Section #1 Quiz 1 Stem and
Leaf Plot (N=29)
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




X|8
2|2255667899999
3|0011222456668
4|00
Mean=29.9; M=30; Mode= 29;
s=6.38;
Section #2 Quiz 1 Stem and
Leaf Plot (N=36)
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
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
X| 7
1|147889
2|244689
3|11122223333444567799
4|002
Mean=29.36; M=32; Mode= 32, 33;
s=8.68;
Part II
Sigma Freud & Descriptive
Statistics
Chapter 5  
Ice Cream and Crime:
Computing Correlation Coefficients
What you will learn in Chapter 5


What correlations are and how they
work
All about correlations...



How to compute them
How to interpret them
Other types of correlations that exist
What they are not

Correlations only tell us about the
relationship and the strength of the
relationship.

Correlations do NOT tell us about
cause and effect.
Chapter 6
5
What they are not


Correlations do not imply causation
Examples








Chapter 6
Marijuana use and heroin
Milk use and cancer
Church attendance and drug use
Lead levels and behavior
Cigarette smoking and Alzheimer’s
Education and sexual activity
Sex life and longevity
Coffee and suicide risk
6
What Correlations are about…


Examines the relationship between
variables
How the value of one variable changes
in relation to changes in another
variable



Range between -1 and 1
Bivariate correlation (2 variables)
Pearson product-moment correlation

Karl Pearson
Types of Correlation Coefficients

Positive Correlation

Direction Correlation


When variables change in the same direction
Negative Correlation

Indirect Correlation

When variables change in opposite directions
rXY = correlation between X and Y
Relationships Between Variables
Things to Remember

Correlations…




Range in value from -1 to +1
Absolute value indicates strength
Reflect situation where there are at least
two data points
May want to use “indirect” and “direct”
instead of “positive” and “negative” to
keep from assigning value to the
relationship
Computing Simple Correlations

Pearson product-moment…

What do these symbols represent?
Steps in Computation






List the two values for each participant
Compute the sum of X values, and
compute the sum of Y values
Find square of sum for x and y
Find sum of squares for x and y
Find the sum of the XY products
Now “plug” these values into the formula
Pearson’s product-moment
Steps in the process

Step 1:

Calculate






Chapter 6
Σx
Σx2
(Σx)2
Σy
Σy2
(Σy)2
13
Pearson’s product-moment
Steps in the process

Step 2:



Calculate Σxy
Sometimes referred to as the sum of the
cross-products
Step 3:

Substitute the values derived above into
the formula

Chapter 6
Note that N = number of pairs of scores
14
The Visual Picture

Scatterplot
Strong Positive Relationship
Strong Negative Relationship
Correlation Matrix
Income Education Attitude Vote
Income
Education
Attitude
Vote
1.00
0.574
-0.08 -0.291
1.00
-0.149 -0.199
1.00 -0.169
1.00
Interpreting Correlation Coefficients
Is Rate My Professor Valid?

The Rate My Professor system relies
on students who are willing to rate
their professors anonymously. While
this could encourage more candid
feedback, the anonymous system has
also at times provided what could be
inaccurate ratings.
Is Rate My Professor Valid?

One study showed the easier a class was
and the more attractive the teacher, the
more likely they would get a good rating on
Rate My Professor. Others have expressed
worry that Rate My Professor listings often
give good ratings to teachers that may not
provide the most comprehensive,
educational, or quality courses available.
Now You Try!!
Participant
Hours/Week Video Games
College GPA
1
3
3.8
2
15
2.1
3
22
2.5
4
30
0.6
5
11
3.1
6
25
1.9
7
6
3.9
8
12
3.8
9
17
1.7
Chapter 6
22
Computing Simple Correlations

Pearson product-moment…

What do these symbols represent?
Variance Explained

Coefficient of Determination



rxy = .70
.702 = .49 or 49%
Coefficient of Alienation



rxy = .70
.702 = .49
1.00 - .49 = .51 or 51%
How Variables Share Variance

Remember: Association NOT Causation
Different Types of Correlations
Using the Computer

Computing Correlation Coefficients
using SPSS
SPSS Output
SPSS Scatterplot

Selecting Variables
SPSS Scatterplot

Entering variables
SPSS Scatterplot

Simple Scatterplot
Glossary Terms to Know


Pearson-product moment correlation
Direct correlation


Indirect correlation


Positive correlation
Negative correlation
Scatterplot