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1
Measures of Relationship:
Covariation, Covariance, &
Correlation
1
Working with Pairs of Variables
• Until now we have focused on analyzing
one variable at a time
– Frequency distributions displayed scores on a
single variable
– Bar graphs and histograms illustrated the
frequency of a variable
– Measures of central tendency and variability
were computed on a single variable
• We can also study two variables at a time to
consider the
relationship between variables
2
Working with Pairs of Variables
• When you study the relationship between
two variables you analyze
pairs
of
variables for each subject
– e.g., To see if a student’s grades across
his/her classes are related, you could record
their grades in English and Math class…
giving each subject a pair of scores in the
data (their grade in each of the courses)
• Pairs of scores
are kept together through
the analysis and analyzed simultaneously
3
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2
Working with Pairs of Variables
• When one variable was being studied the
notation used to refer to the variable was
simply
X
• When two variables are being studied, the
X
notation is retained to identify one of the
variables and another notation,
Y
, is
added to refer to the second variable in
analysis
4
Possible Types of Relationships
Between Pairs of Variables
•
POSITIVE RELATIONSHIP
:
as one variable increases, the other
variable also increases OR
equivalently as
one variable decreases, the other variable
also decreases
– e.g., the more food you consume, the more
weight you will gain; or the less food you
consume, the less weight you will gain
5
Possible Types of Relationships
Between Pairs of Variables
•
POSITIVE RELATIONSHIP
:
If a relationship is positive then it means if
a person is above the mean on one
variable (X) they will likely be above the
mean on the other variable (Y);
if a
person is below the mean on one variable
(X) they will likely be below the mean on
the other variable (Y)
6
9/1/2010
3
Possible Types of Relationships
Between Pairs of Variables
•
POSITIVE RELATIONSHIP
:
Pairs a (+) deviation score with a (+)
deviation score or pairs a () deviation
score with a () deviation score
So the product of deviations for a positive
relationship will always be positive
7
1
1
2
3
3
1
8
3
X
M
X
X
Y
Y
M
Y
2
X
M
5
Y
M
0
)
(
X
M
X
0
)
(
Y
M
Y
= 3
= 3
Examples of Positive
Relationship Between Variables
• SAT scores and college GPA
• Age and reading ability
• Years of education and salary
• Height and weight
• Death rate and speed limit
• Insurance rates and speeding tickets
• HW scores and tests scores in a class
8
Possible Types of Relationships
Between Pairs of Variables
•
NEGATIVE RELATIONSHIP
:
as one variable increases, the other
variable decreases OR
equivalently as
one variable decreases, the other variable
increases
– e.g., the more you exercise per week the less
weight you will gain; or the less you exercise
a week the more weight you will gain
9
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4
Possible Types of Relationships
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This note was uploaded on 02/17/2011 for the course PYSC 227 taught by Professor Fairchild during the Spring '10 term at South Carolina.
 Spring '10
 Fairchild

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