1. Creswell, Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. Correlational Designs Chapter 11 This multimedia product and its contents are protected under copyright law. The following are prohibited by law: any public performance or display including transmission of any image over a network; preparation of any derivative work, including the extraction, in whole or in part, of any images; any rental, lease, or lending of the program.

2. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 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. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 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 Statistic that expresses linear relationships is the product-moment correlation coefficient

4. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 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. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 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. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-6 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

7. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-7 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

8. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-8 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)

9. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-9 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

10. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-10 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 -

11. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-11 Associations Between Two Scores Direction (positive or negative) Form (linear or nonlinear) Degree and strength (size of coefficient)

12. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-12 Association Between Two Scores: Linear and Nonlinear Patterns A. Positive Linear (r = +.75) B. Negative Linear (r = -.68) C.No Correlation (r =.00)

13. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-13 Linear and Nonlinear Patterns E. CurvilinearF. Curvilinear D. Curvilinear

14. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-14 Nonlinear Associations Statistics Spearman rho (r s ): 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

15. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-15 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.

16. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-16 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

17. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-17 Simple Regression Line Slope Depression Scores Regression Line Hours of Internet Use per Week 141520105 50 41 40 30 20 10 Intercept

18. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-18 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

19. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-19 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

20. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-20 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?

21. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-21 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?

22. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4e – Creswell ISBN: 0132755912 © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. 11-22 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?