1. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved Chapter 11: Correlational Designs Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research Edition 5 John W. Creswell

2. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-2 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

3. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-3 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 Product-moment correlation coefficient: statistic that expresses linear relationships

4. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-4 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

5. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-5 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.

6. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-6 Types of Correlational Designs The explanatory design The prediction design

7. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-7 The 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 (or advanced form) Interpretation based on statistical test results indicate that the changes in one variable are reflected in changes in the other

8. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-8 The 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 variable(s) usually measured at one point in time; the criterion variable measured at a later point in time Purpose is to forecast future performance

9. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-9 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)

10. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5e – Creswell ISBN: 0132755912 © 2015, 2012, 2008 Pearson Education, Inc. All rights reserved. 11-10 Displays of Scores in a Scatterplot Hours of Internet use per week Depression (scores from 15– 45) + Depression scores Y=D.V. 50 40 30 20 10 M M + - - Hours of Internet Use X=I.V. 510 1520 29.39.7Mean Score 4818Jamal 172Maxine 306Jose 207Angela 4415Todd 255Rosa 20 9 Bill 18 5 Patricia 41 13 Chad 3017Laura

11. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-11 Displays of Scores in a Correlation Matrix 1. School satisfaction 2. Extra-curricular activities 3. Friendship 4. Self-esteem 5. Pride in school 6. Self-awareness 1 2 3 4 5 6 - - - - - 33 **.24 -.03 -.15. 65 **.24 * -.09 -.02.49*.16.29** -.02.39**.03.22 *p <.05 **p <.01 -

12. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-12 Associations Between Two Scores Direction (positive or negative) Form (linear or nonlinear) Degree and strength (size of coefficient) From -1.0 to +1.0 0 indicates no correlation

13. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-13 Association Between Two Scores: Linear and Nonlinear Patterns A. Positive Linear (r = +.75)B. Negative Linear (r = -.68) C. No Correlation (r =.00)

14. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-14 Linear and Nonlinear Patterns E. CurvilinearF. Curvilinear D. Curvilinear

15. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-15 Nonlinear Associations Statistics Spearman rho (r s ): Correlation coefficient for nonlinear ordinal data Point-biserial correlation: Used to correlate continuous data with a dichotomous variable Phi-coefficient: Used to determine the degree of association when both variable measures are dichotomous

16. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-16 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.

17. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-17 Multiple Variable Analysis: Partial Correlations Independent Variable Dependent Variable Time on TaskAchievement R =.50 r squared=(.50) 2 Partial Correlations: Use to determine extent to which a mediating variable influences both independent and dependent variables Motivation Time-on-TaskAchievement Motivation r squared = (.35) 2

18. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-18 Simple Regression Line Slope Depression Scores Regression Line Hours of Internet Use per Week 141520105 50 41 40 30 20 10 Intercept

19. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-19 Regression Line Y is the predicted score (i.e., criterion variable) X is the predictor variable b is the regression coefficient (i.e., slope of the line) a is the intercept or constant Y(predicted) = b (X) + a

20. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-20 Meta-Analysis Intent – to summarize the results of two or more studies on the same or similar issues Steps in conducting a meta-analysis Problem formation Search databases and gather studies Criteria for review of studies Effect sizes and statistical analysis of results of studies’ Calculate the summary effect Interpret the meaning of the summary effect across all studies

21. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-21 Using Advanced Correlational Statistical Procedures Factor analysis Discriminant function analysis Path analysis Structural equation modeling Hierarchical linear modeling

22. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-22 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 or editing data Stating cause and effect when data show patterns of relationships Not reporting effect sizes or significance testing Plagiarizing others Not reporting contradictory findings Not sharing data reports with others

23. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-23 Conducting a Correlational Study Determine if a correlational study best addresses the research problem Identify individuals to 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?

24. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-24 Evaluating a Correlational Study Adequate sample for hypothesis testing Display of correlational results in a table or graph Selection of an appropriate statistical test Interpretation about the direction, form, and magnitude of association Assessment of magnitude of association based on the coefficient of determination, p values, effect size, or coefficient size

25. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 5 th Ed. © (2015, 2012, 2008) by Pearson Education, Inc. All Rights Reserved 11-25 Evaluating a Correlational Study (cont’d) Identification of the predictor and criterion variables In a visual model, presentation of the expected (or predicted) relationships based on observed data