Measures of Association Quiz
1.
What do phi and b (the slope) have in common?
2.
Which measures of association are chi square based?
3.
What do gamma, lambda & r2 have in common?
4.
When is it better to use Cramer’s V instead of lambda?
In-Class Exercise

Creating causal hypotheses


XY
Write down a factor that you hypothesize to
influence each of the following dependent
variables:
1.
2.
3.
__________ causes criminality.
__________ influences one’s happiness in marriage
__________ plays a role in one’s opinion about Gov.
Pawlenty
Statistical Control
Conceptual Framework
Elaboration for Crosstabs (Nom/Ord)
Partial Correlations (IR)
3 CRITERIA OF CAUSALITY

When the goal is to explain whether X
causes Y the following 3 conditions must
be met:
 Association

X & Y vary together
 Direction

of influence
X caused Y and not vice versa
 Elimination
of plausible rival explanations
Evidence that variables other than X did not cause
the observed change in Y
 Synonymous with “CONTROL”

CONTROL
 Experiments
are the best research method
in terms of eliminating rival explanations

Experiments have 2 key features:
Manipulation. . .
 Of the independent variable being studied
 Control. . .
 Over conditions in which the study takes place

CONTROL VIA EXPERIMENT

Example:
 Experiment
to examine the effect of type of
film viewed (X) on mood (Y)
 Individuals are randomly selected & randomly
assigned to 1 of 2 groups:
Group A views The Departed (drama)
 Group B views Little Miss Sunshine (comedy)

 Immediately
after each film, you administer an
instrument that assesses mood. Score on this
assessment is D.V. (Y)
CONTROL VIA EXPERIMENT

BASIC FEATURES OF THE EXPERIMENTAL DESIGN:
1. Subjects are assigned to one or the other group
randomly
2. A manipulated independent variable

(film viewed)
3. A measured dependent variable

(score on mood assessment)
4. Except for the experimental manipulation, the groups
are treated exactly alike, to avoid introducing
extraneous variables and their effects.
CONSIDER AN
ALTERNATIVE APPROACH…
 Instead
of conducting an experiment, you
interviewed moviegoers as they exited a
theater to see if what they saw influenced
their mood.

Many RIVAL CAUSAL FACTORS are not
accounted for here
STATISTICAL CONTROL
 Multivariate

analysis
simultaneously considering the relationship among
3+ variables
The Elaboration Method

Process of introducing control variables into a bivariate
relationship in order to better understand (elaborate) the
relationship

Control variable –


Zero order relationship


a variable that is held constant in an attempt to understand better
the relationship between 2 other variables
in the elaboration model, the original relationship between 2 nominal
or ordinal variables, before the introduction of a third (control)
variable
Partial relationships

the relationships found in the partial tables
3 Potential Relationships between x, y & z
1. Spuriousness

a relationship between X & Y is SPURIOUS when it is due to
the influence of an extraneous variable (Z)
 (X & Y are mistaken as causally linked, when they are
actually only correlated)
 SURVEY OF DULUTH RESIDENTS  BICYCLING
PREDICTS VANDALISM (Does bicycling cause you to be a
vandal?)

extraneous variable
 a variable that influences both the independent and
dependent variables, creating an association that
disappears when the extraneous variable is controlled
 AGE relates to both bicycling and vandalism  Controlling
for age should make the bicycling/vandalism relationship go
away.
Examples of spurious relationship
X
Z
Y
a. X (# of fire trucks)  Y ($ of fire damage)
Spurious variable (Z) – size of the fire
b. X (hair length)  Y (performance on exam)
Spurious variable (Z) – sex (women, who tend to have
longer hair) did better than men
“Real World” Example
 Research
Question: What is the difference in
rates of recidivism between ISP and regular
probationers?

