Many readers of this blog are familiar with the term ‘general intelligence‘ or g. It is sometimes defined at the most raw form of human intelligence: the ability to handle cognitive complexity. When it come to testing mental abilities, g can manifest itself as crystalized or fluid intelligence. Yet, both factors involve pattern recognition and analogical reasoning. Paul Cooijmans has this to say:
. . .Pattern recognition and Reasoning are, as it were, two aspects or processes of the same – intelligence – that each cover all of the lower factors. To perform a mental task, one first has to recognize pattern, and then one can reason. Reasoning is the menial helper of pattern recognition. It does the straightforward, linear processing, the labour. . .
So I ask: what differentiates crystalized from fluid IQ tests if both types involve the same basic reasoning processes?
A mental ability test will contain questions with varying structure and content. It might include analogies, antonyms, calculations, cultural history, and specific items on things one learns over the span of one’s lifetime. However, the content of those questions has very little to do with differentiating crystalized from fluid IQ tests. This is due to the criterion of the indifference of the indicator. Grady Towers explains:
This principle was enunciated by Charles E. Spearman in 1923, and says, in effect, that the specific content of an item in an intelligence test is unimportant, so long as all persons taking the test understand it. No item can be without content, of course, but the principle emphasizes that the content of an item or a test is merely the vehicle for measuring g, and is unimportant in itself. That’s why a test of verbal analogies can be used to estimate an individual’s mathematical ability. Or why a test of number series can be used to predict a person’s ability to write poetry or solve anagrams. That’s why intelligence is conceived to be a general ability, and why it’s given the symbol g. . .(It may seem at first glance that the existence of fluid g and crystallized g are violations of the same principle, but this is a misunderstanding. The distinction between culture fair tests and culture loaded tests is often mistakenly thought to be the same as the distinction between nonverbal tests and verbal tests. This, however, is simply not the case. Verbal items (or any other kind of item) can be used, in principle, to measure either fluid g or crystallized g, depending on how much prior knowledge is necessary to understand the item. The verbal items on the LAIT, for example, are very nearly pure measures of fluid g. They make little demand on a person’s verbal knowledge, but large demands on his ability to “educe relations.”). . .
This is an interesting point. It seems that what makes a test load on fluid rather than crystalized g isn’t the content, or lack thereof, but the familiarity of the content by the testing population. More exactly, if the testing population is sufficiently familiar with the content of the questions in an IQ test, then it tests much less for crystalized g and more for fluid g. This has interesting implications for the SAT, GRE, and LSAT.
Let’s begin with the older version of the SAT. It’s safe to say that almost every student in high-school is sufficiently familiar with the content of the quantitative section, the mathematics, etc.. It only requires knowledge of algebra and geometry that most students learn by their junior year. It seems prima facie clear that the quantitative section is really mostly testing fluid g even though it consists of much learned content. The verbal section is still a test for crystalized g—not every student is familiar with the vocabulary, for example—but not as much as we might think. I suspect that it evenly tests for both crystalized and fluid g.
But I’m more interested in how Tower’s point applies to the GRE. Disregard the writing section, and consider only the verbal and quantitative sections. If differentiating between crystalized and fluid g depends on the homogeneity of the population being familiar with the content of these sections, then it seems that the verbal section is actually mostly a test of fluid g for those studying the humanities. Here is my reasoning. Take the humanities to consist of studying history, literature, languages, law, philosophy, classics, art, and music. What do all of these disciplines have in common? Undergraduates here spend a great deal of time reading and writing (this is true for art and music history too). This involves developing reading comprehension, vocabulary, and constructing proper sentences—things tested in the verbal section. Undergraduates are, therefore, sufficiently familiar with the content of the verbal section, which thereby ceases to be the focus of what’s being tested in the verbal section. We can, therefore, rank the undergraduates in the humanities by fluid g by looking at their verbal GRE scores. We can in principle do the same with the quantitative section relative to undergraduates in the sciences and engineering, but the section itself improperly discriminates due to its low ceiling. However, you could rank mathematics undergrads by fluid g by looking at their mathematics subject test scores, and you could rank physics undergrads by their physics subject test scores.
We don’t glean anything new from this; obviously, the brightest students with the highest crystalized or fluid g will tend to score the highest on aptitude tests. But we might be able to take this lesson from the criterion of the indifference of the indicator and apply it to new areas.
dan
17 September 2011
“This involves developing reading comprehension, vocabulary, and constructing proper sentences—things tested in the verbal section. Undergraduates are, therefore, sufficiently familiar with the content of the verbal section, which thereby ceases to be the focus of what’s being tested in the verbal section.”
Your hypothesis has quite the counter-intuitive ring to it, I’ll grant you that, but unfortunately it’s just plain incorrect.
Much of the vocabulary that is tested on the GRE is unknown to even the most voracious readers and linguistically adept undergraduate students. Quite frankly, you don’t simple stumble across words like “apotheosis” during the course of ordinary or even advanced (e.g., scholarly) reading unless reading flowery 1st Circuit court decisions is your cup of tea. The test REQUIRES memorization of these words in a crystallized knowledge form.
Obviously I’m ‘projecting’ a little bit here, but I took the test twice. The first time I relied on the fact that I’ve always had a solid vocabulary, so I spent most of my time studying for math. I did great on the math section, but only found myself in the 80th percentile for verbal, so I resigned myself to take the test again. This time I employed wrote memorization to absorb all of those words that I had literally never seen before in my life despite my affection for reading random scholarly articles on a near-constant basis. My percentile score jumped up about 15 points.
QED