Class 6: Chapter 12. Key Ideas. Explanatory Design. Correlational Designs

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1 Class 6: Chapter 12 Correlational Designs l 1 Key Ideas Explanatory and predictor designs Characteristics of correlational research Scatterplots and calculating associations Steps in conducting a correlational study Criteria for evaluating correlational research 2 Explanatory Design Correlate two or more variables Collect data at one point in time Analyze all participants as a single group Obtain at least 2 scores for each individual in the group - 1 per variable Report the use of the correlation statistical test (or an extension of it) in the data analysis Make interpretations or draw conclusions from statistical test results 3 1

2 Prediction Design Predictor Variable: a variable used to forecast an outcome Criterion Variable: the outcome predicted Typically include the word prediction in the title Typically measure the predictor variables at one point in time and the criterion variable at a later point in time. The goal is forecasting future performance 4 Key Correlational Characteristics Graphing pairs of scores to identify the form of association (relationship) direction of the associaiton degree of association 5 Example of a Scatterplot Hours of Internet use per week Depression scores from Laura Chad Patricia 5 18 Bill 9 20 Mary 5 25 Todd Angela 7 20 David 6 30 Maxine 2 17 John Mean Score Depression scores Y=D.V. - M 10 M Hours of Internet Use X=I.V. 6-2

3 Patterns of Association Between Two Variables A. Positive Linear (r=.75) B. Negative Linear (r=-.68) 7 Patterns of Association Between Two Variables C. No Correlation (r=.00) D. Curvilinear 8 Patterns of Association Between Two Variables E. Curvilinear F. Curvilinear 9 3

4 Calculating Association Between Variables Pearson Product Moment correlation coefficient (bivariate) r xy degree to which X and Y vary together r = 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 10 Calculating Association Between Variables Display correlation coefficients in a matrix (r with p *)(page 371) Calculate the coefficient of determination r 2 the proportion of variability in one variable that can be determined or explained by a second variable Test r 2 for statistical significance (effect size) 11 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 Y (predicted) = b(x) a predicted Y, slope, score, constant (Y with X = 0) 12 4

5 Simple Regression Line Depression Scores Regression Line 30 Slope Intercept Hours of Internet Use Per Week 13 Other Measures of Association 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 14 Advanced Statistical Procedures Partial Correlations - use to determine extent to which mediating variable influences both IV and DV Multiple Regression - multiple IVs may combine to correlate with a DV Path analysis Latent variable causal modeling (structural equation modeling) 15 5

6 Common Variance Shared for Bivariate Correlation Independent Variable Time on Task r=.50 Dependent Variable Achievement Achievement Time on Task r 2 = (.50) 2 Shared Variance 16 Common Variance Shared for Partial Correlation Independent Variable Time on Task r=.50 Dependent Variable Achievement Time on Task Achievement Motivation r 2 = (.35) 2 Shared Variance, effects of X2 removed 17 Regression versus Path Analysis Regression Time - on - Task Motivation - Student Learning Prior Achievement Time - on - Task Peer Friend Influence Path Analysis Peer Achievement Motivation Student Learning -.05 Peer Friend Influence 18 6

7 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 19 Criteria For Evaluating Correlational Research 1. Is the size of the sample adequate for hypothesis testing? (sufficient power?) 2. Does the researcher adequately display the results in matrixes or graphs? 3. 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? 5. Is the researcher concerned about the form of the relationship so that an appropriate statistic is chosen for analysis? 21 7

8 6. Has the researcher identified the predictor and criterion variables? 7. 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? 8. Are the statistical procedures clearly defined? 22 8