average—that is: (99 x 10 stone) is 990 stone, plus 40 stone totals 1030 stone, then divide by the 100 people. This gives us an average of around 10 stone 4½ pounds. Quite a surprise when you find the circus fat man and start to wonder why he is so heavy, but by just looking at the average you will entirely miss this variation. Had the average figure been transmitted to a visiting space alien, they might imagine the fat man to belong to some entirely other species.
Plomin, the writer of the standard work on this subject states accurately the following:
High heritability within a group does not necessarily imply that the average differences between groups are due to genetic differences between groups. The average differences between groups could be due solely to environmental differences even when heritability within both groups is very high.
I shall now re-cast this….
High measured ‘heritability’ within a group does not imply that average measured differences between groups are due to genetic differences between groups. The average measured differences between groups could be due solely to environmental differences even when measured ‘heritability’ within both groups is very high. (Note that I have removed the word ‘necessarily’ from the first version).
Note also that ‘heritability’ is a statistical calculation, it does not implyinheritance. Calling the calculation ‘heritability’ tends to insert an assumption; doing this is not careful scientific analysis or language. However, it remains that Plomin’s original statement is accurate, if read carefully. Unfortunately such statements are generally not read carefully; and in my view they are not written carefully.
It is by such rhetorical obfuscation that ‘arguments’
concerning supposed ‘heritable’ differences between groups
are promoted, even though a careful interpretation of the words used carry
a very different (lack of) meaning. Such texts must be read with great
care. Statistical relationships do not
Thus, in the section what is an average weight?, the ‘heritability’ measurements for American and Afghani fatness will both very likely still show around 70%. Absorb this fact into your thinking, and compare it with other claims you see concerning ‘heritability’. Understand that if you could hold environment unchanging (it can’t be done!), you would end up with 100% ‘heritability’ in all ‘tests’. Thus ‘heritability’ measures could easily be interpreted as environmental stability measures. I suppose ‘scientists’ imagine calling the measure an ‘environmental stability measure’ would fascinate ‘news’papers rather less than calling the purely arithmetic calculation a ‘heredity’ measure or, even better perhaps, a heredity index.
But maybe I am being too hard; the measurements can prove interesting, or sometimes even useful, as long as they are treated with much care.
How do I decide that an item is a stone? How do I decide that it is not a rock or a tree or a grain of sand? I suggest that it is by carrying around programmes in my head with average measurements, against which to compare real-world items when deciding into which category I will classify those items.
I classify items for convenience, and for the purpose
of communication with ‘others’. The averages or universals do
not exist in the world outside my head. In the outside world only individuals
exist, and those individuals are arbitrary separations I also
With my idea of ‘a’ stone, I may have an average weight and a range of acceptable values in mind before I term the item a ‘stone’; I may also have in mind an average hardness with another range of values, and so on. Inevitably, my averages and ranges, and even the criteria I have built up through experience, will vary from those of another entity.. My idea of ‘food’ will differ from that of a frog, and also from that of someone who drinks cow ooze—called by some persons, ‘milk’.
The development of ‘statistics’ and averages
in recent centuries have attempted to formalise this process somewhat; usually
without much consciousness of the underlying process, nor
I don’t have a great deal of problem using the word ‘stone’ in common conversation/communication. I might find I have to be more ‘cautious’ or ‘precise’ if discussing ‘stones’ with jewellers, or with road engineers and quarrymen. However, the term ‘IQ’, or even ‘unicorn’, will present much more difficulty.
The problem I have with a word like ‘unicorn’ is the finding of real-world examples to test my notions or averages against. I do have some idea of how a unicorn should appear; I just can’t find any real examples. Then, there are words like ‘god’ and ‘spirit’ where it is even difficult to get most people to define the average criteria for which I should search (see“Logic has made me hated among men).
Most of you have approximately 5 fingers; it’s in the genes.. Sometimes 6 fingers are in the genes; sometimes the environment cuts off a finger or three. Having a brain is in the genes, but some people are born without a forebrain (the thinking bit) and others lose parts of their brain or their brain function by accident or disease. For more on this see Ridley, especially chapter 6.
To what extent ‘normal’ brains vary in efficiency we do not yet know with much certainty. The efficiency of brains appears to vary according to womb condition and certainly, to varying degrees, by adequacy of diet.
At least one gene that has an effect on ‘IQ’-measured ‘intelligence’ may have been identified. It is involved in the efficiency of glucose transport. I would expect many such genes to be identified as our knowledge of the genome increases. As our understanding of the effecting chemical mechanisms continue to grow, it is likely that action may be taken to intervene in the consequences of the genes when people so choose.
My studies lead me to regard elements such as drive and impulse control to be very relevant in the development and use of ‘intelligence’. These behaviour differences do not imply ‘genes’ for ‘calculation’ or ‘chess’ or ‘music’ or ‘the English language’. They are functions of physiological efficiencies or differences. A more sensitive ear may make a person more effective as a musician; it is unlikely to enable them to run a hundred meters more quickly.
