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Comprehensive Guide to Correlational Research: History, Design, and Interpretation

Explore the history, design, and interpretation of correlational research, including explanatory and predictor designs, steps in conducting a study, and advanced statistical procedures. Learn about scatterplots, calculating associations, and using correlations for prediction.

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Comprehensive Guide to Correlational Research: History, Design, and Interpretation

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  1. Chapter 12 Correlational Designs EDUC 640 Dr. William M. Bauer l

  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 l

  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 l

  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 l

  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 l

  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 l

  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 l

  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 l

  9. Key Correlational Characteristics • Graphing pairs of scores to identify • the form of association (relationship) • direction of the associaiton • degree of association l

  10. Example of a Scatterplot Hours of Internet use per week Depression scores from 15-45 Depression scores Y=D.V. 50 - 40 + M 30 - 20 + 10 M 5 10 15 20 Hours of Internet Use X=I.V. l

  11. Patterns of Association Between Two Variables B. Negative Linear (r=-.68) A. Positive Linear (r=+.75) l

  12. Patterns of Association Between Two Variables C. No Correlation (r=.00) D. Curvilinear l

  13. Patterns of Association Between Two Variables F. Curvilinear E. Curvilinear l

  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= l

  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=.49. 49% of variance in Y can be determined or explained by X l

  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 l

  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 l

  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 l

  19. Advanced Statistical Procedures • Partial Correlations - use to determine extent to which mediating variable influences both independent and dependent variable l

  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 l

  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) l

  22. Regression and Path Analysis Regression + Time - on - Task + Student Learning Motivation + Prior Achievement - Time - on - Task Peer Friend Influence .11 .24 Path Analysis .13 .18 Student Learning Motivation Peer Achievement -.05 Peer Friend Influence l

  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 l

  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? l

  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? l

  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? l

  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 l

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