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Lecture 6......
Jeremy Jackson
|     May 5, 2014
NW 3431
|     New Westminster
Carl Sagan: "Science is a way of thinking much more than a body of knowledge"

Key concepts - you will be responsible for knowing a number of definitions of key concepts. You may be asked to give an accurate definition and example of any of the key concepts. Key concepts are in italics, bolded and colored red throughout the notes.

Discussion exercises and class activities - the lecture notes contain a number of discussion questions and class activities. You should conduct these exercises as soon as they are introduced in the notes. Exercises are in italics, bolded and green throughout the notes.

Critical points - there are some points that require extra emphasis because they are fundamental to the example or concept being discussed. Critical points are bolded, in italics and colored orange.

Movies - throughout the notes I have made short videos explaining various ideas.

What is intelligence?

Let's take a look a what at leading text book says about intelligence.

Intelligence is:

1) An inborn general mental capacity.

2) Not something concrete, but a concept.

3) Not a thing.

4) What ever intelligence tests measure.

5) School smarts.

6) A socially constructed concept.

7) Whatever attributes enable success in a given culture.

8) g

9) Emotional intelligence is a form of intelligence that is the ability to perceive, express, understand, and regulate emotion.

10) The brain is a modular system with multiple intelligences.

11) There are multiple intelligences, each relatively independent of each other.

12) There are 3 types of intelligence: analytical, creative, and practical.

13) What we call intelligence…is several culturally adaptive skills.

Why so many definitions?

Well, it turns out that some are theories and some are definitions. There are some people in psychology that think that we don't know what intelligence is yet,  so we must theorize about what it is and test our theories to see which one is the best. These people are called construct validity theorists. A construct validity theorist is a person that believes that it makes scientific sense to theorize about how something should be defined.

Howard Gardner is one of these people. He thinks that intelligence may not just be what we traditionally think it is...that is, the ability to solve problems found in the books and schools of western cultures. Gardner thinks that intelligence is a multifaceted, 9 dimensional construct. To Gardner, it makes sense to hypothesize that there is actually something called bodily or kinesthetic intelligence. That is, that intelligence IS, in part, the ability to dance, skate or play golf. In particular, Gardner believes that intelligence is constituted of 9 separate dimensions. The following is a good documentary about the idea that intelligence may not be a unitary ability (such as g or general intelligence) but a multifaceted set of abilities more similar to those that have been proposed by Gardner.



Howard Gardner


From this point of view, intelligence could be anything really. It could be emotional, social, physical ....anything at all.

Let's look at the logic of construct validity theory a bit more closely. The following is a list of the most basic principles of CV theory:

1) A major goal of science is to find out what things really are. Although we may say we know what intelligence is, we could be wrong. Part of the scientists job is to find out what things like intelligence really are as opposed to what we think they are.

2) Finding out more about something tells us more about what that thing is. So the more we learn about intelligence, the more precise we can  be about what it is. For instance, if we find out that people with high intelligence have larger brains, this might tell us that intelligence IS neurologically measurable.

3) It makes sense to theorize about what things are. It makes sense to have multiple different, competing theories  about what intelligence is. There are a number of different competing theories, for instance, Gardener's theory, Sternberg's theory (mentioned in the text), the theory of emotional intelligence (mentioned in the text) and Jensen's theory.

4) This issue is introduced in point 2. What something correlates with tells us something about what it is. If high depression scores are associated with high serotonin levels in the brain, this tells us that depression is, in part, elevated serotonin levels.

5) Different people can have different definitions of what something is. It is common in this point of view to hear phrases like, "What intelligence is to you, is different that what it is to me". Or "intelligence means different things to different people". This point is made in the text under the heading of "theory-based" approaches to intelligence.

6) Even though we are not taught to measure things like intelligence in the same way we are taught to measure things like height and weight, it still may be possible to measure them. That is, it may be possible to discover how to measure intelligence.  Part of the job of the psychologist is to learn how to measure psychological phenomena such as intelligence, anxiety, depression, etc. People who specialize in the theory and methods of psychological measurement are called psychometricians. I am a psychometrician.

Now let's look at some quotations from a leading Introductory Psychology text to see how this view manifests itself in psychology.

Quote 1:

"Theories of Multiple Intelligences

Since the mid-1980s some psychologists have sought to extend the definition of intelligence beyond Spearman’s and Thurstone’s academic smarts."