Much of outcome depends upon interest in a productive area. This may well be ‘luck’, but it also required drive and judgement. As the folk saying has it, “Genius is 99% perspiration and 1% inspiration”. It is unlikely that you will become a paid baseball player if you spend most of your days in front of a television, or spend the time reading books for that matter.
It is widely imagined, even among some who should know better, that all evolution is by direct pressures upon individuals; but this is not true. The evolutionary pressures, of course, impact always upon individuals. It is the individuals that carry the ‘successful’ genes; but there are also group pressures that determine the genes that are expressed in individuals.
[Cartoon 1 to follow—which came first].
Consider two groups in competition. Imagine that in one case there are equal numbers of breeding males and females with common breeding fitness; while in another local competitive group, the females outnumber the males 10 to 1.
Assume that the propensity to give birth to many more females than males is a genetic characteristic, as is any tendency to give birth to even numbers of males and females. In a large area with many examples of both types of groups, the groups that that tend to produce a considerably higher number of females would quickly come to be dominant by producing greater numbers of descendants. It is evident that before very long, the groups producing a higher ratio of females would be colonising an environment at a far greater rate than the balanced sex-ratio groups.
Look now at this overall situation more carefully.
The situation has now come to be that most females are producing predominantly
females, while many fewer are producing even numbers of males and females.
Clearly, those females producing more males are going to produce more
Given both pressures in a population (inter-group competition
These two pressures are fairly simple to explain and
to understand, the pressures involved in understanding ‘IQ’ are
Consider the possibility of genes determining nervousness or caution; in fact; it is clear such genes exist.  A person who is incautious is likely to act less intelligently than a person who is careful, but eventually over-caution would make one incapable of action; thus a gene having similar effects could have either positive or negative effects according to situations. A person who was heavily aggressed against as a young child, or had spent months at the front in a major war, may learn habitual fear beyond that appropriate to a journey to the shopping centre; thus genes and experience can work in similar or opposite directions.
Another possible situation of reinforcement is when a high tide corresponds with a storm and the combination overwhelms coastal defences; where neither effect alone would cause much trouble. Averages are not enough to understand situations. A naturally impulsive child could well become more intelligent with some judicious constraint, constraint which would be likely to damage the development of a naturally timorous child. Averages are not safe guides to educational practice, nor to judgements in other complex situations.
The general current view in ivory tower academia is that 50% of IQ differences are genetic, some studies in the past have claimed over 80%. Such claims may make some vague sort of sense in Podunk, Connecticut. Such ‘results’ are generally obtained by doing twin studies.
Now, I have taken such twin studies apart.
Of course a moment’s thought will convince most people that a person with a genetic inheritance, but having no environment, is a particularly silly idea. Likewise, there will be a considerable dearth of people with an environment but no genes!
Consider next, an impossible ‘thought’ experiment; as Einstein would have called it. Think that you could provide every person with ‘exactly’ the ‘same’ environment. Now, we again do one of our ‘studies’—the obvious outcome will be that we decide that IQ, or anything else we ‘study’ for that matter, is 100% inherited because there are simply no environmental differences to show. Of course, if we could also clone all our test subjects and thereby obtain one or two hundred ‘identical’ ‘twins’; then the whole damn lot of them should end up with ‘exactly’ the ‘same’ IQ.
Consider ‘identical’ twins reared together. The assumption must be that any differences are due to environment. But the inverse is not the case: similarities can be either due to similar genetics or to similar environmental experiences
There are great similarities in child rearing practices within a culture: most people will use knives and forks or chopsticks or hands according to local customs. Dress fashions will be pretty similar; people will tend to speak a common language, carrying similar concepts and, in the West, most will go to institutionalised schools. Just how is the ‘researcher’ to be convinced that the small differences are to be attributed to genes or experiences? Also remember that humans start off much more similar to one another than humans are to hippopotamuses.
It is reasonable to assume that, within a society, differences in eye colour or height are mostly genetic; at least as long as a particular child has not been starved by incompetent parents, or suffered some unattended to trauma such as broken bones. But what of IQ or ‘intelligence’?
If your parents are ignorant, they will likely not teach you too much how to think or how get on with others. If you are lucky, you may get some education on the street from peers, or be lucky enough to come across a particularly able teacher at a critical time. Though even that is unlikely to fully correct any large disadvantage occurring over the first few years of your life—that is, during the time you are building your basic understanding of the world.
Your society will have the accumulated recorded culture of the ages, which has become very rich indeed in the advanced cultures of the West. However you are much more likely to absorb these thinking patterns if your parents are educated and articulate, if they have time for you and are able to send you into the keeping of the better administered schools. You will learn the patterns of logic built through two or three thousand years and, thus, you will stand intellectually upon the shoulders of your ancestors. On the other hand, should you come from a background of poverty and ignorance, you are far less likely to learn the paradigms of effective thinking that have enabled your society to rise to the complexity of modern civilisation.
