1. Chapter 9: Correlational Research

2. Chapter 9. Correlational Research Chapter Objectives  Distinguish between positive and negative bivariate correlations, create scatterplots to illustrate them, and recognize factors that can influence the size of correlation coefficients  Calculate a coefficient of determination and interpret its meaning  Understand how a regression analysis accomplishes the goal of prediction

3. Chapter Objectives  Describe the research situations in which correlational procedures are likely to be used  Describe the logic of the multivariate procedures of multiple regression and factor analysis, and understand how to interpret the results of these procedures

4. Correlation and Regression: The Basics  Finding the relationship between two variables without being able to infer causal relationships  Correlation is a statistical technique used to determine the degree to which two variables are related  Three types of [linear] correlations:  Positive correlation  Negative correlation  No correlation

5. Correlation and Regression: The Basics  Positive correlation  Higher scores on one variable associated with higher scores on a second variable

6. Correlation and Regression: The Basics  Negative correlation  Higher scores on one variable associated with lower scores on a second variable

7. Correlation and Regression: The Basics  Correlation coefficient Pearson’s r  Statistical tests include: Pearson’s r, Spearman’s rho  Ranges from –1.00 to +1.00  Numerical value = strength of correlation Closer to -1.00 or +1.00, the stronger the correlation  Sign = direction of correlation Positive or Negative

8. Correlation and Regression: The Basics  Scatterplots  Graphic representations of data from your two variables  One variable on X-axis, one on Y-axis  Examples:

9. Correlation and Regression: The Basics  Scatterplots  Creating a scatterplot from data Each point represents an individual subject

10. Correlation and Regression: The Basics  Scatterplots from the hypothetical GPA data for positive (top) and negative (bottom) correlations

11. Correlation and Regression: The Basics  Scatterplots  Correlation assumes a linear relationship, but scatterplot may show otherwise  Curvilinear  correlation coefficient will be close to zero Left half  strong positive Right half  strong negative

12. Correlation and Regression: The Basics  Coefficient of determination  Equals value of Pearson’s r 2 Proportion of variability in one variable that can be accounted for (or explained) by variability in the other variable The remaining proportion can be explained by factors other than your variables r =.60  r 2 =.36 36% of the variability of one variable can be explained by the other variable 64% of the variability can be explained by other factors

13. Correlation and Regression: The Basics  Regression Analysis – Making Predictions  The process of predicting individual scores AND estimating the accuracy of those predictions  Regression line – straight line on a scatterplot that best summarizes a correlation Y = bX + a Y = dependent variable—the variable that is being predicted Predicting GPA from study hours  Y = GPA X = independent variable—the variable doing the predicting Predicting GPA from study hours  X = study hours a = point where regression line crosses Y axis b = the slope of the line Use the independent variable (X) to predict the dependent variable (Y)

14. Correlation and Regression: The Basics  Regression lines for the GPA scatterplots  Study time (X) of 40 predicts GPA (Y) of 3.5  Goof-off time (X) of 40 predicts GPA (Y) of 2.1

15. Interpreting Correlations  Correlations and causality  Directionality problem Given correlation between A and B, A could cause B, or B could cause A  Third variable problem Given correlation between A and B uncontrolled third variable could cause both A and B to occur Partial correlations “partial out” possible third variable

16. Interpreting Correlations  Caution: correlational statistics vs. correlational research  Not identical Correlational research could involve t tests Experimental research could examine relationship between IV and DV  Using correlations  The need for correlational research Some IVs cannot be manipulated Subject variables Practical/ethical reasons e.g., brain damage

17. Combining Correlational and Experimental Research  Research example 27: Loneliness and anthropomorphism  Study 1: correlation between loneliness and tendency to anthropomorphize r =.53  Studies 2 & 3: manipulated loneliness to tests its effects on likelihood to anthropomorphize IV study1 = [false] personality feedback (will be lonely, will have many connections with others) DV study1 = degree of belief in supernatural beings (e.g., God, Devil, ghosts) IV study2 = induce feeling of connection or disconnection DV study1 = anthropomorphic ratings of own pets and others’ pets Results  feelings of disconnection (loneliness) increased Ss likelihood to anthropomorphize

18. Multivariate Analysis  Bivariate vs. multivariate analyses  Multiple regression  One dependent variable  More than one independent variable  Relative influence of each predictor variable can be weighted Examples: predicting school success (GPA) from (a) SAT scores and (b) high school grades predicting susceptibility to colds from (a) negative life events, (b) perceived stress, and (c) negative affect

19. Multivariate Analysis  Factor analysis  After correlating all possible scores, factor analysis identifies clusters of intercorrelated scores First cluster  factor could be called verbal fluency Second cluster  factor could be called spatial skill  Often used in psychological test development