# correlational research

```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
Educational Research 2e: Creswell
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.
Educational Research 2e: Creswell
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
Educational Research 2e: Creswell
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
Educational Research 2e: Creswell
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
Educational Research 2e: Creswell
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
Educational Research 2e: Creswell
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
Educational Research 2e: Creswell
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.
Educational Research 2e: Creswell
Multiple Variable Analysis:
Partial correlations
r=.50
r squared=(.50)2
Independent
Variable
Dependent
Variable
Achievement
Achievement
Motivation
r squared = (.35)2
Partial Correlations:
use to determine extent
to which a mediating variable
influences both independent
and dependent variable
Educational Research 2e: Creswell
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
Educational Research 2e: Creswell
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?
Educational Research 2e: Creswell
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?
Educational Research 2e: Creswell
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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