Take identical twins, reared apart but in similar backgrounds, and it is very likely their understanding of the paradigms of their culture will be similar for both twins. It is most likely that reared apart twins will end up in reasonably similar homes, specially chosen by do-gooding ‘social’ ‘workers’ to closely match the original backgrounds. The homes will very likely be with highly ‘respectable’, conformist and ‘normal’ ‘parents’. But, just now and again by chance, one twin will end up with an odd-ball pair that take education with high seriousness; a couple that have between them, perhaps, some originality and are of lively mind. Or perhaps, the accident was some uncle or teacher who was out of the ordinary run. Meanwhile the other child ends up in a home that suffers accident or disharmony. That particular pair of children are likely to get very different intellectual or ‘emotional’ perspectives.
And so it proves that,
when one forgets for a moment the average correlations over a sizeable
group of such twins in a study, you will find one pair where the difference
may be 20 IQ points. But of course this odd example is averaged
out, this vital bit of data is lost, it is effectively
rejected by the very nature of the correlational method.The
correlation is another form of average.
And it also always applies
Remember that a socio-economic level or a particularly primitive ‘religious’/superstitious sub-group would also be examples of micro ‘environments’. Recall again what was said of ‘heritability’ of fatness in America and Afghanistan.
In summary so far, not only do these studies rely
upon averaging techniques, but also, when an important individual difference
from the average occurs, it is buried in the averaging. That is, the really
useful bit of information is not followed up and studied, it is put out
for the garbage collector. This is called ‘science’ in most
of academia. You may see some references to the real effects that a different
approach to education can have in
It does not apply in any other situation! Such a figure is really
There is a long history of studying relative failure in academia and schools and then attempting to change the situation, instead of taking the intelligent approach: to study success and see how it is done. Perhaps studying failure is considered somehow more altruistic and caring or some such. But it certainly isn’t smart! Or intelligent!!
Remember, a person’s environment includes
the womb, the diet, the home, the school, the street, the factory, friends
and aggressors. That a considerable part of ‘behaviour’ can
be attributed to ‘environment’ does not necessarily tell you
which part of that environment is having most effect. Some recent ‘research’
has suggested that the child’s peer group is far more important
People behave in accord with their drives and beliefs.
A paradigm is a way of looking at things. A paradigm is assembled from a variety of memes. Newtonian physics or Darwinian evolution are paradigms; that is, they are ways of looking a things.
Memes may be in accord with the world or they may be entire non-sense. Many people have a muddle of memes in their heads, some of which test against reality, and some of which are sheer idiocy. I will not call a muddle of ‘inconsistent’ memes a paradigm; the word muddle is sufficient for that purpose!
If a person has a muddle of beliefs, it is not a surprise when they behave in ineffective, or ‘contradictory’ ways. Or perhaps it is a surprise, if you are waiting for sensible behaviour while not having much awareness of the silly notions others often harbour.
IQ is calculated from the number of questions ‘ticked’ as correct in an ‘IQ test’. It doesn’t tell you why a particular person ‘scores’ a particular number, only that they have so scored. Is it because they can ‘think’ more or less quickly, or accurately, than other test takers? Or is it that they have been taught the pattern recognition skills required by the questions in a particular ‘test’?
Has the person who scores most in these (usually timed) tests learnt exam techniques, or are they able to answer quickly because they don’t think with sufficient complexity to notice ambiguities? Or did they just guess right rather more often than the average testee?
Imagine the proposition that the genetic contribution to ‘IQ’ varies approximately 50% within a studied environment. Let’s see where that proposition gets us, if anywhere.
First it suggests that variations in ‘thinking’ ability are 50% due to variations in educational standards within that society. ‘Educational standards’ may include marginal elements, such as diet (in an advanced society); and less marginal elements, such as a ‘mother’ being foolish enough to smoke or drink during pregnancy. A 50% variation suggests that modern education is extremely hit and miss and very widely unprofessiona.
Now, consider, some genius a bit like me came along and invented or discovered a new improved way of looking at the world, and started teaching people to think in this way; and it just so happened that one ‘twin’ ended up in a place where this new method was being taught. You will now know that the ‘scientists’ who were carrying on the study would get the very slightest annoying twitch in their data, like for instance one twin of a pair testing 20 points higher than the other in the ‘study’. Worry not, this higher score is obviously an anomaly; it will clearly be buried in amongst the other 100 or 200 twins tested once it is averaged out or, better still, we might as well drop that untidy bit of data as it was obviously a mistaken measurement. You think I joke; no, these are quite common ‘scientific’ practices.
