Correlational Research

I.  Nature of Correlational Studies

II.  Interpreting Correlational Data

III.  Correlation and Causation

IV.  Improving Correlational Studies

V.  Conclusions

I.  Nature of Correlational Studies

A.  Another tool for the researcher

 1) as a first step prior to experimentation
 2) when experiments cannot be conducted (for ethical or practical reasons)

B.  Types of correlational studies

1) Observational Research

 e.g., class attendance and grades

2)  Survey Research

 e.g., living together and divorce rates

3) Archival Research

 e.g., violence and economics

C.  What a correlation measures:

Example:
 
Why are children aggressive?

 Hypothesis: aggression is a learned behavior as a result of modeling.
 Test:  look for associations between aggressive behavior and . . .

II.  Interpreting Correlations

A.  r scores range from -1 to +1

 r= 0, no relation
example of a near zero r:   hair length and GPA

 r= +1, perfect positive relation
example of a positive r: GPA and scores on SAT

B.  r² = percent of variation accounted for by the relation between x and y

Example: correlation between SAT and college GPA

r = .6, r² = .36  thus 36% percent accuracy in predicting GPA from SAT.

III.  Correlation and Causation

A.  Correlation as a first step in determining causation.

B.  Correlation does not prove causation

1)  directionality problem:

2)  third variable problem:
 
                              Z
                         /          \
                       v            v
                     X   <---->   Y
 

C.  Examples:

1)  smoking and violent crime (Brennan, 1999)

N= 4,169

Controlled for:

 socioeconomic status
 parental psychiatric problems
 age
 fatherís criminal history

Evaluation:

 1)  Is there a directionality problem?

 2)  Is there a possible third variable problem?
 

2)  Meese Commission and pornography:

ìThe objectives of the Commission are to determine the nature, extent, and impact on society of pornography in the United States.î
(Department of Justice, 1985)

Correlated trends in violent crime and trends in the publication of pornographic material.

Conclusion:
ìThis (upward) trend in the content of pornographic material is consistent with the Bureau of Justiceís recent study, showing an increase in crime and violence generally in North America.î

Evaluation:

 1)  Is there a directionality problem?

 2)  Is there a possible third variable problem?

Incidence of violent crime will positively correlate with anything that increased during the same period of time.
Example:  Correlation between the incidence of rape and membership in the Southern Baptist church was +.96 during the same time period (Mould, 1990).

IV.  Improving Correlational Studies

A.  Cross-lagged-panel correlation

1)  As a means to untangle the directionality problem in correlational research
2)  Take two sets of correlations separated by a time interval

Eron, Huesman, Lefkowitz & Walder (1972).

B. Partial Correlation

C.  Multiple Correlation

Example:  estimate the gain in weight due to quitting smoking (Williamson et al., 1991 N.E.J.M.)

taking into account:
age, race, level of education, duration of follow-up, changes in physical activity, and reproductive history

Simple linear correlation:
y = mx + b  (equation for a line).

Multiple correlation:
y = m₁x₁ + m₂x₂ + m₃x₃ + . . .

Where: m₁  = influence of age
             m₂ = influence of race
                 etc.

mean wt. gain attributable to smoking:  3.8 kg (8.4 lbs.)

V.  Conclusions

A.  Correlational studies as a means of looking for relations between variables when experiments cannot be done

B.  How to interpret correlation

C.  Never infer causation

D.  How to come closer to making causal inferences (partial and multiple r).