# Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning,

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Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition Chapter 12 Correlational Designs

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.2 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.3 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.4 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.5 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.

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.6 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.7 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.8 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)

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.9 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.10 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.11 Associations Between Two Scores Direction (positive or negative) Form (linear or nonlinear) Degree and strength (size of coefficient)

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.12 Association Between Two Scores: Linear and Nonlinear Patterns A. Positive Linear (r = +.75) B. Negative Linear (r = -.68) C.No Correlation (r =.00)

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.13 Linear and Nonlinear Patterns E. CurvilinearF. Curvilinear D. Curvilinear

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.14 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.15 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.

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.16 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

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.17 Simple Regression Line Slope Depression Scores Regression Line Hours of Internet Use per Week 141520105 50 41 40 30 20 10 Intercept

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.18 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?

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.19 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?

Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition 12.20 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?