Chapter 12 Correlational Designs Power Point Slides by

Chapter 12 Correlational Designs Power Point Slides by Ronald J. Shope in collaboration with John W. Creswell

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 2 e: 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 2 e: 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 2 e: 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 • 1970 s and 1980 s computers give the ability to statistically control variables and do multiple regression Educational Research 2 e: 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 2 e: 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 2 e: 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 5 Educational Research 2 e: Creswell + M 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 2 e: Creswell 6 -

Associations between two scores • Direction (positive or negative) • Form (linear or non-linear) • Degree and strength (size of coefficient) Educational Research 2 e: 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 2 e: Creswell

Linear and non-linear patterns D. Curvilinear E. Curvilinear F. Curvilinear Educational Research 2 e: 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 2 e: 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 2 e: Creswell

Multiple Variable Analysis: Partial correlations r=. 50 r squared=(. 50)2 Time on Task Independent Variable Dependent Variable Time-on-Task 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 2 e: Creswell Motivation

Simple Regression Line 50 41 40 Depression Scores 30 Slope 20 10 Intercept 5 10 14 15 Hours of Internet Use Per Week Educational Research 2 e: 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 2 e: 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 2 e: 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 2 e: Creswell