Correlation and
Correlational
Research
Passer Chapter 5
Slides Prepared by Alison L. O’Malley
Correlation
• Correlations reveal the degree of statistical
association between two variables, and can
be computed in experimental and nonexperimental research designs
•Correlational research establishes whether
naturally occurring variables are
statistically related
•How does correlational research differ
from experimental research?
Correlational Research
• In correlational research, variables are
measured rather than manipulated
• Manipulation is the hallmark of
experimentation which enables
researchers to draw causal inferences
• This distinction between measurement
and manipulation drives the oft-cited
mantra “correlation does not equal
causation”
Thinking Critically about
Correlational Research
What information do you need to know in
order to determine whether a study uses an
experimental or correlational research
design?
Generate a research question that lends
itself to a correlational research design but
not an experimental research design.
Direction of Relationship: Positive
•Two variables tend to increase or decrease
together
•Higher scores on X are associated with
higher scores on Y
•Lower scores on X are associated with
lower scores on Y
•Envision two people in an elevator
Direction of Relationship: Negative
•Two variables tend to move in opposite
directions
•Higher scores on X are associated with
lower scores on Y
•Lower scores on X are associated with
higher scores on Y
•Envision two people on a see-saw
Examine the pattern of association
between (a) X and Y1 and (b) X and Y2
Correlation Practice
Generate your own example of each of the
following:
• A positive relationship
• A negative relationship
• A relationship that is not significantly
different than zero
Measuring Correlations
What scale of measurement are we dealing with?
• Pearson product-moment correlation
coefficient
• Pearson’s r
• Variables measured on interval or ratio scale
• Spearman’s rank-order correlation coefficient
• Spearman’s rho
• One or both variables measured on ordinal
scale
Interpreting Correlations
In addition to considering the direction of
the relationship (i.e., positive or negative),
we need to attend to the strength of the
relationship.
-1.00
0.00
+1.00
Interpreting Correlation Strength
• Is the relationship between two variables
weak? Moderate? Strong?
Guidelines from
Absolute value
Cohen (1988)
Weak
.10 - .29
Moderate
.30 - .49
Strong
> .50
Interpreting Correlations
• Pay close attention to how variables were
coded
• In most (but not all) cases, higher values
reflect more of the underlying attribute
[Note: this does not apply to nominal
data]
Interpreting Correlations
If a psychological scientist establishes a
correlation of .33 between integrity and job
performance, can one say that the two
variables are 33% related?
Interpreting Correlations
If a psychological scientist establishes a
correlation of .33 between integrity and job
performance, can one say that the two
variables are 33% related?
No. r2 (coefficient of determination) reveals
how much of the differences in Y scores are
attributable to differences in X scores.
Interpreting Correlations
How much “overlap” is there?
?
Y
X
Y
Interpreting Correlations
How much “overlap” is there?
?
Y
X
Y
If r = .33, then r2 = .11
11% of the variance in Y is attributable to X
Interpreting Correlations: Scatter
Plots
How are the properties of correlation
coefficients – sign and strength – reflected
in each of these scatter plots?
Correlation ≠ Causation
Review the three criteria used to draw
causal inferences…
Which criterion/criteria is/are impacted by
the bidirectionality problem? The thirdvariable problem?
Correlation ≠ Causation
Strategies to Reduce Causal Ambiguity
1. Statistical approaches
• Measure and statistically control for
(i.e., partial out) a third variable
2. Research design approaches
• When possible, conduct longitudinal
studies
Why are longitudinal studies preferable to
cross-sectional studies?
Longitudinal Research Designs
• Prospective design
• X measured at Time 1, Y measured at Time 2
• Rules out bidirectionality problem
• Cross-lagged panel design
• Measure X and Y at Time 1
• Repeat X and Y measurement at Time 2
• Examine pattern of relationships (i.e., crosslagged correlations) across variables and time
Cross-Lagged Panel Design
What does it mean when a correlation
is “spurious”?
Drawing Causal Conclusions
• How do we rule out all plausible third
variables (confounds) using
correlational research designs?
• We can’t… only the control afforded by
rigorous experimentation provides
strong tests of causation.
• So what good are correlational
studies?
Correlation and Prediction
• A goal of science is to forecast
future events
• In simple linear regression, scores
on X can be used to predict scores
on Y assuming a meaningful
relationship (r) has been
established between X and Y in
past research
Linear Regression
• E.g., Scores on a job interview (X)
can be used to predict job
performance (Y)
• X is the predictor; Y is the criterion
• Interview scores plugged into
regression equation and hiring
decisions made based on results
• This is an illustration of criterion
validity
Regression
Regression line generated through application
of regression equation
Multiple Regression
•Multiple predictors are used to predict a
criterion measure
•Strive for as little overlap as possible
between predictors (i.e., want to account
for unique variance in criterion)
Multiple Regression
Which scenario is preferable?
(a)
General
CAT
Structured
Interview
Criterion
Work
Sample
(b)
Structured
Interview
General
CAT
Criterion
Work
Sample
Nonlinear Relationships
Pearson’s r is useless in cases
where X and Y do not relate in a
linear fashion. See the curvilinear
relationship below.
test
performance
sleepy
alert
Alertness
panic
Range Restriction
Special Considerations
• Make sure to examine your scatterplot
• Are X and Y related in a linear fashion?
• Do your data reveal range restriction?
• What scales of measurement are you dealing
with?
If the relationship of interest is nonlinear and/or
you have range restriction and/or you have
nominal data, calculating r will produce
inaccurate, misleading results!
Closing Considerations
•Correlation is a powerful statistical tool
and correlational research can shed light
on important questions…
•But make sure to employ these tools
wisely! Unfortunately, the media and even
some researchers can report misleading
findings.
• And remember, by itself correlation does
not establish causation!