Transcript Slide 1

Chapter 12
Correlational Designs
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
By the end of this chapter,
you should be able to:
Define the purpose and use of correlational
designs
Describe how correlational research developed
Describe types of correlational designs
Identify key characteristics of correlational
designs
List procedures used in correlational studies
Evaluate correlational studies
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.2
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
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.3
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
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.4
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.
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.5
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
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.6
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
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.7
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)
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.8
Displays of Scores in a Scatterplot
Hours of Depression
Internet (scores from
use
15–45)
per week
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
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Depression scores
Y=D.V.
50
-
40
30
+
M
20
+
10
M
5
-
10 15 20
Hours of Internet Use
X=I.V.
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.9
Displays of Scores in a Correlation
Matrix
1
1.School satisfaction
-
2. Extra-curricular activities -.33**
3. Friendship
.24
2
-.03
3
-
4
5
6
-
4. Self-esteem
-.15
.65** .24*
5. Pride in school
-.09
-.02
.49** .16
-
6. Self-awareness
.29** -.02
.39** .03
.22
-
*p < .05
**p < .01
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.10
Associations Between Two Scores
Direction (positive or negative)
Form (linear or nonlinear)
Degree and strength (size of coefficient)
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.11
Association Between Two Scores:
Linear and Nonlinear Patterns
A. Positive Linear (r = +.75) B. Negative Linear (r = -.68)
C. No Correlation
(r = .00)
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.12
Linear and Nonlinear Patterns
D. Curvilinear
E. Curvilinear
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
F. Curvilinear
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.13
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
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.14
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 .
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.15
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 variables
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Motivation
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.16
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
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
20
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.17
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?
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.18
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?
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.19
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?
John W. Creswell
Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research, third edition
Copyright © 2008 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
12.20