Key Ideas • Purpose and use of correlational designs • How correlational research developed • Types of correlational designs • Key characteristics of correlational designs • Procedures used in correlational studies • Evaluating a correlational study Educational Research 2e: Creswell 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. Educational Research 2e: Creswell When do you use correlational designs? • To examine the relationship between two or more variables • To predict an outcome – Co-vary – Use one variable to predict the score on one variable using knowledge about the other variable • Statistic that expresses linear relationships is the Product-Moment Correlation Coeffieicnt Educational Research 2e: Creswell How did correlational research develop? • 1895 Pearson develops correlation formula • 1897 Yule develops solutions for correlating two, three and four variables • 1935 Fisher pioneers significance testing and analysis of variance • 1963 Campbell and Stanley write about experimental and quasi-experimental designs • 1970s and 1980s computers give the ability to statistically control variables and do multiple regression Educational Research 2e: Creswell 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 Educational Research 2e: Creswell 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 is a word in the title • Predictor variables usually measured at one point in time and the criterion variable at a later point in time. • Purpose is to forecast future performance Educational Research 2e: Creswell Displays of scores in a Scatterplot Hours of Internet Depression use scores per week from 15-45 Depression scores Y=D.V. 50 - 40 30 20 + 10 M 5 Educational Research 2e: Creswell + M - 10 15 20 Hours of Internet Use X=I.V. Displays of scores in a correlation matrix 1 1.School satisfaction - 2. Extra-curricular activities -.33** 3. Friendship .24 2 -.03 3 - 4 5 - 4. Self-esteem -.15 .65** .24* 5. Pride in school -.09 -.02 .49** .16 - 6. Self-awareness .29** -.02 .39** .03 .22 Educational Research 2e: Creswell 6 - Associations between two scores • Direction (positive or negative) • Form (linear or non-linear) • Degree and strength (size of coefficient) Educational Research 2e: Creswell Association Between Two Scores Linear and non-linear patterns A. Positive Linear (r=+.75) B. Negative Linear (r=-.68) C. No Correlation (r=.00) Educational Research 2e: Creswell Linear and non-linear patterns D. Curvilinear E. Curvilinear F. Curvilinear Educational Research 2e: Creswell Non-linear 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 Educational Research 2e: Creswell 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. Educational Research 2e: Creswell Multiple Variable Analysis: Partial correlations r=.50 r squared=(.50)2 Time on Task Independent Variable Dependent Variable Time-on-Task Achievement Achievement Motivation r squared = (.35)2 Partial Correlations: use to determine extent to which a mediating variable influences both independent and dependent variable Educational Research 2e: Creswell Motivation Simple Regression Line Regression Line 50 41 40 Depression Scores 30 Slope 20 10 Intercept 5 10 14 15 Hours of Internet Use Per Week Educational Research 2e: Creswell 20 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 • Is the size of the sample adequate for hypothesis testing? Educational Research 2e: Creswell Evaluating a correlation 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? • Is the researcher concerned about the form of the relationship so that an appropriate statistic is chosen for analysis? Educational Research 2e: Creswell Evaluating a correlation study • 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 2e: Creswell