Types of Relationships
• Social scientists are interested in
discovering functional relationships
between variables.
• In particular, researchers look for:
– correlations (association,
covariation) among vaariables
– differences between groups or
conditions
The nature of causation
• Cause-effect relationships--causation is
always inferred, never directly observed
• “functional” relationships
– one thing correlates with, or is associated with
another (correlation)
– one thing predicts or explains the amount of
variance in another (analysis of variance)
– one thing has a direct effect on another (path
analysis, multiple regression)
Graphic Representations of
Relationships
(dependent
variable)
Y-axis
(independent variable)
X-axis
Note: “3/4 rule”
the convention is
to make the Y axis
3/4 of the length
of the x axis
Correlations
• displaying correlations using a scattergram
• linear relationship
– can be positive or negative
• curvilinear relationship
– also known as nonmonotonic relationships,
quadratic trends, “u-shaped” or “inverted-u”
– requires a minimum of three levels of the variable
being investigated
• no correlation
• spurious effect
Do employees who drink a lot of coffee take more
bathroom breaks?
frequency table
employee
cups of
coffee
consumed
bathroom
trips
Fifi
1
2
Rex
2
1
Trudy
3
3
Pedro
3
4
Lulu
4
6
Thaddeus
5
5
Rudolfo
6
5
scatterplot
Illustration of Scatterplots
• Scatterplots that are
closer to a straight
line have correlations
closer to +1.0 or -1.0
• Must have interval or
ratio data
• Correlation does not
prove causation
Linear versus curvilinear relationships
Linear relationship
Curvilinear relationship
Differences Between Groups
or Conditions
• main effect (changes produced by one
independent variable alone)
– one-way interaction
• interaction effect (changes produces by
independent variables acting together, or
in concert
– two-way interaction
– three-way interaction
interpersonal touch, social labeling, and
the foot-in-the-door effect
touch
no touch
positive
FITD
.15
.40
negative
FITD
.45
.25
communicator physical attractiveness
and persuasion
attractive
criminal
swindler
burglar
unattractive
criminal
5.45
4.35
2.80
5.20
non-significant-interaction
A characteristic feature of
non-significant interaction
effects is that the lines are
parallel, or nearly parallel
potentially significant interaction
(ordinal)
potentially significant interaction
(disordinal or “crossed”)
potentially significant interaction
(ordinal)
Illustration of an interaction effect
2
3
3
6
Attitude change
0 1 2 3 4 5 6 7
Source Credibility
low
high
evidence quality
low
high
high quality
evidence
low quality
evidence
low
high
Source Credibility
COLD
ROOM
500
HOT
ROOM
900
HARD
TEST
60%
60%
EASY
TEST
60%
Test score
80%
0 10 20 30 40 50 60 70 80 90 100
Illustration of an interaction effect
Easy test
Hard test
500
900
Overlapping normal distributions
• Which
distribution has
the higher
mean? Which
has the higher
standard
deviation?
Nonnormal distributions
• Positively
skewed,
negatively
skewed , or a
normal
distribution?
What kind of correlation?
• Are people in richer nations happier??