CHC Theory, Cognitive Assessment, Psychometrics

g Factor Removed from Correlation Matrices, Vizualized

As a follow up to yesterday’s post, I extracted a g factor from the matrix of each battery and made these pictures of the residual matrices. I filtered out all the negative residuals to de-clutter the image.

KABCNog DASNog WISCNog WJNog SB5Nog

I am not sure what can be learned from such pictures other than getting a sense of the magnitudes of the the differences in strength of the different factors. You can see that Gc is generally much stronger than the other factors (except in the case of the SB5).

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CHC Theory, Cognitive Assessment, Psychometrics

Correlation Matrices from Five Cognitive Ability Tests, Visualized

Sometimes it is interesting to look at something familiar in a new way. Here are the correlations among the subtests of five major cognitive ability batteries (data comes from the standardization samples). Stronger correlations are thicker and darker. What do you see?

WJCorrelations KABCCor SB5Correlation WISCCor DASCorrelations

Figures made with semPlot.

Note that color schemes across batteries are not theoretically consistent.

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CHC Theory, Cognitive Assessment, Principles of assessment of aptitude and achievement

Needing Glasses for the Ears: Explaining Phonological Dyslexia to Parents

ME: Tell me about why you decided to be evaluated.

ADULT CLIENT: I think I might have HDHD and dahlexia.

ME (unsure): You think you might have ADHD and dyslexia?

ADULT CLIENT (embarrassed): Right, ADHD…but I think I have dahlexia, too.

Auditory processing problems are among the hardest problems to explain. If you were to give parents a simple, technically correct definition of auditory processing (e.g., the ability to perceive patterns in sound), you are likely to be misunderstood. Parents know that “auditory” has something to do with hearing and are likely to think that their child has a hearing problem or has difficulty understanding speech. Auditory processing is the ability that I spend the most time explaining so that I do not cause confusion. If a child has auditory processing problems, I say something like this to the parents:

Auditory processing is not the ability to hear. Your daughter can hear just fine. The problem that she has is difficult to explain so I am going to start by comparing her problem to vision problems (She does not have a vision problem, either. I am just comparing the two problems.). Near-sighted people are not blind. Up close, they see well. Things that are far away, however, are blurry. Making lights brighter does not help; near-sighted people need glasses. In the same way that someone who is near-sighted is not blind, your daughter is not deaf; she is not even hard of hearing. However, for her, speech sounds are a little blurry for her. It is as if she needs glasses for her ears, to make sounds clearer. Unfortunately, no such thing exists. A hearing aid would not help because it is not the volume of the sound that is the problem.

The problem is that the sounds in words are hard for her to distinguish. I’ll explain what I mean. Words are made of different sounds blended together. We usually think of the word cat as one big blob of sound – /cat/. However, whenever we need to, we can break cat into three separate sounds – /c/ /a/ /t/. With a word like cat, this is easy to do and even your daughter does not have much trouble with it. However, when she hears a long word or a word with a lot of consonants bunched together, it is hard for her to break the word into individual sounds. For example, the word strength has only one syllable but it has six sounds – /s/ /t/ /r/ /e/ /ŋ/ /θ/. With cat there are three letters, one for each sound. With strength it gets complicated because the n and the g form a single sound /ŋ/ and the t and the h make the sound /θ/. If I pronounce both the n and the g separately – /stren/ /g/ /θ/ – it sounds strange. With a word like strength, your daughter can hear the first sound and the last sound but gets lost in the middle and starts leaving sounds out or guessing wrong sounds.

Now, if you say the word strength out loud, she can hear it and she understands it. She is not confused. She can even pronounce the word correctly. Why? I’ll make another comparison to vision. When you are driving and you see a road sign from far away, you might not be able to see every letter on the sign distinctly. However, you might be able to make out the shape of the word and because you know what different signs are likely to say, you can tell someone what the word on the sign is. This is sort of like what you daughter can do. She hears the word and can say what it is based on the overall features of the word. However, she has difficulty hearing each of the sounds as distinct from each other.

If the only thing that were wrong was that she could not split words into different sounds, there would be no cause for concern. However, it turns out that this ability to hear the sounds in words as distinct rather than as big blobs of sound is really important to learn to read. If you can hear the different sounds in words, you can hear why the words are spelled as they are (if they are words with regular spelling). If you are reading and you come across a new word, you can sound it out like they do on Sesame Street.