In the first sentence of this section it says that psychologists are seeking to extend the definition of intelligence. The text is saying here that we have new theories about how intelligence should be defined.


Quote 2:

"PSYCHOLOGISTS DEBATE: Should we consider intelligence as one aptitude or many? As linked to cognitive speed? As neurologically measurable?"

This is a clear statement that psychologists debate about what intelligence is. This means, of course, that different psychologists have different definitions/theories about what intelligence is.


Quote 3:

Some scholars, however, are concerned that emotional intelligence stretches the concept of intelligence too far.

The authors indicate that there is disagreement amongst psychologists about whether emotional intelligence really is a type of intelligence. Some psychologists think it is, others do not. This shows that there are different theories about what intelligence is and that different people have different definitions of intelligence.

Quote 4:

The neurological approach to understanding intelligence (and so many other things in psychology) is currently in its heyday. Will this new research reduce what we now call the g factor to simple measures of underlying brain activity? Or are these efforts totally wrongheaded because what we call intelligence is not a single general trait but several culturally adaptive skills? The controversies surrounding the nature of intelligence are a long way from resolution.

In discussing a number of research findings that show a relationship (correlation) between brain size and intelligence test scores the book wonders whether intelligence really is some kind of neurological capacity. This quote indicates that the question of what intelligence is (the nature of intelligence) is: a) an ongoing controversy  and b) determined in part by what intelligence test scores correlate with (e.g., brain size).

To an OPERATIONIST, however, it makes no sense to theorize about what things like intelligence (things that are already defined) really are. The operationist says that intelligence is already defined (it's in the dictionary) so there is no sense to theorizing about what it is.

Now, the operationist takes one further step. They also say that intelligence itself is an ordinary, everyday concept and as such, it is rather vague and somewhat subjective. For this reason, it's not precise or objective enough to be employed in a scientific context.

So the operationist develops a NEW concept that is roughly related to intelligence but NOT THE SAME THING. They simply INVENT a new concept that they make precise and objective so that it can be used in science.

This notion of inventing a new concept is an important idea in operationism. Operationists believe that what something is (the definition of the word that denotes the thing) is made up. What is a chair you ask? Well, it's just what we made up the word chair to mean. What is a tree? Whatever we say the word means!! It's that simple. So to an operationist, it makes no sense to say that we have discovered what intelligence is. Why? Because we don't discover what things are, we make it up!

I once had an interesting conversation with an old biology lecturer from Princeton. His name was Henry. I asked Henry one day ....."Henry, over your career as a university professor, what has been the most difficult idea to convey to your young biology students." He did not hesitate. He said, "It's the idea that all our natural categories, all the taxonomies of living things we have are just made up by us. There is no such thing as an amoeba really, there is just the concept of amoeba that we have made up to refer to certain kinds of natural beings." Henry was an operationist.

So to an operationist, the problem of what intelligence is, is really a rather simple one. There is nothing deeply rooted in our minds, no mysterious ability somehow fundamentally distinct from others, there is nothing waiting to be discovered in the brain that will reveal what intelligence really is. There are just people that can do things and a word people have made up to denote certain aspects of our human abilities.

So what is the NEW CONCEPT that psychologists made up (invented) that can be used to scientifically study abilities that have something to do with intelligence? This is IQ! IQ is a concept invented by the operationist as a way to make precise, objective, clear measurements of something to do with (but not exactly the same thing as) intelligence.

Let's take a look at the concept of IQ as developed by psychologists.

There are two operational definitions of IQ that depend upon the age of the person that IQ is being determined for. If we are measuring the IQ of any non-adult, we measure IQ according to what I will call the “Stern method”. This is called the "Ratio IQ" in the text. If we are measuring the IQ of an adult, we measure IQ using what I will call the “modern method”. This is called the "Deviation IQ" in the text.

The Stern method (or ratio IQ) is defined as follows:

IQ = MA/CA x 100

Where MA = mental age, and CA = chronological age.

Mental age is determined using age group norms. An age group norm is comprised of the scores on an intelligence test of a comparison group made up of a random sample of children of a given age. For example, suppose we give an intelligence test to 1,000 randomly sampled 12 year old Canadian children. The scores on this test for each of the 1,000 children is the 12 year old norm. Suppose we were to plot the scores in a histogram, and they looked like this:


We can see here that the average score for this norm group of 12 year old Canadians was 52%. Now let's look at a norm group of 13 year old Canadians.