There is plentiful data available that shows improved child rearing and education producing remarkable results; however, these results are widely ignored. One reason for this is that many of these results have been obtained by parents working on their own in opposition to institutionalised ‘education’; and it is true that many of these parents have ‘pushed’ the children without much concern for the social comfort of the children (see also child prodigy and franchise by examination, education and intelligence). The data available also highlights the extreme incompetence of most institutional ‘education’; but, of course, “it wasn’t invented here"” and, anyways, looking too closely at the data would not reflect well on the vested interests that run ‘the system’.
I do not want to suggest that things are not improving; they are, even if far too slowly. Analysis of IQ data over many decades shows that IQ is rising by about 1 standard deviation every 40 years. This change is about equivalent to a person who, 80 years ago, would have been regarded as average or ‘normal’ intelligence, but in today’s world would be rated as borderline mentally defective! It is abundantly clear that this change is due to improved educational standards, despite the constant bleating of the old Jonahs ‘that it was far better in the olden days’. This change has been identified and tracked by J. Flynn and is now known as The Flynn Effect.
Flynn argues that if the effect were real; we would now be seeing a veritable renaissance and claims that no such renaissance is apparent. I strongly dissent from this view—we have not come from horse and buggy to Concorde and computers in many homes and most western schools in a century without a very clear renaissance; but very much more does remain to be done.
Naturally, the person from 80 years ago was not, by virtue of some genetic difficulty, more daffy than the average person of today, but they were less aware because they were raised and educated in a far more simple world. Raised again with modern education, an 80 year-old with equivalent ability would, doubtless, have faired quite as well in current society. Paradigms matter.
Forcing the test results to conform to the normal curve
The ‘normal’ distribution relies upon
There are at least three separate elements contributing to an outcome IQ score, none of which can be guaranteed, or are even likely, to conform to ‘equal’ intervals. IQ is a very much more complex notion than height, or the number of your fingers!
First, an IQ test
is made up of single questions, each one of which is marked as either
correct or incorrect, thus the data does not conform to continuity. It
is not possible to claim that each question on a test has an ‘equal’
‘amount’ of IQ associated with it. The normal curve
In order to make the distribution of IQ appear to fit the normal curve, the following process is carried out. Take this next part slowly, give yourself time to think and return until you believe it!
It is to be noted that, even ignoring these forcing measures, measured IQ still does not in fact conform fully to the normal curve (see Is IQ normally distributed by Cyril Burt, 1963).
Second, it is individuals that are being ‘tested’ by an IQ ‘test’. In order to meet the assumptions of the normal curve, it is necessary that there is an assumption that environmental differences that are ‘causing’ the IQ to vary are, in the real world, occurring in even steps. This is clearly not the case, for if one person comes from an articulate family who attend to the questions of children and concern themselves with the child’s education, while another comes from a much less sophisticated family; this will clearly not result in some continuum of education. It would be easy to imagine that parents, at least to some degree, are either competent or not competent; rather than to believe that parents occur at every minute degree of competence in between, in some neatly ordered fashion.
Third and finally, there is no easy certainty that the effects of the various genes that may contribute to ‘intelligence’ are each of ‘equal’ effect.
Some naÏve optimism that this chaos will somehow result, by luck, in an approximately normal distribution may be innocently charming, but it does not enable a person to think clearly about how and where interventions may be effective in raising individual performance.
It is one thing to be able to recognise a ‘tree’,but quite another to know how to raise trees in an effective and healthy manner. One might hope to have an approximate idea of what ‘intelligence’ looks like and some ability to recognise ‘it’. Far more difficult is it to analyse ‘intelligence’, and then to learn to nurture and develop ‘it’ systematically and reliably.
What is intelligence? Well, one common, three-parts serious definition is “that which IQ tests measure”! (For more on this see the Turing test and intelligence) But how does a new born child get to the stage of dealing effectively with an IQ test? Intelligence is a symptom with a variety of ‘causes’.
Clearly, an individual must have a reasonably functioning brain, be fed regularly, be taught (or imbibe by one means or another) the basic mental ‘logical’ tricks required to answer the questions. Even to ‘work them out’ requires considerable knowledge of patterns. Much of providing an effective environment for learning is to know what not to do, rather than just acting automatically from the habits of your own ancestors.
Remember that the next generation are not going to have to cope with your life! In a fast-changing culture, they are going to have to learn to deal with their culture and their own world, your rules of thumb may often be counter-productive. This is thought to be a possible reason why the young seem to come already adapted to learn from peers, at least as much as from their parents.
Fundamental errors of education
The error of ‘trying to think’
[Cartoon 2 to follow—they all look the same]
‘Difference’ and ‘similarity’ depend upon context and your interests. The categories are most certainly
Which category you make, and which categories matter to you, will depend on your current attention and interest.
I can tell several species of conifers apart, most people cannot. Some people can taste the difference between different varieties of chilli, I cannot.
What you can distinguish apart is very dependent upon your experience and what you have been taught.
