1. 1

2. 2

3. We are making a big assumption here – that the relationship is a straight line
Wouldn’t life be so much easier if all relationships are straight lines?
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4. The Pearson correlation r is a numeric index of the relationship between two numeric
variables
Caution: if a variable is categorical (e.g., gender – male vs. female; ethic – white, black,
asian) you cannot correlate it with another variable. Pearson r can only be calculated
between two number variables (e.g., age, salary, height, weight)
R tells us how much the relationship is a straight line
These graphs are possible ways two variables relate to one another
The more the graph looks like a straight line, the stronger the r value is
The graphs that resemble a circle indicate very low or even no correlation between the two
variables
The direction of the line indicates whether the correlation is positive or negative
If the line goes up to the right, it’s a positive relationship (meaning, when X goes up, Y goes
up too)
If the line goes down to the right, it’s a negative relationship (meaning, when X goes up, Y
goes down)
For example, if when we get older, we also get wiser. If this is true, that means there should
be a positive and strong Pearson correlation r between the age variable and the wisdom
variable.
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5. If we are less happy when we have more money, that means there should be a negative
Pearson correlation r between the happiness variable and the money variable
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6. As you can see from these charts, Pearson correlation r becomes stronger as the data
points cluster more tightly around a straight line
When the data points are distributed like a round circle, that means the X and Y variables
have little relationship to each other
Note that most of these (except for the first one) have positive correlations, although some
of them are weaker (more rounded) than others (more straight lines)
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7. The same principle applies to the negative correlations. The trend goes down to the right
when the correlation is negative
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8. Again to summarize there are two components to the correlation value:
It’s direction, and it’s strength
What kind of correlation are you predicting for your group project?
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9. Caution:
Correlation measures the linear relationship between two variables
When the assumption of normality is violated, weird things happen
This slide illustrates 4 different datasets all with the same correlation
The moral of the story is that we should always inspect the scatterplot when running
correlations. Numbers should be interpreted sensibly
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10. We can never stress enough that correlation is not the same as causation
One of my favorite examples by a student is about shoe size and intelligence. A positive
correlation was found between shoe size and intelligence levels leading people to think
that bigger feet = smarter people. Then they realized that bigger shoe size also generally
means older people and in fact it wasn’t the size of peoples’ feet that was causing
increased intelligence, it was simply the fact that they were older and therefore scored
higher on tests!
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11. We all want to have a positive relationship with our family, friends, coworkers, etc. Who
wants a negative relationship, right?
In that spirit, why would anyone want a negative correlation? And we should celebrate
every time we have a positive correlation, right?
How about a positive correlation between GDP and obesity level? How about a positive
correlation between smoking and cancer? How about a positive correlation between the
CEO’s compensation and corruption level?
Now let’s look at some negative correlations that are supposed to be “depressing:” more
exercise associated with lower levels of obesity, more education associated with lower
crime rate, fewer meetings associated increased productivity, and, how about more
relaxing weekends associated with lower stress levels?
What’s the moral of the story? Correlation is what it is – it’s a number that indicates the
strength and direction of a relationship between two numerical variables. Whether the
relationship is good for the mankind or not is beyond the scope of the humble little
number’s job!
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12. Assigning numbers to categorical variables do not make them numeric variables
This is because we can only do math with numeric variables. Basic math principles don’t
apply to categorical variables, even if they have numbers associated with them.
For example, 1+1=2
In the gender case, this means that if you add a female and another female together, that’s
equal to a male.
Another math principle is that 2 is twice as big as 1
In the gender case, that would mean that a male is twice as big as a female.
All this madness would happen if we try to use categorical variables in numeric ways.
Keep in mind that the Pearson correlation r value is calculated based on a math formula. If
you try to feed the gender variables into SPSS as numbers, SPSS can calculate a Pearson
correlation value for you but using that number requires you to make the kinds of crazy
assumptions illustrated above
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