Warning : long posting. Doug:
R-squared per se may or may not be indicative of the 'scientific value' of the finding. On the one hand, R-squared is often interpereted as the 'improvement in prediction,' mening % reduction in variance on the dependent variable (which is the 'error' or deviation from the mean) by knowing the values on the independent variable. Thus, a 10% improvment is still a non-zero improvment i.e. better than nothing. On the other hand, however, even a high R-square (say, 60% reduction of error) does not mean much, if you work with a bullshit model to begin with.
To illustrate that with a simple example, if you study the relationship between the height of siblings, and you regress the height of the younger siblings (the depenedent variable) on the height of the older siblings (the independent variable), you will probably get a reasonably high R-squared, meaning that there is a strong correlation between the two variables in question. Yet, despite the high value of R-squared, th emodel itself is bullshit, beacuse th ecausal relationship it stipulates is spurious. That is, even though the statistical correlation is high between these two variables, the height of the older sibling is NOT the cause of the height of the younger sibling. The high level of correlation is a mere coincidence that results from the fact that both variables are affected in the same way by a third variable - the height of the parents - which is not included in the regression equation.
Of course, in the example I just cited we know beforehand that the relationship between the height of older and younger siblings is spurious, because we understand that the height of children is often affected by the height of the parents, but other than taht, there is no connection between the hight of siblings. In other words, we already know what the cause of that height is, and we use the regression not to determine the cause, but to make the prediction more accurate. So from that standpoint, it makes sense, say, for school officials, to regress the height of the pre-schoolers on the height of their siblings already in schools - to predict the height of today's pres-schoolers when they reach the school age. To reiterate, this is just the practcal aspect of making prediction from the available information WITHOUT making a cause-effect argument.
However, finding a causal relationship using the regression method takes much more than finding strong correlations (high R-squares). I mean, the regression models can be very sophisticated in that respect, but now matter how sophisticated your model is - you have to do one thing before you start crunching any numbers, namely, construct your causal model. No regression will do that - you can use regression results to disprove or support models already constructed, but not to construct the model.
So my problem with socio-biology (or so-so biology, as one of my professors disparagingly called it), that is, attempts to establish a causal link between biological factors and social behavior is that it does a really sloppy job in constructing its models. The generations of Murrays & Co. screw up royally on two fronts: in defining what they want to explain (the outcome), and in defining what causes what they want to explain. That is why I think they are quacks, not doctors.
1. Defining what is to be explained. The first major problem with socio-biology is that it is very fuzzy about what observable phenomenon it tries to explain. Of course the root of the problem lies in that the quacks that practice this kind of 'science' really want to accomplish what science is not equipped to do - namely to 'prove' moral superiority of one group over another. However, since 'moral superiority' is not an an empirically observable fact, these qucks usually look for different proxies, such as social status, income, educational achivements, or intelligence.
Of course, studying variations in social status or wealth can be a legitimate social science, but socio-biologists do a subtle trick here. Namely, they assume meritorcatic ideology claiming that status and wealth are achieved largely through individual merits (rather than through social opportunities) which, in turn, are identified with mental aptitude. Then, they foucs on finding factors that are supposed to explain differences in mental aptitude.
This is mental prestidigitation pure and simple. Mental aptitude, or intelligence are absolutely meaningless, they have no empirical content per se, unless they are linked to some observable behavior. Their real value for so-so biologists lies in their meritocratic connotations so dear to the college-processed minds ('we the educated folks are better than everyone else by virtue of our mental prowess'). However, with that asusmption in the background, these prestidigitators switch the focus and claim that mental capacity is measured by the performance of supposedly 'objective' cognitive tasks (rather than social status and wealth), such as those used by the generations of the IQ tests.
This is charlatanery of the first class that makes one forever wonder what these master of illusion are trying to explain: why the subjects differ in performing on an IQ test - a dull, uninteresting , and inconsequential endeavour, or why the subjects differ in 'social mewrits' and 'moral worth,' an unscientific but emotioanlly charged topic. The trick hinges on the dubious correlation between IQ and the performance in the "real" world - which is sneaked into the argument rather than explicitly tested.
Now, the validity of IQ tests as the measure of intellgence is highly questionable, as aptly shown in Gould's book _The mismeasure of man_. To summarize his argument, IQ test is composed of a multitude of tasks which are supposed to be indicative of some mental capacities. The problem is, however, how many mental capacities? Since mental capacities cannot be observed, their existence must be inferred. And here we come to contact with regression again.
The technique used to link the multiple indicators (IQ test tasks) to a small number of mental capacities, called factor analysis, is a regression-based procedure that treats that unobserbavle mental capacity as a dependent variable, while the observed indicators (test tasks) are independent variables. So the relationships between that unknown mental variable and each of the indicators included in the test can be written as a series of regression equations. The problem is, however, that there is no unique mathematical solution of those equations, unless addtional and arbitrary assumptions are made. To illustrate, suppose there are only three indicators: x1, x2 and x3 (the test tasks). Then:
y1 = b1*x1 y2 = b2*x2 y3 = b3*x3
where y1, y2 and y3 are the unknown values of the hypothetical variable representing menatal capacities; x1, x2 and x3 are known scores on the indicator tasks, and b1, b2 and b3 are unknown regression coefficients representing the relationship between the unknown mental capacities and the known indicator scores. For the sake of simplicity, I skipped some of the other expressions that usually go into these equtions (intercepts and error terms).