Again, the differences are not ”out there”by some holy edict.
‘Differences’ have no pre-determined rank of ‘importance’. Height is not ‘more important’
than weight, smell is not ‘more important’ than colour.
Categories are formed for purposes. Can this be eaten? Is this heavy enough to act as an anchor?
Why do we care if a person has frizzy hair or blue eyes? Is it because they are familiar or unfamiliar to us, and we learnt during our evolution to beware of the strange?
Comparing categories among the maelstrom of sense data that assails us gradually allows us to improve our lot. We may establish relationships between illness and smoking cigarettes. We may show a relationship between inundating children with images of violence, and those same children imitating violent acts (see children and television violence).
A test case:
In order to compare categories, it becomes essential to define those categories as well as you can. Defining categories with some ‘complete certainty’ is not possible, therefore you must cautiously do the best you can; and then remain very aware of difficulties of classification.
If one of your categories that you choose should be ‘black’ people, then you must decide upon exactly how black they must be in order to qualify for your category. It would be sensible to set up careful criteria. For example, blackness would be tested with a photometer (a device for measuring light levels) under standard pre-arranged conditions; perhaps a 500-watt photoflood lamp, 3 metres from the skin of the subject would suffice. Naturally you would want to pick a standard area of skin, such as the neck, while making sure to avoid reflections and shadows.
Of course, the amateurs who usually do IQ against ‘race’ do not bother with such niceties, in general they tend to just look and know. Some later ‘work’ has attempted to discern the ‘percentage’ of ‘blackness’ by trying to collect family histories of who was ‘black’ in the ancestry of ‘subjects’. Just in case you should wonder, the word ‘subject’ is ‘more’ ‘scientific’ than a mundane word like ‘person’. Unfortunately, deciding the amount of ‘blackness’ by skin reflectivity of ancestors is rather difficult.
It is genes that tend to make a person’s skin ‘black’ or ‘white’, but there is a slight problem or two. Sitting in the sun tends to darken the skin; therefore, it would be wise to keep intended ‘subjects’ indoors for a few weeks, or outside if you prefer; in order to remove any environmental confusions. For, remember, we are eventually going to attempt to separate ‘environmental’ from ‘genetic’ effects (see genes, IQ and paradigms).
Generations of our great ‘race’ ‘scientists’ have, for some obscure reason, attempted to correlate skin reflectivity with ‘IQ’. I must assume that they suspect there to be some genetic connection between skin reflectivity and the ability to answer some ‘logic’ questions, preferably at high speed. Why they have this notion I am not entirely sure, but ‘science’ must go where ‘science’ will. Why they did not choose blue eyes and IQ, or height or weight or toe lengths I am also unsure (see varieties of genes). But let me continue—as if you were intent on stopping me!
Right, we have the ‘blackness’ variable clearly defined and neatly lined up. Now I shall turn to the IQ variable, which is rather a great bit more complicated. We can be fairly content to assume that ‘blackness’ or even ‘whiteness’ is, at least, fairly simply related to a few, not very complicated, genes. IQ is a rather more difficult proposition.
Considering that, if there is any real difference in the distribution of scores (a most uncertain question even after decades of ‘study’), it is quite clear that a great deal of the distributions will still overlap. Thus, taking one member from the higher end of the lower distribution; that one person would clearly score higher that the greater majority of the higher distribution.
[illustration to follow: double curve]
Assuming that after great scientific endeavours,
it were possible to find some correlation betwixt skin shade and the ability
to answer closed-system questions at high speed, I remain completely mystified
as to just what possible use could be made of such a snippet of data.
For the correlation would give you not the slightest data concerning any
particular individual. Many ‘scientists’ have given considerable
tranches of their lives to this fascinating pursuit, but I have yet to
find the slightest plausible use for such data. If any reader can think
of any remotely
No, I’m not going to give you a great, complicated lesson on genes, that is available in a many a thousand places; but I do need to review some rather basic bits, in order that you may appreciate the marsh that underlies the neat, ‘simple’ notions that are casually pattered out in classrooms, books and media.
Genes, you will be told, are inherited in ones—they are either there or not there. This is basic Mendelism, to which is then added various complications about recessive genes and different versions of genes, and much else. Mendelian genetics work rather well for eye colours and for the crinkliness of sweet pea seeds. Other matters, like IQ start to complicate the situation; it is widely assumed that IQ is inherited to approximately 50%, the other 50% being down to environmental effects, and so it may be. But the logic is not as secure as many appear to think.
The general assumption is that IQ is effected by many genes, just how many is pure speculation at the moment; though the rapidly growing knowledge of genetics will doubtless advance our understanding. Not only do we not know how many genes are involved; naturally therefore, we also have no idea how much the contribution of various genes may make to ‘intelligence’. To incline you to caution, remember that some genes will contribute to bone structure and muscles—with no bone structure, you’d have nowhere to put your brain; while without muscles, holding up your head would prove problematic!
