Key Ideas
• Purpose and use of correlational
designs
• How correlational research developed
• Types of correlational designs
• Key characteristics of correlational
designs
• Procedures used in correlational studies
• Evaluating a correlational study
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What is correlational research?
• In correlational research designs,
investigators use the correlation
statistical test to describe and measure
the degree of association (or
relationship) between two or more
variables or sets of scores.
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When do you use correlational
designs?
• To examine the relationship between two or
more variables
• To predict an outcome
– Co-vary
– Use one variable to predict the score on one
variable using knowledge about the other variable
• Statistic that expresses linear relationships is
the Product-Moment Correlation Coeffieicnt
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How did correlational
research develop?
• 1895 Pearson develops correlation formula
• 1897 Yule develops solutions for correlating two,
three and four variables
• 1935 Fisher pioneers significance testing and
analysis of variance
• 1963 Campbell and Stanley write about
experimental and quasi-experimental designs
• 1970s and 1980s computers give the ability to
statistically control variables and do multiple
regression
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Types of correlational designs:
Explanatory design
•
•
•
•
Correlate two or more variables
Collect data at one point in time
Analyze all participants as a single group
Obtain at least two scores for each individual in
the group - one for each variable
• Report the correlation statistic
• Interpretation based on statistical test results
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Types of correlational designs:
Prediction designs
• Predictor Variable: a variable that is used to
make a forecast about an outcome in the
correlational study.
• Criterion Variable: the outcome being
predicted
• “Prediction” usually is a word in the title
• Predictor variables usually measured at one
point in time and the criterion variable at a
later point in time.
• Purpose is to forecast future performance
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Displays of scores in a
Scatterplot
Hours of
Internet Depression
use
scores
per week from 15-45
Depression scores
Y=D.V.
50
-
40
30
20
+
10
M
5
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+
M
-
10 15 20
Hours of Internet Use
X=I.V.
Displays of scores in a
correlation matrix
1
1.School satisfaction
-
2. Extra-curricular activities -.33**
3. Friendship
.24
2
-.03
3
-
4
5
-
4. Self-esteem
-.15
.65** .24*
5. Pride in school
-.09
-.02
.49** .16
-
6. Self-awareness
.29** -.02
.39** .03
.22
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6
-
Associations between two
scores
• Direction (positive or negative)
• Form (linear or non-linear)
• Degree and strength (size of coefficient)
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Association Between Two Scores
Linear and non-linear patterns
A. Positive Linear (r=+.75) B. Negative Linear (r=-.68)
C. No Correlation
(r=.00)
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Linear and non-linear patterns
D. Curvilinear
E. Curvilinear
F. Curvilinear
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Non-linear associations
statistics
• Spearman rho (rs) - correlation
coefficient for nonlinear ordinal data
• Point-biserial - used to correlate
continuous interval data with a
dichotomous variable
• Phi-coefficient - used to determine the
degree of association when both
variable measures are dichotomous
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Association Between Two Scores
Degree and strength of association
• .20–.35: When correlations range from .20
to .35, there is only a slight relationship
• .35–.65: When correlations are above .35,
they are useful for limited prediction.
• .66–.85: When correlations fall into this range,
good prediction can result from one variable
to the other. Coefficients in this range would
be considered very good.
• .86 and above: Correlations in this range are
typically achieved for studies of construct
validity or test-retest reliability.
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Multiple Variable Analysis:
Partial correlations
r=.50
r squared=(.50)2
Time on Task
Independent
Variable
Dependent
Variable
Time-on-Task
Achievement
Achievement
Motivation
r squared = (.35)2
Partial Correlations:
use to determine extent
to which a mediating variable
influences both independent
and dependent variable
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Motivation
Simple Regression Line
Regression Line
50
41
40
Depression
Scores
30
Slope
20
10
Intercept
5
10
14 15
Hours of Internet Use Per Week
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20
Steps in conducting a
correlational study
• Determine if a correlational study best addresses the
research problem
• Identify the individuals in the study
• Identify two or more measures for each individual in
the study
• Collect data and monitor potential threats
• Analyze the data and represent the results
• Interpret the results
• Is the size of the sample adequate for hypothesis
testing?
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Evaluating a correlation study
• Does the researcher adequately display the results in
matrixes or graphs?
• Is there an interpretation about the direction and
magnitude of the association between the two
variables?
• Is there an assessment of the magnitude of the
relationship based on the coefficient of determination,
p-values, effect size, or the size of the coefficient?
• Is the researcher concerned about the form of the
relationship so that an appropriate statistic is chosen
for analysis?
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Evaluating a correlation study
• Has the researcher identified the predictor and
criterion variables?
• If a visual model of the relationships is advanced,
does the researcher indicate the expected
relationships among the variables, or, the
predicted direction based on observed data?
• Are the statistical procedures clearly defined?
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