Children who have difficulty hearing speech sounds distinctly, often have trouble learning to spell and to read. Most children learn their letters and the sounds they make and then can figure out how to read and spell most words (at least the ones with regular spelling). Without the ability to sound out a word, learning to read and spell depends mostly on memorizing each word one-by-one. New words have to be taught explicitly to the child. Some children with this problem figure out how to work around it; some have help. When children with this problem fall behind in their ability to read, we call the problem dyslexia.

I want to be clear what dyslexia is and what it is not. You may have heard that dyslexia is when children see words backwards. This is not true. I have been doing this for a long time and I have seen many children with dyslexia. Not one of those children saw anything backwards. However, many of them jumble their letters and, like younger children, sometimes they write their letters backwards. This is not due to seeing things backwards. Instead, these mistakes are due to ordinary memory errors. If you give me a long list of groceries to buy, I might remember most of the items on the list but I might not remember them in the right order. When children with dyslexia learn a new word, they might remember which letters were in the word but might forget their order. They will probably remember the first and last letters but might mix up the middle letters. If they could sound out the words, they would be able to see that the order was wrong but that does not happen as often as it otherwise would.

The reason that young children often write letters backward is that letters are very unusual. Most things have the same name no matter what angle we view them from [I demonstrate with a pen, rotating it and turning it]. This pen is called a pen no matter what I do with it. Letters are not like that. The letter b changes its name, depending on how it is rotated or flipped. It can be a d, a p, or even a q. A backwards j does not even have a name. This is weird for children and it takes a while for them to get the hang of it. Children with dyslexia have a bit of a problem remembering which sounds go with which letters and thus continue making these sorts of errors longer than do most children. The problem is blurry sounds, not backwards vision.

Of course, I would probably not say all this in one long speech but try to make the discussion more interactive.

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.

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CHC Theory, Cognitive Assessment, Principles of assessment of aptitude and achievement

Explaining the difference between vision and visual-spatial processing to parents.

Vision is the ability to see something and visual-spatial processing helps you make sense of what you see.

Vision is the ability to see what is there. Visual-spatial processing is the ability to see what is not there, too, in a sense. With good vision you can see what something looks like; with good visual-spatial processing you can imagine what something would look like if you turned it around or if you were standing somewhere else or if something else was covering part of it.

With good vision you can see objects; with good visual-spatial processing you can see how they might fit together.

With good vision you can see a bunch of lines and splotches of colors; with good visual-spatial processing you can see how those lines and splotches of color form meaningful patterns.

This is the ability that sculptors, painters, designers, engineers, and architects need. It comes in pretty handy for the rest of us too.

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.

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CHC Theory, Cognitive Assessment, Principles of assessment of aptitude and achievement

IQ Tests: Is Knowledge of Useless Knowledge Useless?

Now I wish I could write you a melody so plain

That could hold you dear lady from going insane

That could ease you and cool you and cease the pain

Of your useless and pointless knowledge

– Bob Dylan “Tombstone Blues”

There is much pleasure to be gained from useless knowledge.

– Bertrand Russell

When critics look though the items in a general verbal information test, they, with some justification, sometimes sneer at the usefulness of the content. Is there any money in being able to list off the names of the planets? Can I oppose injustice, armed with my knowledge of state capitals? Will any babies be saved because I know who Julian the Apostate was? Probably not.

Many (most?) facts I have learned are unlikely to ever be of practical use. If I knew which ones they were, I might happily surrender them to forgetfulness. However, because it is impossible to know what might be useful in the future, I will hang onto my useless and pointless knowledge for a little while longer, thank you very much.

When Francis Bacon wrote parenthetically that “knowledge itself is a power…” in the context of an argument attempting to discredit the theological beliefs of certain religious sects, he probably did not mean the phrase in the sense that it is invoked today (i.e., that knowledge confers power). However, the phrase “knowledge is power” has survived because it resonates with our experience and pithily expresses something that is increasingly true in an age that gives increasing returns to those who can profit from information.

Good items in a test of General Information should not be about random facts. Easy items should not be merely easy (e.g., “What is the color of the sky?”). Rather, they should test for knowledge of information considered essential for living independently in our culture. A person who does not understand why dishes should be washed is not ready to live unsupervised. More difficult items should not be merely difficult (e.g., “What is the largest city in Svalbard? How many teeth does an orca whale have?”). Rather, they should measure knowledge that is relevant to what is considered core aspects of our culture (e.g., “Why do banks loan people money? Why do people still learn Latin and ancient Greek? Who was Isaac Newton? What is the purpose of the United Nations?”).

