Correlational Designs Chapter 12 Correlational Designs Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Explanatory Design Investigators correlate two or more variables Researchers collect data at one point in time Investigator analyzes all participants as a single group Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Key Correlational Characteristics Graphing pairs of scores to identify the form of association (relationship) direction of the associaiton degree of association Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Example of a Scatterplot Hours of Internet use per week Depression scores from 15-45 Depression scores Y=D.V. 50 - 40 + 30 M 20 - + 10 M 5 10 15 20 Hours of Internet Use X=I.V. Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Patterns of Association Between Two Variables A. Positive Linear (r=+.75) B. Negative Linear (r=-.68) Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Patterns of Association Between Two Variables C. No Correlation (r=.00) D. Curvilinear Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Patterns of Association Between Two Variables E. Curvilinear F. Curvilinear Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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= Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Advanced Statistical Procedures Partial Correlations - use to determine extent to which mediating variable influences both independent and dependent variable Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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) Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

Regression and Path Analysis + Time - on - Task + Student Learning Motivation + Prior Achievement - Time - on - Task Peer Friend Influence .24 .11 Path Analysis .13 .18 Student Learning Motivation Peer Achievement -.05 Peer Friend Influence Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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? Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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? Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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? Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.

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 Educational Research by John W. Creswell. Copyright ©2002 by Pearson Education. All rights reserved.