Causal inferences

1
Causal inferences

• Most of the analyses we have been performing
  involve studying the association between two or
  more variables.
• We often conduct these kinds of analyses because,
  implicitly, we have an assumed causal model in
  mind.
• The best way to test a hypothesized causal
  relationship is through experimental methods.

2
Causal inferences

• Unfortunately, we cannot experimentally study a
  lot of the important questions in personality for
  practical or ethical reasons.
• For example, if were interested in how a
  persons prior history in close relationships
  might influence his or her future relationships,
  we cant use an experimental design to manipulate
  the kinds of relational experiences that he or
  she had.

3
Causal inferences

• How can we make inferences about causality in
  these circumstances?
• There is no fool-proof way of doing so, but today
  one kind of tool that is commonly used partial
  correlation methods.

4
Statistical Control

• The biggest problem with inferring causality from
  correlations is the third variable problem. For
  any relationship we may study in psychology,
  there are a number of confounding variables that
  may interfere with our ability to make the
  correct causal inference.

5
Statistical Control

• Stanovich, a psychologist, has described an
  interesting example involving public versus
  private schools.
• It has been established empirically that children
  attending private schools perform better on
  standardized tests than children attending public
  schools.
• Many people believe that sending children to
  private schools will help increase test scores.

6
Statistical Control

• One of the problems with this inference is that
  there are other variables that could influence
  both the kind of school a kid attends and his or
  her test scores.
• For example, the financial status of the family
  is a possible confound.

test scores
quality of school


financial status
7
Statistical control

• One commonly used method for controlling possible
  confounds involves statistical techniques, such
  as multiple regression and partial correlation.
• In this we statistically control for the
  potential effects of the confounding variable to
  see how this impacts the correlation between the
  variables of interest.

8
Statistical control

• If you know the correlations among three
  variables (e.g, X, Y, and Z), you can compute a
  partial correlation, rYZ.X. A partial correlation
  characterizes the correlation between two
  variables (e.g., Y and Z) after statistically
  removing their association with a third variable
  (e.g., X).

9
Statistical control

• If this diagram represents the true state of
  affairs, then here are correlations we would
  expect between these three variables

Y
Z
test scores
quality of school
.5
.5
financial status

• We expect Y and Z to correlate about .25 even
  though one doesnt cause the other.

X
10
Statistical control
Y
Z
test scores
quality of school
.5
.5
financial status

• The partial correlation between Y and Z is 0,
  suggesting that there is no relationship between
  these two variables once we control for the
  confound.

X
11
Statistical control

• What happens if we assume that quality of school
  does influence student test scores?
• Here is the implied correlation matrix for this
  model

Y
Z
.5
test scores
quality of school
.5
.5
financial status
X
12
Statistical control
Y
Z
.5
test scores
quality of school
.5
.5
financial status

• The partial correlation is .65, suggesting that
  there is still an association between Y and Z
  after controlling X.

X
13
Statistical control

• Statistical control is not a foolproof method.
  If there are confounding variables that have not
  been measured, these unmeasured variables can
  produce a correlation between two variables.
• In short, if one is interested in making causal
  inferences about the relationship between two
  variables in a non-experimental context, it is
  wise to try to statistically control possible
  confounding variables.

14
Partial Correlations in SPSS

• In the Analyze menu, choose correlate and
  then partial.
• A new window will appear. Select the variables
  of interest and shoot them over to the
  Variables box.
• Select the variable you want to control for and
  shoot it over to the Controlling for box.
• Click the Ok button to run the analysis.

15

• The output shows a correlation table based on
  partial correlation methods. Notice that in this
  example, the partial correlation between school
  quality and test scores virtually disappears when
  family financial status is statistically
  controlled.

16
How would you write up these kinds of results?

• Table 1 shows the correlations among the quality
  of school attended, test scores, and family
  financial status. As can be seen, children
  attending better schools tended to have higher
  test scores (r .29). However, both variables
  also correlated positively with family financial
  status. To determine whether the correlation
  between school quality and test scores still held
  once controlling for family financial status, we
  conducted a partial correlation analysis. The
  partial correlation between school quality and
  test scores virtually disappeared (r .04) once
  we controlled for family financial status. Taken
  together, these findings suggest that the
  relationship between school quality and
  performance is due to the shared effects of
  family financial status. In other words, it does
  not appear that good schools necessarily produce
  good students once the potential confound of
  family financial status is taken into account.