Just as language development consists of many narrow abilities, there are many sub-categories in General Information. Typically these sub-categories consist of academic domains such as knowledge of the humanities and knowledge of the sciences. These categories have further subdivisions (e.g., physics, chemistry, biology, and so forth – and each of these, in turn have further subdivisions).

General Information consists of knowledge that each person in a culture is expected to be familiar with (or would be admired if he or she knew). However, much (if not most) of a person’s knowledge is not of this sort. For example, although it is expected that everyone in this culture should know what airplanes are, only pilots are expected to know how to fly them. In CHC Theory, knowledge that is expected to be known only to members of a particular profession or enthusiasts of a particular hobby, sport, or other activity is classified as Domain-Specific Knowledge (Gkn). Most subject-specific academic achievement tests (e.g., European History, Geology, Contemporary American Literature) would be considered measures of Gkn, not Gc. That is, typically (but not always) achievement measures are the relevant outcomes we wish to explain, not explanatory aptitudes. In contrast, measures of General Information (e.g., WISC-IV Information) are intended to be estimates of the body of knowledge from which a person can draw to solve a wide range of problems.

Like Lexical Knowledge, General Information has a bi-directional relationship with reading comprehension. Very little of what is written is fully self-contained; authors presume that readers have considerable background knowledge and often do not bother to explain themselves. Drout (2006) describes how difficult and amusing it is to explain to non-native speakers of English what newspaper headlines such as “Under Fire from G.O.P., White House Hunkers Down” mean.[1] Children who know more understand more of what they read. Understanding more makes reading more enjoyable. Reading more exposes children to more knowledge, much of which is inaccessible via oral culture.


[1]Why would anyone be under a fire?

It means being shot at.

People are shooting at the White House?

No, it is just a vivid way of saying that the G.O.P. is criticizing the administration, which is symbolized by the White House, where the president lives.

Who is the G.O.P.?

It stands for the Grand Old Party.

If they are old, why haven’t I heard of them?

They are the Republicans.

Oh! Is the Democratic Party the new party?

No, they have been around longer than the Republicans. The nickname GOP was first used when the party was only a few decades old.

I don’t understand.

I don’t either, really. I just know that “old” is an affectionate way of describing something you have liked for a long time.

Could I say that I enjoy old ice cream?

No, that doesn’t sound right. You should probably just avoid using “old” that way.

What does “hunker”mean?

I really have no idea. I just know that when you are under fire, you should hunker down.

If you don’t know what it means, how do you know what to do?

True! I just looked it up. It means “to squat, to sit on your haunches.” I guess it all makes sense now.

So, when the Republicans criticize the president, he sits on his haunches?

That is an amusing image, but no. It means that you stick to your guns…er…I mean…

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.

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GcVisualized

CHC Theory, Cognitive Assessment

Crystallized Intelligence, Visualized

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CHC Theory, Cognitive Assessment, Principles of assessment of aptitude and achievement

Why do IQ tests measure vocabulary?

If Lexical Knowledge (understanding of words and their uses) is simply memorizing the definitions of fancy words, then, at best, it is a trivial ability valued by academics, pedants, and fuddy-duddies. At worst, its elevation by elitists is a tool of oppression. There is some truth to these views of Lexical Knowledge but they are myopic. I will argue that vocabulary tests are rightfully at the center of most assessments of language and crystallized intelligence. Some words have the power to open up new vistas of human experience. For example, when I was thirteen, learning the word “ambivalence” clarified many aspects of interpersonal relationships that were previously baffling.

A word is an abstraction. The need for labels of simple categories is perfectly clear. Knowing the word anger (or its equivalent in any other language) frees us from having to treat each encounter with the emotion as a unique experience. Being able to communicate with others about this abstract category of experience facilitates self-awareness and the understanding of interpersonal relations. We can build up a knowledge base of the sorts of things that typically make people angry and the kinds of reactions to expect from angry people.

It is less obvious why anger has so many synonyms and near-synonyms, some of which are a bit obscure (e.g., iracund, furibund, and zowerswopped!). Would it not be easier to communicate if there were just one word for every concept? It is worthwhile to consider the question of why words are invented. At some point in the history of a language, a person thought that it would be important to distinguish one category of experience from others and that this distinction merited a single word. Although most neologisms are outlived even by their inventors, a few of them are so useful that they catch on and are used by enough people for enough time that they are considered “official words” and are then taken for granted as if they had always existed.[1] That is, people do not adopt new words with the primary goal of impressing one another. They do it because the word succinctly captures an idea or a distinction that would otherwise be difficult or tiresome to describe indirectly. Rather than saying, “Because Shelly became suddenly angry, her sympathetic nervous system directed her blood away from her extremities toward her large muscles. One highly visible consequence of this redirection of blood flow was that her face turned white for a moment and then became discolored with splotches of red.” It is simply more economical to say that “Shelly was livid with rage.” By convention, the use of the word livid signals that Shelly is probably not thinking too clearly at the moment and that the next thing that Shelly says or does is probably going to be impulsive and possibly hurtful.

