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Lecture 5......
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.


Before we begin our discussion of measurement and intelligence, we need to understand the concept of correlation. Correlation will play an important role in understanding much of the research on intelligence and many of the methods of measurement in psychology. This material is not in the text so read carefully and ask questions if you have them.

Suppose we were to ask each member of the class two questions:

a) How long do you spend talking or text messaging on your cell phone every day?

b) How long do you spend washing/drying your hair in the morning?

We can plot the answers to these two questions for each person in the course in a scatter plot. It would look something like this:


Notice that as the length of time doing hair goes up, so do the number of minutes on the phone. That is, students that spend a long time on the phone also spend a long time doing their hair. This is known as a positive relationship. Large scores on one factor are associated with large scores on the other factor and small scores on one factor are associated with small scores on the other factor.

In this case, the relationship is fairly strong. There appears to be a clear trend in this graph. The trend also appears to be linear. This means  that a straight line can be placed through the points so that all of the points would fall roughly around the line.

Now, there is a way to quantify how much of a linear relationship there is between two factors. This is called the Pearson correlation coefficient or Pearson r. The Pearson r varies between -1 and 1. Here are some things to know about it:

1) If the Pearson r is 1 or -1, the linear correlation between two variables is perfect. The following graph shows a perfect linear correlation of 1.  This is a perfect linear correlation because all of the points fall exactly on a straight line.



2) A positive correlation is a correlation in which high values of 1 variable go with high values of the other variable. A negative correlation occurs when high values of 1 variable go with low values of the other variable. The graph below shows a negative correlation:



The correlation in the graph above is negative and strong. It's negative because high values of one variable go with low values of the other and vice-versa. It is strong because all the points fall close to a line that could be drawn through the center of the points. See the graph below:


Because the line that fits the points well slopes from high on the left to low on the right, this correlation is negative. But also, because the points are all fairly close to the line, the correlation is strong. In fact, this correlation is -.95. Very close to the strongest negative correlation possible which is -1.

3) A 0 correlation exists when the points do not slope one way or the other. The following graph shows a zero correlation.


4) Correlations between -.2 and .2 are known as weak. Correlations above .6 and below -.6 are known as strong.

5) A correlation between two factors does not indicate that there is a causal relationship between those factors. For example, look at the relationship below between how long it takes to do your hair and your shoe size.


Now, the question is, does a large shoe size CAUSE a person to take a short amount of time to do their hair. The answer of course is no. So what's going on here then? Take a look at the color of the points. The purple points are males and the blue points are females. Males have large feet and take a short time to do their hair (but with social changes in vanity, males are now taking more time to do their hair than they once did). Females have small feet and take a long time to do their hair. But WITHIN males their is no relationship and WITHIN females there is also no relationship (move the cursor over the image to see males and females identified). The relationship is caused by a 3rd factor ....gender. 

So let's agree on how to talk about a situation like this....there IS a correlation between shoe size and time doing hair. It is negative (about -.6 in the example here). However, the correlation is caused by a third factor which is gender. We say that the PARTIAL correlation between hair and shoe size with the influence of gender removed (we say partialled out) is practically 0.

Now, it's important you know how to use MS Excel just a little in order to analyze data for your projects. In the following video, I'd like to show you how to use Excel to calculate a Pearson Correlation (we call it the Pearson r) and what happens to it when certain values are changed.


1) Video 1: Calculating the Pearson r in Excel.

2) Video 2: What happens to the Pearson r with changes in the values?


Go ahead and open MS Excel and see if you can do the following:

For the following data:

X: 2 3 2 5 4 5 3 4 5 6 5 6 5 4 5 6 7 6 7

Y: 4 3 5 6 5 4 5 6 7 6 7 8 7 8 7 8 9 8 9

1) Generate a scatter plot. Name the plot and label the axes.

2) Calculate the Pearson r between the two variables.

3) Change the last pair of numbers from X=7, Y=9 to X=50 and Y=50. Now what is the Pearson r?

More About Scatter Plots

Scatter plots can be used in many interesting ways in science. Watch the following fascinating video on religion and population demographics by Hans Rosling for some inspiring ideas - Hans_Rosling.

Just a few things about that incredible video. Below is a screen shot of one slide from the talk. Take a look:



This is a scatter plot. However, professor Rosling has modified it to show more than 2 dimensions. That is, more than just babies per woman and income. Here are some things to consider about this plot:


1) Each point is not a person, as they are in the graphs I showed you above. Here, each point is a country. It's important to understand that when we say that our research has some number of "subjects", we do not always mean that subjects are people. Here, the subjects are country and there are about 130 subjects in the scatter plot.

2) As I did above professor Rosling has indicated the major third factor in his plot by coloring the points. The third factor is religion and each religion has a different color.

3) We could, however, consider other possible third factors in any given situation. Here professor Rosling has shown us two other possible third factors. We have the size of the country indicated by the size of the point and we have time (just put the cursor over the graph to see the effect of time).

4) So in this simple 2-dimensional space created by the X and Y axes of the graph, there are actually 5 variables we can analyze. Lovely!


So why does knowing about correlation matter for our understanding of intelligence testing? It's pretty straightforward really. It's just that most people in psychology would argue that what a mental test correlates with tells us something about what it measures. So, although it may be the case that questions on a test don't look much like intelligence questions, if they correlate with "intelligence like" phenomena, they may well be measuring intelligence. For instance, if people that score well on a test end up as theoretical physicists and people that score poorly on the test end up as janitors, this is evidence that the test measures something to do with intelligence.

People that think this way are called construct validity theorists.

Now let's go on to the next lecture on intelligence measurement.

SA Questions

1) Draw graphs to illustrate the difference between a positive, negative, small and large correlation. Also, provide your own example of a case in which a 3rd factor could be responsible for the correlation between two variables.









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