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

l 2 Key Ideas Brief history of correlational research Brief history of correlational research Explanatory and predictor designs Explanatory and predictor designs Characteristics of correlational research Characteristics of correlational research Scatterplots and calculating associations Scatterplots and calculating associations Steps in conducting a correlational study Steps in conducting a correlational study Criteria for evaluating correlational research Criteria for evaluating correlational research

l 3 A Brief History of Correlational Designs 1895 Pearson develops correlation formula 1895 Pearson develops correlation formula 1897 Yule develops solutions for correlating two, three and four variables 1897 Yule develops solutions for correlating two, three and four variables 1935 Fisher prisoners significance testing and analysis of variance 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 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 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 Investigators correlate two or more variables Researchers collect data at one point in time Researchers collect data at one point in time Investigator analyzes all participants as a single group 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 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 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 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. Predictor Variable: a variable that is used to make a forecast about an outcome in the correlational study. Criterion Variable: the outcome being predicted Criterion Variable: the outcome being predicted

l 8 Prediction Design: Characteristics The authors typically include the word “prediction” in the title 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 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 The authors are interested in forecasting future performance

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

l 10 Example of a Scatterplot Hours of Internet use per week Depression scores from M M Depression scores Y=D.V. Hours of Internet Use X=I.V

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

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

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

l 14 Calculating Association Between Variables Pearson Product Moment (bivariate) r xy Pearson Product Moment (bivariate) r xy degree to which X and Y vary together degree to which X and Y vary together degree to which X and Y vary separately degree to which X and Y vary separately Uses of Pearson Product Moment Uses of Pearson Product Moment “+” or “-” linear association (-1.00 to +1.00) “+” or “-” linear association (-1.00 to +1.00) test-retest reliability test-retest reliability internal consistency internal consistency construct validity construct validity confirm disconfirm hypotheses confirm disconfirm hypotheses r=

l 15 Calculating Association Between Variables Display correlation coefficients in a matrix Display correlation coefficients in a matrix Calculate the coefficient of determination Calculate the coefficient of determination assesses the proportion of variability in one variable that can be determined or explained by a second variable assesses the proportion of variability in one variable that can be determined or explained by a second variable Use r 2 e.g. if r=.70 (or -.70) squaring the value leads to r 2 = % of variance in Y can be determined or explained by X Use r 2 e.g. if r=.70 (or -.70) squaring the value leads to r 2 = % of variance in Y can be determined or explained by X

l 16 Using Correlations For Prediction Use the correlation to predict future scores Use the correlation to predict future scores Plotting the scores provides information about the direction of the relationship 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 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 Use a regression line (‘best fit for all”) for prediction

l 17 Simple Regression Line Slope Depression ScoresRegression Line Hours of Internet Use Per Week Intercept

l 18 Other Measures of Association Spearman rho (r s ) - correlation coefficient for nonlinear ordinal data Spearman rho (r s ) - correlation coefficient for nonlinear ordinal data Point-biserial - used to correlate continuous interval data with a dichotomous variable 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 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 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 Time on Task Achievement 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 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) Path analysis and latent variable causal modeling (structural equation modeling)

l 22 Regression and Path Analysis Regression Time - on - Task Motivation Prior Achievement Peer Friend Influence Peer Achievement Motivation Student Learning Peer Friend Influence Student Learning Path Analysis Time - on - Task

l 23 Steps in Conducting a Correlational Study Determine if a correlational study best addresses the research problem Determine if a correlational study best addresses the research problem Identify the individuals in the study Identify the individuals in the study Identify two or more measures for each individual in the study Identify two or more measures for each individual in the study Collect data and monitor potential threats Collect data and monitor potential threats Analyze the data and represent the results Analyze the data and represent the results Interpret the results Interpret the results

l 24 Criteria For Evaluating Correlational Research Is the size of the sample adequate for hypothesis testing? (sufficient power?) Is the size of the sample adequate for hypothesis testing? (sufficient power?) Does the researcher adequately display the results in matrixes or graphs? 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 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 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? 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? 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? 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? 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 The research problem and use of quantitative research Use of the literature Use of the literature The purpose statement and research hypothesis The purpose statement and research hypothesis Types and procedures of data collection Types and procedures of data collection Types and procedures of data analysis and interpretation Types and procedures of data analysis and interpretation The overall report structure The overall report structure