Now anyone with the 6th grade math skills can tell that this system of equations has no unique solution - there are too many unknowns (six: three y's and three b's). But that is hardly an obstacle for missionary zeal. If an IQ warrior assume that there is single mental capacity - a highly desirable number because it allows arranging individuals in an ascending hierarchy of perfection - there is a light at the end of the tunnel. A single factor means that the unknown y-values are equal to one another, i.e. y1=y2=y3, hence our equations can be re-written as
y1 = b1*x1 y1 = b2*x2 y1 = b3*x3
Now, instead of three equations and six unknowns we have three equations and four unknowns (y and b's) - still one too many for a unique solution, but if we further limit the range within which the unknowns can vary, we can find a solution by a trial-and-error process (called iterations in the stats lingo).
So presto, by the researcher's fiat we can solve the problem both mathematically and politically. Of course, when the number of indicators (and equations) increases, we have a choice between declaring the existence of a single factor (or 'general intelligence') to which all indicators are related, or multiple factors (either realted or unrelated to one another) different indicators being related to different factors -- and still be able to find a solution through the iterative process.
So the bottom line is that the interpretation of the performance of the cognitive tasks included in an intellegence test hinges on the researcher's fiat, or a decision he or she must make so the problem can be mathematically solved. That fiat ranges between choosing a single factor representing 'general intelligence' and multiple factors representing diverse mental capacities. In fact, the researcher must enter the number of factors he/she wants the comupter to find (SPSS uses defaults, but that does not change the story). But whether one factor or many, the solution will 'fit' the data anyway (i.e. be consistent with the recorded performance scores on the indicator tasks). So the choice is, in fact, political - so-so biologists opt for a single mental capacity (general intelligence) because it allows a hierarchical ranking of individuals better than multiple capacities.
And that is the second, not immediately apparent, trick in defining what these quacks try to explain. Not only the audience is lead to believe that mental capacity is tantamount to social merits and moral worth, but it is also tricked to believe that such capacity is singular, thus allowing hierarchical ranking of human beings on a single scale.
2. Defining what causes what is to be explained. Having tricked their audience that IQ is an indicator of a single individual 'merit' and thus 'moral worth' - these prestidigators do another, this time a very crude trick.
Even accepting the highly questionable validity of IQ as a measure of intelligence, there is still room for legitimate research to find factors that may be related to it. Those factors usually fall into two popularly defined groups, culture and nature. Although the separation of what goes to 'culture' and what goes to 'nature' is often problemtic, it is still possible to test the culture vs. nature hypothsis by using a regression model.
One way of doing it is the 'nested models,' or introduction, in stages, different sets of variables that represent "culture" and 'nature" and see what change in the R-squares that produces. So, if we first include the variables representing 'culture' (socio-economic status of the parents, amount of education, etc.) and record the R-square i.e. the % of variance these variables explain, and then we introduce variables representing "nature" and these variables add an addtional 10% to the R-square - that finding by itself means that 'culture' does not tell the whole story, and 'nature' adds something significant to it.
The problem is, however, that while we can easily identify variables representing "culture" - it ain't so easy with the 'nature' part. We can of course, identify factors such as birth defects, nutrition, exposure to diseases, etc. which are more or less unambiguoulsy "nature" (and ignore the social aspect of them) - but that poses a serious problem for the so-so biologists, because these factors are not uniquely related to groups that are supposed to be 'superior' or 'inferior'. In other words, both Blacks and Whites can have birth defects, poor nutrition, etc.
Of course the scientifically proper way of proceeding would be to find a genetic combination that (i) is unique to ethnic groups and (ii) is known to affect cognitive capacity. However, that is not the way so-o biologists proceed. In fact, they are doing a real hatchet job here.
Instead identifying a genetic trait that meets both of the two conditions outline above, these clowns find a genetic trait that meets only the first condition -- being unique to an ethnic group -- and want us to believe that that trait is also related to cognitive capacities. In other words, they want us to believe that the genetic trait that causes variations in skin color or facial features also causes variation in cognitive capacities.
Even for someone whose knowledge of genetics is rather limited, that proposition sounds like utter bullshit for one reason alone - these clowns have no way of knowing that, simply because only a very small portion of human genens have been mapped and even a smaller portion linked to specific physiological or cognitive functions. In other words, a paper and pencil pushing social commentator claims to know more about genetics than geneticists doing the actual reserach. Bullshit squared.
So to summarize, the Belle KKKurve variety of 'research' is a real hatchet job not science - because the variables are very poorly defined or invalid indicators of what they are supposed to indicate. Seeing those shortcomings requires nothing more than basic knowledge of research methodology, as I demonstrated above.
What really intrigues me is how did this pseudo science get published? There are only two possible explantions: editors at the Free Press (Belle KKKurve publisher) and Co. are idiots incapable of telling good research from a hatchet job, or that they had their reasons behind publishing bullshit. I find the first explanation unlikely. I think they, or rather their owners had a good reason: as the captains of industry define the new world order, the public is instigated to fight the culture wars over 19th century issues, and thus not to pay the attention what the captains are doing.
Conspiracy? I prefer another term - 'strategic planning.'
Regards,
Wojtek Sokolowski