However, to keep things fairly ordered, let’s
It is generally assumed that genes are transmitted somewhat independently of one another, an assumption particularly popular with some fundamentalists. But, of course, a gene for blue eyes makes not much sense for a fruit fly, let alone for a tree. In fact, live forms comprise packages of genes, a very great many of which are common to every member of a species, and even common between species. For example, I have seen it emphasised that over 98% of human genes are identical with chimpanzee genes. While humans are clearly somewhat more intelligent than chimpanzees, it is very obvious that chimps possess no mean intelligence. In fact, any differences in the genes determining intelligence may be rather small with a few more recent mutations defining the differences which we, perhaps for vanity’s sake, are rather inclined to exaggerate (see also Emergent behaviour).
Plomin, page 34 – 35, reads as follows: “he second is the adoption study, which separates genetic and environmental influences. For example, when biological parents relinquish their children for adoption at birth, any resemblance between these parents and their adopted away offspring can be attributed to shared heredity rather than to shared environment, if there is no selective placement. In addition, when these children are adopted, any resemblance between the adoptive parents can be attributed to shared environment rather than to shared heredity.” Now this is the most incredible, egregious nonsense. Let us analyse part of this quotation from Plomin in order to appreciate the full enormity of this idiocy. According to the statement above, any resemblance of the adopted children to their new parents must be due to environmental influence, if they have two hands and five toes and the adoptive parents also have two hands and five toes; well, obviously that is an environmental effect!! (see varieties of genes). However, if the child turns out to have an inclination to brush their teeth in the mornings just like their original parents, that then must be a genetic effect.
Consider a child adopted by an elephant—go on, you can do it if you really try! If the child ate food and their parents also ate food, why, then clearly eating food is genetic; but should they incline to eat current buns thrown to them and their parents never ate current buns, clearly the eating of current buns must be environmental. Now this last is the foundation for further deep thoughts. Is the eating genetic and the type of food eaten environmental? Remember that environment cannot be separated from genes.
The inclination to eat is shared by elephants and
by humans, as even is the ability to think. The inclination for various
humans to think has quite a lot of common ground even with elephants
Be clear that average differences do not apply
to individuals. These genetic versus environmental ‘studies’
are inherently statistical by their structure, they are average guesses
or generalisations and, therefore, do not apply to any particular individual.
If, by careful education, the ‘thinking abilities’ of individuals
can be changed, and it is clear that they can, all that the averages tell
you is the
Statistics are useful for governments planning for large numbers. Examples would be: deciding how many hospitals or schools an area needs, on average, for the local population; how many surgeons in a speciality were likely to be required in 10 years time and, therefore, how many training places will be needed right now. For the last example, to achieve approximately correct numbers, it would be necessary to assess what percentage were likely to drop out and how many were likely to go abroad for, what they perceived to be, better conditions.
Given average scores in IQ tests, a teacher can have a rather rough idea of how well a pupil is doing relative to a test population and, therefore, how well their reading is advancing compared with their general understanding. Testing could also be used to identify weaknesses in performance, thus indicating what the person had not yet understood clearly (see educating intelligence).
What testing cannot do is tell you why a person got the way they are, nor can it give you a clear indication how much can be done about it at some later stage. Because not enough has yet been clearly analysed or formalised, it often takes a teacher of considerable skill and experience to identify and correct the problems a child has inherited from home and genes. Such pedagogic ability remains in very short supply, and teacher education is usually very weak.
In other words, averages tell you very, very little about individual cases. In order to understand the use and interpretation of statistics, it is essential that this lesson is thoroughly learnt and internalised, to the extent that it becomes instinctual.
Correlations may give you hints of where to look, they cannot give you anything more. When studies continually pick out cigarettes as dangerous to health, you may do well to throw the filthy things away; but detailed chemical links have to wait for much more investigation. And your particular granny may still smoke until she is 90 and get away with it.
What I am proposing and describing widely on this site are better ways to think about complex situations. Suppose that such methods are indeed more effective, and consider further that such methods were widely practiced in Western education. Then it is likely that expectations of IQ measurements and personal development would be near to unrecognisable, when compared with current results. My experience leads me to regard such a fundamental cultural advance to be well within reach, with better educational methods (see franchise by examination, education and intelligence).
Thus, I suggest that a change in basic thinking paradigms would nullify most current educational and ‘IQ’ expectations. Such a change, I naturally regard as very positive and to be a harbinger for a much more successful and productive society. Appropriate links are provided throughout this document for following up details of the changed educational paradigm I am seeking.