Using near synonyms interchangeably is not merely offensive to word nerds and the grammar police. It reflects, and possibly leads to, an impoverishment of thought and a less nuanced understanding of the world. For example, jealousy is often used as a substitute for envy. They are clearly related words but they are not at all the same. In fact, in a sense, they tend to be experienced by people on opposite sides of a conflicted relationship. Envy is the painful, angry awareness that someone else enjoys some (probably undeserved) advantage that we covet. Jealousy is the angry, often vigilant, suspicion we may lose our beloved to a rival. Unaware of this distinction, it would be difficult to benefit from or even make sense of the wisdom of Rochefoucauld’s observation that “Jealousy is born with love, but does not die with it.”

Lexical Knowledge is obviously important for reading decoding. If you are familiar with a word, it is easier to decode. It is also obviously important for reading comprehension. If you know what a word means, it is easier to comprehend the sentences in which it appears. It is probably the case that reading comprehension also influences Lexical Knowledge. Children who comprehend what they read are more likely to enjoy reading and thus read more. Children who read more expose themselves to words that rarely occur in casual speech but the meaning of which can be inferred from how it is used in the text. Finally, Lexical Knowledge is important for writing. Children with a rich understanding of the distinctions between words will not only be able to express what they mean more precisely, but their knowledge of certain words will enable them to express thoughts that they might not otherwise have had. For example, it seems to me unlikely that a student unfamiliar with the word “paradox” would be able to write an essay about two ideas that appear to be contradictory at first glance but at a deeper level are consistent with each other.


[1] Of course, dictionaries abound with antique words that were useful for a time but now languish in obscurity. For example, in our more egalitarian age, calling someone a cur (an inferior dog because it is of mixed breed) is not the insult that it once was. It is now used mostly for comedic effect when someone affects an aristocratic air. My favorite example of a possibly soon-to-be antique word is decadent, which is nowadays almost exclusively associated with chocolate.

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.

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CHC Theory, Cognitive Assessment, Principles of assessment of aptitude and achievement

Fluid Intelligence, Defined

Mentioning fluid intelligence at cocktail parties as if it were a perfectly ordinary topic of conversation carries with it a certain kind of cachet that is hard to describe unless you have experienced it for yourself. Part of Gf’s mystique can be attributed to Cattell’s (1987) assertions that Gf is linked to rather grand concepts such as innate ability, genetic potential, biological intelligence, mass action, and the overall integrity of the whole brain.[1] Heady stuff indeed!

At the measurement level, Gf tests require reasoning with abstract symbols such as figures and numbers.[2] Good measures of Gf are novel problems that require mental effort and controlled attention to solve. If a child can solve the problem without much thought, the child is probably making use of prior experience. Thus, even though a test is considered a measure of fluid intelligence, it does not measure fluid intelligence to the same degree for all children. Some children have been exposed to matrix tasks and number series in school or in games. Fluid intelligence is about novel problem solving and, as Kaufman (1994, p. 31) noted, wryly pointing out the obvious, a test is only novel once. The second time a child takes the same fluid intelligence test, performance typically improves (by about 5 points or 1/3 standard deviations, Kaufman & Lichtenburger, 2006). This is why reports that fluid intelligence can be improved with training (Jaeggi, Buschkuehl, Jonides, & Perrig, 2008) cannot be taken at face value.[3] Just because performance has improved on “Gf tests” because of training does not mean that Gf is the ability that has improved.

At the core of Gf is the narrow ability of Induction. Inductive reasoning is the ability to figure out an abstract rule from a limited set of data. In a sense, inductive reasoning represents a person’s capacity to acquire new knowledge without explicit instruction. Inductive reasoning allows a person to profit from experience. That is, information and experiences are abstracted so that they can be generalized to similar situations. Deductive reasoning is the ability to apply a rule in a logically valid manner to generate a novel solution. In CHC Theory, deductive reasoning is called General Sequential Reasoning. Although logicians have exquisitely nuanced vocabularies for talking about the various sub-categories of inductive and deductive reasoning, it will suffice to say that everyday problem solving typically requires a complex mix of the two.

