1. Correlational Designs
Chapter 12
Correlational Designs
Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved.

2. Key Ideas Brief history of correlational research
Explanatory and predictor designs
Characteristics of correlational research
Scatterplots and calculating associations
Steps in conducting a correlational study
Criteria for evaluating correlational research
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

3. A Brief History of Correlational Designs
1895 Pearson develops correlation formula
1897 Yule develops solutions for correlating two, three and four variables
1935 Fisher prisoners significance testing and analysis of variance
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

4. A Brief History of Correlational Designs
1963 Campbell and Stanley write on experimental and quasi-experimental designs
1970’s and 1980’s computers give the ability to statistically control variables and do multiple regression
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

5. Explanatory Design Investigators correlate two or more variables
Researchers collect data at one point in time
Investigator analyzes all participants as a single group
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

6. Explanatory Design
Researcher obtains at least to scores for each individual in the group - one for each variable
Researcher reports the use of the correlation statistical test (or an extension of it) in the data analysis
Researcher makes interpretations or draws conclusions from statistical test results
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

7. Prediction Design: Variables
Predictor Variable: a variable that is used to make a forecast about an outcome in the correlational study.
Criterion Variable: the outcome being predicted
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

8. Prediction Design: Characteristics
The authors typically include the word “prediction” in the title
The researchers typically measure the predictor variables at one point in time and the criterion variable at a later point in time.
The authors are interested in forecasting future performance
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

9. Key Correlational Characteristics
Graphing pairs of scores to identify
the form of association (relationship)
direction of the associaiton
degree of association
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

10. Example of a Scatterplot
Hours of
Internet
use
per week
Depression
scores
from 15-45
Depression scores
Y=D.V. 50 - 40 + 30 M 20 - + 10 M 5 10 15 20
Hours of Internet Use
X=I.V.
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

11. Patterns of Association Between Two Variables
A. Positive Linear (r=+.75)
B. Negative Linear (r=-.68)
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

12. Patterns of Association Between Two Variables
C. No Correlation (r=.00)
D. Curvilinear
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

13. Patterns of Association Between Two Variables
E. Curvilinear
F. Curvilinear
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

14. Calculating Association Between Variables
Pearson Product Moment (bivariate) rxy
degree to which X and Y vary together
degree to which X and Y vary separately
Uses of Pearson Product Moment
“+” or “-” linear association (-1.00 to +1.00)
test-retest reliability
internal consistency
construct validity
confirm disconfirm hypotheses r=
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

15. Calculating Association Between Variables
Display correlation coefficients in a matrix
Calculate the coefficient of determination
assesses the proportion of variability in one variable that can be determined or explained by a second variable
Use r2 e.g. if r=.70 (or -.70) squaring the value leads to r2= % of variance in Y can be determined or explained by X
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

16. Using Correlations For Prediction
Use the correlation to predict future scores
Plotting the scores provides information about the direction of the relationship
Plotting correlation scores does not provide specific information about predicting scores from one value to another
Use a regression line (‘best fit for all”) for prediction
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

17. Simple Regression Line
Depression Scores
Regression Line 50 41 40
Slope 30 20 10
Intercept 5 10 14 15 20
Hours of Internet Use Per Week
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

18. Other Measures of Association
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 by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

19. Advanced Statistical Procedures
Partial Correlations - use to determine extent to which mediating variable influences both independent and dependent variable
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

20. Common Variance Shared for Bivariate Correlation
Independent Variable
Independent Variable
Achievement
Time on Task
r=.50
Time on Task
Achievement
r squared = (.50)2
Shared Variance
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

21. Advanced Statistical Procedures
Multiple Correlation or Regression - multiple independent variables may combine to correlate with a dependent variable
Path analysis and latent variable causal modeling (structural equation modeling)
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

22. Regression and Path Analysis+
Time - on - Task +
Student Learning
Motivation +
Prior Achievement -
Time - on - Task
Peer Friend Influence
.24
.11
Path Analysis
.13
.18
Student Learning
Motivation
Peer Achievement
-.05
Peer Friend Influence
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

23. 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
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

24. Criteria For Evaluating Correlational Research
Is the size of the sample adequate for hypothesis testing? (sufficient power?)
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?
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

25. Criteria For Evaluating Correlational Research
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 by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

26. Criteria For Evaluating Correlational Research
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 by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

27. Applying What you Have Learned: A Correlational Study
Review the article and look for the following:
The research problem and use of quantitative research
Use of the literature
The purpose statement and research hypothesis
Types and procedures of data collection
Types and procedures of data analysis and interpretation
The overall report structure
Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.