We see now that 13 year old children score higher on average than 12 year old children. The average score for 13 year old children is 55% and for 12 year old children it is 52%. So scores on the test increase with age. This occurs until about age 17-18. This idea is central to the concept of IQ as defined in the Stern method because it determines how we quantify mental age.

To see how mental age works, imagine that a 12 year old child scored 55% on the IQ test. By using the norms we can see that 55% is actually the average for 13 year old children. This means that this 12 year old is scoring at the same level as the average 13 year old. This makes their mental age 13. But of course, their chronological age is 12. To calculate their IQ we simply apply the formula above to get 13/12x100=108.3.

As you can see, when a child performs above the average for their age group, their IQ will be over 100. When they score the same as their age group, their mental age and chronological age will be the same and their IQ will be 100.

You can see that this definition of IQ is precise and objective. It's a single number that states the exact IQ of a given child. Now if we are calculating the IQ of an adult, we use a method I call the modern method. The modern method (or deviation IQ) is defined as follows:

IQ = 15{(x-μ)/σ} + 100


μ = the mean of the norm group

σ = the standard deviation of the norm group

X = the individual’s score on the intelligence test

To see how this works, suppose the norm for Canadian adult males on a particular intelligence test is as follows:


This distribution has a mean of 64 and a standard deviation of 3.

Now imagine that an individual Canadian male writes the test and gets 64% correct. We see from the formula that their IQ would be:

IQ = 15{(64-64)/3} + 100

The result is 100. So when an adult scores the same as the norm group their IQ is 100. This is why the average IQ is 100....it is DEFINED to be this way.

Now imagine that an individual Canadian male writes the test and scores 67%. Their IQ would be:

IQ = 15{(67-64)/3} + 100

The result is 115. If you look at the graph above you will see a value of 1 below 67 and a value of 115 below 1. in fact, the formula merely converts the % correct to an IQ score according to the graph above. Do you see that the standard deviation of the norm is 3? And do you see that the score of 67 is 3 units above the mean of 64? Since the standard deviation is 3 and 67 is 3 units above 64, the score of 67 is 1 standard deviation above 64. We are merely converting percentage units (which we call raw scores) to standard deviation units.

This is why we convert a raw score of 70 to a score of 2. 70 is 6 raw units above 64. 3 goes into 6, 2 times so 70 is 2 standard deviation units above 64.  This is what (x-μ)/σ} does. It converts raw units into standard deviation units. Just apply the formula for a value of 70 to see how this works. We have: (70-64)/3. (70-64)=6. We now divide 6 by 3 and get 2. This shows us that a score that is 6 raw units above the average of 64 is 2 standard deviation units above the average of 64.

Now, once we have converted a percentage into standard deviation units, we then convert standard deviation units into IQ score units. The part of the formula that does this is shown in green below:

IQ = 15{(x-μ)/σ} + 100

The following video explains how this conversion works.


So what does this mean for our interpretation of IQ scores?

1) IQ scores are RELATIVE. Notice that the raw percentage correct is not relative. It is simply the percent correct one got on the test. However, the IQ score is relative in the sense that it is determined by comparing a raw score to a norm group. This is much like height in cm vs how tall a person is. Height is not relative, how tall a person is, is relative. For example, a person that is 100cm high is tall if they are 2 years old but short if they are 15 years old. When we say a person is tall or short we are making a RELATIVE or COMPARITIVE statement about the person. When we say a person is 150 cm high we are making an absolute statement about height.

One implication of this is something called the Flynn Effect. This is the finding that over time, people score better on IQ tests. This means that if we compare scores for people of your generation to people of previous generations, your generation will do better. Watch the following video of James Flynn, the inventor of the Flynn Effect:

2) It follows from point 1 above that a person's IQ is highly dependent on who they get compared to.   Suppose you are a 20 year old Canadian female that has never attended college. Is it reasonable to compare you to a 30 year old Canadian female that has a university degree? What if English is your second language? Should you be compared to a norm group of English as a first language people? Should males be compared to males, or should they be compared to all adults? Unfortunately, this is an unanswered question for the moment.