Inductive and deductive reasoning can be found in multiple places in CHC Theory. Whenever inductive and deductive reasoning are applied to quantitative content, they are called quantitative reasoning. For mysterious reasons, inductive and deductive reasoning with quantitative stimuli tend to cluster together in factor analyses. Inductive and deductive reasoning also make an appearance in Gc. Whenever inductive and deductive reasoning tasks rely primarily on past experience and previous knowledge, they are classified as measures of crystallized intelligence. Many researchers have supposed that the Similarities subtest on Wechsler tests contains an element of fluid reasoning because inductive reasoning is used to figure out how two things or concepts are alike. If the question is something like, “How are a dog and a cat alike?” then it is very unlikely that a child arrives at the correct answer by reasoning things out for the first time. Instead, the child makes an association immediately based on prior knowledge.

Researchers are not satisfied with accepting Gf as a given. They wish to know the origins of Gf and to understand why some people are so much more adept at abstract reasoning than other people are (Conway, Cowan, Bunting, Therriault, & Minkoff, 2002). One hypothesis that is still being explored is that fluid reasoning has a special relationship with working memory. Working memory is the ability to hold information in mind while using controlled attention to transform it in some way (e.g., rearranging the order of things or applying a computational algorithm). Many researchers have noted that tests of fluid reasoning, particularly matrix tasks (e.g., WISC-IV Matrix Reasoning), can be made more difficult by increasing the working memory load required to solve the problem. Kyllonen and Christal (1990) published the provocative finding that individual differences in Gf could be explained entirely by individual differences in working memory. Many studies have attempted to replicate these finding but have failed. Most studies find that Gf and working memory are strongly correlated (about 0.6) but are far from identical (Kane, Hambrick, Tuholski, Wilhelm, Payne, & Engle, 2004).

Just as we have distinguished between statistical g and theoretical g, it is important to note that there is a difference between the Gf that is measured by Gf tests and the Gf that is written about by theorists. Some of Cattell’s hypotheses about Gf have stood the test of time, whereas others have not held up very well. For example, the heritability of Gf is not higher than that of Gc, as Cattell’s theory predicts. I mention this because it is probably not justified to claim that because a child scores well on Gf tests, the child has high innate talent or that the child’s biological intelligence is high.

Most of the effects of Gf on academic achievement are mediated by Gc (i.e., better reasoning leads to more knowledge which leads to higher achievement). However, Gf seems to have a special relationship with complex problem solving in mathematics. Because Gf tests measure abstract reasoning, it is unsurprising that they would predict performance in an abstract domain such as mathematics (Floyd, Evans, & McGrew, 2003).


[1] Horn (1985) tended to de-emphasize the biological/genetic interpretation of fluid intelligence.

[2] Test developers have tried to create Gf measures with verbal content (e.g., WJ-R Verbal Analogies or SB5 Verbal Fluid Reasoning) but find that verbal Gf tests do not always load on the same factor as traditional Gf tests (Canivez, 2008; Woodcock, 1990). It is possible that the KAIT Logical Steps subtest may be the only commercially available verbal Gf test that does not have substantial loadings on Gc (Flanagan & McGrew, 1998; Immekus & Miller, 2010), possibly because it does not use the verbal analogy format.

[3] See Moody (2009) for a discussion of other methodological problems that may have compromised the validity of the Jaeggi et al (2008) study.

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.

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CHC Theory, Principles of assessment of aptitude and achievement

CHC Theory: Love, Marriage, and a Giant Baby Carriage

CHC Theory is the child of two titans, Carroll’s (1993) lumbering leviathan, the Three-Stratum Theory of Cognitive Abilities and Cattell and Horn’s two-headed giant, Gf-Gc Theory (Horn & Cattell, 1964). Given that Horn was as staunchly anti-g as they come (Horn & Blankson, 2005) and that Carroll was a dedicated g-man (though not of the g-and-only-g variety; Carroll, 2003), it surprising that these theories even had a courtship much less a marriage.

From 1986 to the late 1990s, in a series of encounters initiated and chaperoned by test developer Richard Woodcock, Horn and Carroll discussed the intersections of their theories and eventually consented to have their names yoked together under a single framework (McGrew, 2005). Although the interfaith ceremony was officiated by Woodcock, the product of their union was midwifed primarily by McGrew (1997). Woodcock, McGrew and colleagues’ ecumenical approach has created a space in which mono-g-ists and poly-G-ists can engage in civil dialogue or at least ignore one another politely. CHC Theory puts g atop a three-stratum hierarchy of cognitive abilities but g’s role in the theory is such that poly-G-ists can ignore it to the degree that they see fit.

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford.

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