Most every well-educated 16 year old knows more maths and physics than did Newton, one of the great contributors to the advance of human knowledge. Set them both down to do a pre-university exam and it is probable that an 18 year-old would score better. It is clear from evidence that a modern child will general score considerably better on IQ tests than their fairly recent ancestors. The difference is not genes; it is paradigm, the way information is now organised and taught. The idea that Newton was somehow less intelligent than a large percentage of the population makes no sense. The idea that something called genetic intelligence has advanced radically over a very small number of decades, again, makes little serious sense. What has advanced, at incredible rates in the last one hundred years, is the sum of available human knowledge. That process is continuing apace and its insights should be incorporated into educational and political processes.
‘Scientists’ widely rely upon sponsors or wages for their daily bread. In universities, they rely upon ‘results’ for fame and promotion. Finding correlations widely counts for ‘results’. You don’t become popular if a tobacco company is paying your wages and you come up with ‘results’ that show that cigarettes are harmful. You don’t make yourself useful at the Megaoil Corporation by finding problems with pollution. You don’t have published in ‘learned journals’, papers showing no correlational relationship. You don’t receive grants from the PioneerFund for finding blacks are scoring as well as whites. You don’t get promotion at Drugsforall by constantly finding bad side effects, or even for finding no effects at all (see placebos and anti-depressants...).
To deal with this widespread problem, ‘scientists’
often indulge in what is called
If you buy a lottery ticket, you have one chance of ‘winning; if you buy two you have twice the chance, and so on. If you seek a correlation between two items, there is but one chance of ‘getting a result’. If you deal with 3 items, you have 3 chances: A-B, B-C and A-C. With 4 possibilities, you have 6 chances! And so on. You want significant results—try a dozen different variables, and now you have 66 possible pairs and thence 66 chances of a ‘result’!
If you have 66 chances to achieve a result, or
preferably the kind of result you want, you are a lot better off than
with just one go. When you publish your results, you carefully refrain
from mentioning that you had 66 tries or, if you are more honest, you
mention it in passing, or in an obscure footnote. The headline will read
something like “
Very great caution is advised when reading ‘scientific’ ‘reports’, always check who is paying the ‘scientist’ for their ‘work’. Always ask the questions that are not being emphasised. Scientists and science are not the innocent disinterested world you are widely encouraged to believe.
You cannot know what is in the mind of another.
Many humans hold superstitious beliefs that there exist in the real world distinguishable ‘races’ or ‘cultures’. Race is the more outlandish of these superstitions and, therefore, the simpler to analyse. I shall therefore start with that delusion.
Genes naturally vary in frequency around the world; in particular, a new mutation will, of course, spread from the location in which it arises. A member of a local group with a particular gene may become an explorer cast up on a pacific island, or be carried off by a slave ship. Thus, their genes may be transported large distances to other places where, once again, they may spread from a new centre. Other genes may hop from village to village over decades, or hundreds, or thousands of years.
Much has been made in recent years of the fact that, at the very top of sport, people with ‘black’ skin have dominated sprint racing. From this, some simple folks tend to arrive at the notion that there is a ‘black’ race with distinctive features. Perhaps, they assume it is the ‘black’ skin that enables these people to run so fast that a few of them can beat most other people on the planet who happen to have skin which reflects more light.
Of course, such a notion is very dubious; there is no reason at all that the genes which result in a darker skin have any relationship to how fast these people can waggle their feet down a short length of track. The idea that there is a black ‘race’ is about as meaningful as the notion that there is a fast foot-waggling ‘race’. Genes are not people, genes travel their own routes; fast foot-waggling genes don’t hang around making sure they are taking a dark skin along for the ride, or vice versa.
There is no such thing as ‘race’
In order to define a ‘race’, it would be necessary to choose a list of genes (or other recognition marks) and then make some decisions. Shall we suggest 10 such markers or, perhaps, 20? Shall we put a person in the box marked ‘the fast feet-waggling race’ if they have 6 out of ten markers (60%), or will we demand all 10? Which of the markers shall we choose? Exactly how ‘black’ must the skin be? Just how fast must they be able to waggle their feet? What if they have the fast foot-waggling gene, but through a life of chip and chocolate eating they weigh 150 kilos? Clearly, these earth-shattering decisions will require well-funded government committees of race technicians just to make sure there are no slip-ups.
You will see from the above, that similar techniques will be needed in order to define a ‘culture’. A list again will be required such as “does this person speak ‘English’?” Be aware that every person who speaks ‘English’ has a differing concept of the meaning of every word in ‘that’ language. Further, some users of English know a thousand or two thousand words, where others may know ten or twenty thousand words. Is each of these people to be regarded as ‘speaking English’? Will 5 words do? Or 367? Decisions decisions decisions!
Can they play cricket? Do they know the rules? Are they any good at cricket? Must they like cricket? How will you tell? What if they have one leg? Is it a square leg?
Do they like warm beer? Can they hold down 10 pints without throwing up? We must know.
How many items ticked off on the list are enough to qualify as a full-blooded English citizen? How many items are required on the list? Who is going to make the list? What about marginal cases where the aspiring member of the English club can only down 9 pints? Is there an allowance for weight or sex? What about requiring some ‘English’ genes?