3) It follows from 2 above that any individual has as many IQ scores as there are reasonable groups to compare them with. Since we do not precisely define the norm group that every individual should be compared with, we must accept that IQ scores are NOT UNIQUE.

4) There are many accepted IQ tests in use today with many different kinds of questions on them (i.e., verbal, mathematical, spatial, etc). We do not score the same on all tests. For example, a given individual may do fairly well on one kind of IQ test and not so well on another kind of IQ test. If a test involves many mathematical questions a person with low math ability (but high verbal ability) will do relatively poorly on that kind of test. It follows then that each individual has an IQ score for each accepted IQ test in use today. Again, this means that IQ scores are not unique.

5) It follows from the above that any individual's score on an IQ test is a function of the kinds of questions on the test and the norm group with which they are compared. The kinds of questions one can answer well is, in part, a function of past life experience including education, training, culture, upbringing and so on.

There have been attempts to create what we call "culture free" IQ tests. These are IQ tests that make no reference to culturally specific knowledge or abilities such as language, factual knowledge, etc. One such very well known and extensively used test (I was given one in grade 6 to determine if I should skip a grade), is called the Raven's Progressive Matrices Test.

There are 60 questions on the test.

VERY ROUGHLY, one would convert their score as follows:

IQ= 15(your score out of 60-48)/6+100

So, if you got 54 out of 60 your IQ would be:


To get an IQ score here, I have used a mean of 48 and standard deviation of 6. Where did I get that from? These parameters were derived from a 16 year old norm group of Scottish children tested in 1979. Their mean was 47 and their standard deviation was about 6. I estimated that adult mean scores in 2010 would be a little higher due to the Flynn Effect and the fact that 20-24 year old scores tend to be slightly higher than 16 year old scores. However, Canadian scores would be slightly lower than Scottish scores. In the end then, I estimated that mean scores for Canadian 20-24 year olds in 2010 would about 48. Is that right? I don't know but I'm pretty confident that it's not too far off.

But let's be clear about one thing here. This is a spatial rotation and pattern recognition test. That's it right! This is a test of how good you are at this specific thing. According to the operationist, there is nothing deeper than this. So, to what extent should we be confident that this is a measure of something more than this; something like, for instance, intelligence?

The ONLY reason we might generalize beyond this specific task to some more broad or general ability is that scores on this test TEND to correlate with scores on other cognitive tasks. For instance, there is a positive Pearson r between scores on this test and math test scores. But recall from last lecture what a positive Pearson r shows. It shows a TENDENCY. It does not follow that if you do well on this test you will also do well on a math test (or verbal test, or in college or whatever). It also does not follow that if you do poorly on this test you will do poorly in a math test, etc.

6) According to the operationist, IQ is NOT intelligence. It is meaningless to say that IQ tests are biased because they don't measure intelligence. The operationist agrees that IQ is not the same thing as intelligence. When we look intelligence up in the dictionary we do not see equations and norm groups. The definition of IQ is technical and scientific. Intelligence is not a technical, scientific concept.


So now let's leave this issue of the nature of intelligence and it's relation to IQ and look at some empirical facts about IQ. Your book is an excellent source here, so I will not repeat it. Below, I have just put together a short summary table of empirical facts we have discovered about IQ.

Empirical Facts About IQ

1) IQ is hereditary in the sense that the closer the genetic relationship between two people, the more likely their IQ scores are to be similar. The following chart gives the Pearson correlations for various genetic relationships (Note: A correlation of greater than .7 would be considered very high):


2) Native Indians and African Americans score approximately 1 standard deviation lower on IQ tests than do Caucasian’s. Caucasian's reliably score lower than Asian's.

3) Within gender, IQ scores are positively related to head size and brain size.

4) IQ scores are modestly higher for children raised in enriched environments in comparison to children raised in impoverished environments.

5) High IQ is predictive of socioeconomic status and education levels.

6) All mental ability tests correlate positively with each other.

7) IQ can be increased very slightly via enrichment programs. The gains are not consistently observed, and the extent of gain depends upon the nature of the IQ test.

8) Some people perform reliably better on some types of mental ability tasks than others. For example, females tend to perform better on verbal tasks, and males tend to perform better on spatial tasks.

9) In North America, performance on IQ tests has increased steadily over the last 30 years. This is the Flynn effect.

Now go ahead and test yourself on the concepts and ideas from this lecture.



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