Ideal way to study: Randomly assign 600
probationers to either ISP or regular probation.
300 probationers experience ISP
 300 experience regular
 Follow up after 1 year to see who recidivates


Problem: CJ folks do not like this idea—reluctant to
randomly assign.
“Real World” Example

If all we have is preexisting groups (random assignment is not
possible) we can use STATISTICAL control

Bivariate (zero-order) relationship between probation type &
recidivism:
Recidivism
Regular
ISP
Totals
Yes
100 (33%)
135 (45%)
235
No
200
165
365
Totals
300
300
600
2 = 8.58 (> critical value: 3.841)
CONCLUSION FROM THIS TABLE?
“Real World” Example
• 2 partial tables that control for risk:
LOW RISK (2 = 0.03)
Recid.
Regular
ISP
Totals
Yes
30 (17%)
15 (17%)
45
No
150
71
220
180
86
266
HIGH RISK (2 = 0.09)
Recid.
Regular
ISP
Totals
Yes
70 (58%)
120 (56%)
190
No
50
94
144
120
214
334
“Real World” Example

Conclusion: after controlling for risk, there is no
causal relationship between probation type and
recidivism. This relationship is spurious.

Instead, probationers who were “high risk” tended
to end up in ISP
IN OTHER WORDS….
X
Z
Y
X = ISP/Regular
Y = Recidivism
Z = Risk for Recidivism
3 Potential Relationships between x, y & z
#2
 Identifying
an intervening variable
(interpretation)

Clarifying the process through which the original
bivariate relationship functions

The variable that does this is called the
INTERVENING VARIABLE
a variable that is influenced by an independent variable,
and that in turn influences a dependent variable
 REFINES the original causal relationship; DOESN’T
INVALIDATE it

Intervening (mediating) relationships
XZY
Examples of intervening relationships:
a. Children from broken homes (X) are more likely to
become delinquent (Y)
Intervening variable (Z): Parental supervision
b. Low education (X)  crime (Y)
Intervening variable (Z): lack of opportunity
3 Potential Relationships between x, y & z

#3
the conditions for a relationship –
determining WHEN the bivariate relationship occurs
 Specifying

aka “specification” or “interaction”
 Occurs
when the association between the IV and DV
varies across categories of the control variable


One partial relationship can be stronger, the other weaker.
AND/OR,
One partial relationship can be positive, the other negative
Example Interaction Effect

An interaction between treatment and risk for
recidivism
 Treatment
had an impact on recidivism for high risk
offenders, but not low risk offenders
 Low Risk
Treatment = 30% recidivism
 Control = 30% recidivism


High Risk
Treatment = 45%
 Control = 75%

Limitations of Table
Elaboration:
1.
Can quickly become awkward to use if controlling
for 2+ variables or if 1 control variable has many
categories
2.
Greater # of partial tables can result in empty
cells, making it hard to draw conclusions from
elaboration
Partial Correlation
 “Zero-Order”

Correlation
Correlation coefficients for bivariate relationships

Pearson’s r
Statistical Control with IntervalRatio Variables
 Partial

Partial correlation coefficients are symbolized as
ryx.z


Correlation
This is interpreted as partial correlation coefficient that
measures the relationship between X and Y, while
controlling for Z
Like elaboration of tables, but with I-R variables
Partial Correlation

Interpreting partial correlation coefficients:

Can help you determine whether a relationship is direct
(Z has little to no effect on X-Y relationship) or (spurious/
intervening)

The more the bivariate relationship retains its
strength after controlling for a 3rd variable (Z), the
stronger the direct relationship between X & Y

If the partial correlation coefficient (ryx.z) is much
lower than the zero-order coefficient (ryx) then the
relationship is EITHER spurious OR intervening
Partial Correlation

Example: What is the partial correlation coefficient
for education (X) & crime (Y), after controlling for
lack of opportunity (Z)?
 ryx
(r for education & crime) = -.30
 ryz (r for opportunity & crime) = -.40
 rxz (r for education and opp) = .50
 ryx.z = -.125

Interpretation?
Partial Correlation

Based on temporal ordering & theory, we would
decide that in this example Z is intervening (X  Z
 Y) instead of extraneous

If we had found the same partial correlation for
firetrucks (X) and fire damage (Y), after controlling
for size of fire (Z), we should conclude that this
relationship is spurious.
Partial Correlation
 Another

example:
What is the relationship between hours studying
(X) and GPA (Y) after controlling for # of
memberships in campus organizations(Z)?
 ryx
(r for hours studying & GPA) = .80
 ryz (r for # of organizations & GPA) = .20
 rxz (r for hrs studying & # organizations) = .30
 ryx.z

= .795
Interpretation?