Creswell Chapter 11 - Correlational Designs
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Transcript Creswell Chapter 11 - Correlational Designs
Chapter 11
Correlational Designs
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Creswell, Educational Research: Planning, Conducting, and
Evaluating Quantitative and Qualitative Research, 4e
© 2012, 2008, 2005, 2002 Pearson Education, Inc.
All rights reserved.
By the end of this chapter,
you should be able to:
Define correlation research, and describe when to
use it, and how it developed
Identify the two types of correlational designs
Describe the key characteristics of correlational
designs
Identify potential ethical issues in conducting
correlational research
Identify steps in conducting a correlational study
List the criteria for evaluating a correlational study
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-2
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
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
Statistic that expresses linear
relationships is the product-moment
correlation coefficient
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-3
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
When to Use Correlational
Designs
To examine the relationship between
two or more variables
To predict an outcome:
Look at how the variables co-vary together
Use one variable to predict the score on
another variable
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-4
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
The Development of
Correlational Research
1895 Pearson develops correlation formula.
1897 Yule develops solutions for correlating two, three,
and four variables.
1935 Fisher pioneered significance testing and analysis
of variance.
1963 Campbell and Stanley write about experimental and
quasi-experimental designs (including correlational
designs).
1970s and 1980s computers give the ability to statistically
control variables and do multiple regression.
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-5
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
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
indicate that the changes in one variable are
reflected in changes in the other
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-6
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
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 used in the title
Predictor variables usually measured at one
point in time; the criterion variable measured
at a later point in time
Purpose is to forecast future performance
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-7
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Characteristics of
Correlational Designs
Displays of scores (scatterplots and
matrices)
Associations between scores (direction,
form, and strength)
Multiple variable analysis (partial
correlations and multiple regression)
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-8
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Displays of Scores in a
Scatterplot
Depression scores
Hours of
Internet
use
per week
Depression
(scores from 15–
45)
Laura
17
30
Chad
13
41
Patricia
5
18
Bill
9
20
Rosa
5
25
Todd
15
44
Angela
7
20
Jose
6
30
Maxine
2
17
Jamal
18
48
Mean Score
9.7
29.3
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
Y=D.V.
50
-
40
30
20
+
10
M
5
11-9
+
M
-
10 15 20
Hours of Internet Use
X=I.V.
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Displays of Scores in a
Correlation Matrix
1
1.School satisfaction
2
-
2. Extra-curricular activities 33**
3. Friendship
-
.24
-.15
.
5. Pride in school
-.09
-.02
*p < .05
**p < .01
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
-
-.03
4. Self-esteem
6. Self-awareness
3
65**
.29** -.02
11-10
.24*
4
5
6
-
.49* .16
-
.39** .03 .22
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
-
Associations Between Two
Scores
Direction (positive or negative)
Form (linear or nonlinear)
Degree and strength (size of
coefficient)
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-11
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Association Between Two Scores:
Linear and Nonlinear Patterns
A. Positive Linear (r = +.75) B. Negative Linear (r = -.68)
C. No Correlation
(r = .00)
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-12
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Linear and Nonlinear Patterns
D. Curvilinear
E. Curvilinear
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
F. Curvilinear
11-13
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Education, Inc.
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Nonlinear 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: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-14
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
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: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-15
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Multiple Variable Analysis:
Partial Correlations
R = .50
r squared=(.50)2
Time on Task
Independent
Variable
Dependent
Variable
Achievement
Time-on-Task
Achievement
Motivation
r squared = (.35)2
Motivation
Partial Correlations:
Use to determine extent
to which a mediating variable
influences both independent
and dependent variables
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-16
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
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: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-17
20
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Meta-Analysis
Intent – to summarize the results of many
correlational studies
Process:
Locate correlational studies on a single topic
Note the results for each study
Calculate an overall result for all of the studies
Reports this result
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-18
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Potential Ethical Issues in
Correlational Research
Not measuring appropriate controls
Not having a sufficient sample size and meeting the
assumptions of the statistic
Making up data
Stating cause and effect when data show patterns of
relationships
Not reporting effect sizes
Plagiarizing others
Not reporting contradictory findings
Not sharing data reports with others
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-19
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
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: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-20
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Evaluating a Correlational
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?
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-21
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.
Evaluating a Correlational
Study (cont’d)
Is the researcher concerned about the form of
the relationship so that an appropriate statistic is
chosen for analysis?
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?
Educational Research: Planning, Conducting,
and Evaluating Quantitative and Qualitative
Research, 4e – Creswell
ISBN: 0132755912
11-22
© 2012, 2008, 2005, 2002 Pearson
Education, Inc.
All rights reserved.