Next week we’ll do ‘religion’! And witches!!
For your homework you will be expected to have read….
|Related further reading|
|Intelligence: misuse and abuse of statistics||drugs, smoking and addiction|
|establishment psycho-bunk||cause, chance and Bayesian statistics|
|on temperature and statistics||correlation - a little knowledge is dangerous|
|For related empiric reasoning documents, start with
Why Aristotelian logic does not work
I refer to the first three books for background reading, but the argument that I am presenting is directed to the dubious use of statistical reasoning in the matter of ‘IQ’, not primarily to the content of these books. These books sometimes look at parts of the overall difficulties I have analysed above, and are also useful or interesting of themselves. But the cited books are not highly focussed on the logical framework with special regard to the ‘IQ’ problem, which has been my prime direction in this document.
Genome: The autobiography of a species in 23 chapters
This is a useful general read, outlining current thinking and progress in understanding of the gene.
|R. Plomin et al.||Behavioural Genetics||[out of print] 1997, 3rd ed, New York, W. H. Freeman, 0716728249|
|E. Sober and D. S. Wilson||Unto Others: The Evolution and Psychology of Unselfish Behavior|
|Bonobo: the forgotten ape|
|R J Hermstein and C. Murray||The Bell Curve|
|C. S. Fischer et al.||Inequality by Design,|
|emipric (or empirical) : based or acting on observation or experiment, not on theory.|
|See also Responsibility and mental set.|
| p.84, Plomin et
al., Behavioural Genetics
This book is by far the best I know of on this subject. It is both accurate and contains considerable information. Unfortunately, it is not extremely well organised or elegantly written.
|See also Hume on cause.|
|See universals and individuals.|
|See the error called ‘equality’.|
|Genes can have more than one effect; effects can be both positive and negative for the same gene. It is incorrect to think of most genes as the cause of disease, most genes make you what you are and that includes being alive! But some genes give both positive and negative effects. A famous example is the sickle cell anaemia mutation/gene, which can both cause anaemia and give some protection against malaria.|
|For further discussion, see Sober and Wilson, especially chapter 1, and in particular from p. 38 on.|
|For an example, see Plomin, p.60, on mice and open field activity.|
|A further example of a confused average is found in the environment of flying a fighter plane. These machines make so much noise that it causes problems to the pilot. Some years ago, it was found that feeding sound waves to the pilot’s head-set, which were the inverse of the sounds in the cockpit, the two sounds would cancel out, thus much improving the pilot’s working environment.|
|See also correlation.|
|My concern is consistency with empiric and pragmatic reality, not some artificial notion of internal ‘logical’ consistency. See also this box about consistency for more than you will probably want to know!|
|Standard deviation: a measure of how measurements are spread in a set of data, which data is assumed to conform to the normal curve. I do not intend to cover this further here, but it can easily be found in any primer on basic statistical studies, including Plomin p. 282, and at a multitude of web sites.|
This would widely be referred to as 2 generations. A generation is usually approximated as 20 or 25 years, that is to say, the time between birth and that child in turn giving birth – and it can become a lot more complicated than that.
|Also known as the Gaussian or bell curve. I shall not cover this further here, but information can easily be found in any primer on basic statistical studies, and at a multitude of web sites.|
|The normal distribution approximates the binomial distribution for large numbers. I will not cover this further here, but details can easily be found in any primer on series, with further information at web sites and in books on statistical studies.|
|Required by the normal distribution.|
|That is 5% of all the takers of the test, i.e. 5% of 100%.|
|More on this can be found in Inequality by Design by C. S. Fischer et al. Click for more comment.|
|Hallucinations can include misinterpreting patterns of shadows as ‘ghosts’ or unusual sounds as ‘voices’.|
|By the mid 1860s, Mendel, a monk, had worked out the basics of genetic inheritance, but no-one took much notice of his results for nearly 35 years. The work of Darwin and Galton would have been helped had they been aware of the significance, or even the existence, of Mendel’s work. The history of Mendel and his genetic studies is interesting for those who are curious about scientific development.|
|Look up, for example: Down’s syndrome, fragile X and phenylketonuria.|
|Not only are chimpanzees our closest evolutionary neighbours, we are theirs. In other words, they are closer to us genetically (even as much as 99.4% DNA similarity—see here) than to any other ape or monkey (see de Waal & Lanting, p.5).|
|Another term for in-house magazines.|
|12 times 11, divided by 2. That is, the number of items, times the number of items minus one, all divided by two. A first-step probability lesson will show you why.|
Most mutations are not viable and, therefore, will not spread at all! I am concerned here with mutations that have little effect, or those that confer some advantage.
email abelard at abelard.org
© abelard, 2002, 23 june
the address for this document is http://www.abelard.org/statistics_intelligence.php