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Chapter 12

Chapter 12 . Correlational Designs. 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

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Chapter 12

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  1. Chapter 12 Correlational Designs John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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 John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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 John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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 John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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. John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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 John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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 John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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) John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  9. Depression scores Y=D.V. Hours of Internet use per week Depression (scores from 15–45) 50 - Laura 17 30 40 Chad 41 13 Patricia 18 5 + M 30 Bill 20 9 Rosa 5 25 20 Todd 15 44 + - Angela 7 20 10 Jose 6 30 M Maxine 2 17 5 10 15 20 Hours of Internet Use X=I.V. Jamal 18 48 Mean Score 9.7 29.3 Displays of Scores in a Scatterplot John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  10. Displays of Scores in a Correlation Matrix 1 2 3 4 5 6 - • 1.School satisfaction • 2. Extra-curricular activities • 3. Friendship • 4. Self-esteem • 5. Pride in school • 6. Self-awareness - -.33** - .24 -.03 - -.15 .65** .24* - -.09 -.02 .49**.16 - .29** -.02 .39**.03 .22 *p < .05 **p < .01 John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  11. 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

  12. B. Negative Linear (r = -.68) A. Positive Linear (r = +.75) • No Correlation • (r = .00) Association Between Two Scores: Linear and Nonlinear Patterns John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  13. D. Curvilinear E. Curvilinear F. Curvilinear Linear and Nonlinear Patterns John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  14. 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

  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 . John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  16. Multiple Variable Analysis: Partial Correlations Independent Variable Dependent Variable R = .50 r squared=(.50)2 Time on Task Achievement Time-on-Task Achievement Motivation 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

  17. Simple Regression Line Regression Line 50 41 40 Depression Scores Slope 30 20 10 Intercept 5 10 14 15 20 Hours of Internet Use per Week John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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? John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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? John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

  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? John W. Creswell Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, third edition

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