1. Measures of Association Quiz
What do phi and b (the slope) have in common?
Which measures of association are chi square based?
What do gamma, lambda & r2 have in common?
When is it better to use Cramer’s V instead of lambda?

2. In-Class Exercise Creating causal hypotheses
X  Y
Write down a factor that you hypothesize to influence each of the following dependent variables:
__________ causes criminality.
__________ influences one’s happiness in marriage
__________ plays a role in one’s opinion about Gov Pawlenty

3. Statistical Control Conceptual Framework
Elaboration for Crosstabs (Nom/Ord)
Partial Correlations (IR)

4. 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”

5. 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

6. 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)

7. 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.

8. 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

9. STATISTICAL CONTROL Multivariate analysis
simultaneously considering the relationship among 3+ variables

10. The Elaboration Method
Process of introducing control variables into a bivariate relationship in order to better understand (elaborate) the relationship
Control variable –
a variable that is held constant in an attempt to understand better the relationship between 2 other variables
Zero order relationship
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
The elaboration method  the process of introducing control variables into a bivariate relationship in order to better understand (elaborate) the relationship.
The third variable enhances (or elaborates) the understanding of a two-variable relationship.
Control variable  a variable that is held constant in an attempt to understand better the relationship between 2 other variables
Another way to think about control variables:
When you control for a variable, you are subtracting the effects of that variable to see what a relationship would be without it.

11. 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.

12. Examples of spurious relationshipZ 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

13. “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.

14. “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
300
600
2 = 8.58 (> critical value: )
CONCLUSION FROM THIS TABLE?

15. “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

16. “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

17. IN OTHER WORDS…. X Z Y X = ISP/Regular Y = Recidivism
Z = Risk for Recidivism

18. 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

19. 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

20. 3 Potential Relationships between x, y & z#3
Specifying the conditions for a relationship – determining WHEN the bivariate relationship occurs
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

21. 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%

22. Limitations of Table Elaboration:
Can quickly become awkward to use if controlling for 2+ variables or if 1 control variable has many categories
Greater # of partial tables can result in empty cells, making it hard to draw conclusions from elaboration

23. Partial Correlation “Zero-Order” Correlation
Correlation coefficients for bivariate relationships
Pearson’s r

24. Statistical Control with Interval-Ratio Variables
Partial Correlation
Partial correlation coefficients are symbolized as ryx.z
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

25. 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

26. 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?

27. 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.

28. 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?