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© 2011 Pearson Education, Inc. All rights reserved.
Correlations
•
Human (logical) thought tends to reflect linearity
If “A”
then “B”
• Measures of relationship between variables
• Can permit future predictions of one variable from
knowledge of another
• Can raise questions about cause-and-effect patterns
(can only be established with experimental research)
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The Nature of Correlational Research
•
•
•
Purpose is to discover corelationships between two or
more variables; seeks out conditions that covary, or
correlate, with each other
A corelationship exists when an individual’s status
(score) on one variable tends to reflect the status (score)
on another
Correlations help us:
» Understand related events, behaviors, etc.
» Predict future events, etc. from what we know about
another
» Sometimes obtain strong suggestions that one
variable may be causing another
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Cautions about Cause-and-Effect…
Post hoc fallacy, Post hoc ergo propter hoc.
“after the fact, because of the fact”
»
The “cause” can actually be the “effect” (or vice versa)
»
This is a common fallacy of logical thinking
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Topics for Correlational Research
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If a relationship is suspected
•
If you wish to predict values on one variable from
another
•
If you need to establish instrument validity or reliability
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Correlational Research Design
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Typically oriented by research questions or hypotheses
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A relatively straightforward design:
»
Identify variables for inclusion
»
Formulate questions or hypotheses
»
Select a random sample (preferably with n > 30)
»
Obtain data for each member of the sample on each
variable being investigated
»
Compute correlations in order to determine degree
of relationship
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Types of Bivariate (2 variables)
Correlation Coefficients
•
Pearson product-moment correlation (a.k.a., Pearson r
or r)—correlation between two continuous variables
•
Biserial correlation—one continuous variable and one
artificial dichotomous variable
•
Point-biserial correlation—one continuous variable and
one natural dichotomous variable
•
Phi correlation ()—two natural dichotomous variables
•
Tetrachoric correlation—two artificial dichotomous
variables
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Types of Bivariate (2 variables)
Correlation Coefficients (cont’d.)
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Spearman rho (rs)—two ranked variables, with larger
samples
•
Kendall’s tau ()—two ranked variables, with
samples < 10
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Types of Multivariate (> 2 variables)
Correlation Coefficients
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•
•
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Partial correlation (partial r)—correlation between two
variables with the effects of a third variable “partialed
out”
Multiple regression—used to determine degree of
relationship between one continuous dependent
variable (“criterion variable”) and a combination of
independent variables (“predictor variables”)
Discriminant analysis—analogous to MR, but criterion
variable is categorical (e.g., “pass-fail”)
Factor analysis—used with a large number of
correlated variables; variables are statistically grouped
into clusters, known as “factors”
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© 2011 Pearson Education, Inc. All rights reserved.
Interpretation of Correlation
Coefficients
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•
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Most coefficients range from -1.00 to +1.00 (some range
from 0 to +1.00)
1.00 = a perfect correlation/relationship; 0 = no
correlation/relationship
General rule of thumb for interpretation:
-1.00
-.70
-.30
0
+.30
+.70
+1.00
|------|------|------|------|------|------|
weak relationship
moderate
relationship
moderate
relationship
strong
relationship
strong
relationship
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Published Example of Correlational
Research
“Influence of Reading Attitude on Reading
Achievement:
A Test of the Temporal-Interaction Model”
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Applying Technology…
Web sites related to correlational research
• Dr. Rousey’s discussion of "Correlational Research"
(www.fractaldomains.com/devpsych/corr.htm)
• A second page of examples from Dr. Rousey
(www.fractaldomains.com/devpsych/corr2.htm)
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Causal-Comparative Research
• Explores the possibility of cause-and-effect
relationships when experimental and quasiexperimental approaches are not feasible
• Used when manipulation of the independent variable is
not ethical or is not possible
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The Nature of Causal-Comparative
Research
• Conducted to explore possible cause-and-effect
relationships
• Differs from experimental and quasi-experimental
research:
» Independent variable is not manipulated
» Focuses first on the effect, then tries to determine
possible causes (ex post facto)
• Questions will remain about the effect following the
cause, or vice versa
• Other conditions must also be considered as “plausible
causes”
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Published Example of CausalComparative Research
“Blended Learning and Sense of Community: A
Comparative Analysis with Traditional and Fully Online
Graduate Courses”
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