CHAPTER NINE Correlational Research Designs

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 2 Study Questions What are correlational research designs, and why are they used in behavioral research? What patterns of association can occur between two quantitative variables? What is the Pearson product-moment correlation coefficient? What are its uses and limitations? How does the chi-square statistic assess association?

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 3 Study Questions What is multiple regression, and what are its uses in correlational research? How can correlational data be used to make inferences about causal relationships among measured variables? What are the limitations of correlational designs in doing so? What are the best uses for correlational designs?

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 4 Correlational Research Designs Correlational research designs –Used to search for and describe relationships among measured variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 5 Associations Among Quantitative Variables A sample data set.

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 6 Organizing the Data Scatterplot –Uses a standard coordinate system where The horizontal axis indicates the scores on the predictor variable The vertical axis represents the scores on the outcome variable –A point is plotted for each individual at the intersection of his or her scores on the two variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 7 Regression Line Regression line –The straight line of “best fit” drawn through the points on a scatterplot

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 8 Scatterplot A scatterplot with regression line.

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 9 Linear and Nonlinear Relationships Linear relationship –When the association between the variables on the scatterplot can be easily approximated with a straight line Nonlinear relationships –Not all relationships between variables can be well described with a straight line

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 10 Patterns of Relationships Between Two Variables Examples of linear relationships.

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 11 Patterns of Relationships Between Two Variables Independent: When there is no relationship at all between the two variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 12 Patterns of Relationships Between Two Variables Curvilinear relationships: Relationships that change in direction

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 13 The Pearson Correlation Coefficient Pearson product-moment correlation coefficient –Used to summarize and communicate the strength and direction of the association between two quantitative variables –Frequently designated by the letter r –Values range from r = to r = +1.00

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 14 The Pearson Correlation Coefficient The direction of the relationship is indicated by the sign of the correlation coefficient –Positive values of r indicate positive linear relationships –Negative values of r indicate negative linear relationships The strength or effect size of the linear relationship –Indexed by the absolute value distance of the correlation coefficient from zero

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 15 Interpretation of r A significant r indicates there is a linear association between the variables. Coefficient of determination –The proportion of variance measure for r –It is r 2

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 16 Restriction of Range Restriction of range –Occurs when most participants have similar scores on one of the variables being correlated –The value of the correlation coefficient is reduced and does not represent an accurate picture of the true relationship between the variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 17 Restriction of Range

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 18 The Chi-Square Statistic Chi-square statistic (  2 ) –Must be used to assess the relationship between two nominal variables –Technically known as the chi-square test of independence –Calculated by constructing a contingency table, which displays the number of individuals in each of the combinations of the two nominal variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 19 Reporting Correlations and Chi-Square Statistics An example of reporting a correlation in a research report is r (20) = 0.52, p < 0.01 where  20 is the sample size (N)  0.52 is the correlation coefficient  0.01 is the p-value of the observed correlation

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 20 Correlation Matrix Correlation matrix –A table showing the correlations of many variables with each other

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 21 A Correlation Matrix A correlation matrix reported in APA format.

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 22 Multiple Regression Multiple regression –A statistical analysis procedure using more than one predictor variable to predict a single outcome variable The regression analysis provides –Multiple correlation coefficient –Regression coefficients or beta weights

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 23 Multiple Regression The simultaneous impact of three measured independent variables as predictors of college GPA.

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 24 Multiple Regression Multiple correlation coefficient (R) –The ability of all of the predictor variables together to predict the outcome variable Regression coefficients or beta weights –Indicate the relationship between each of the predictor variables and the outcome variable

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 25 Correlation and Causality Correlational research –Cannot be used to draw conclusions about the causal relationships among the measured variables –Although the researcher may believe the predictor variable is causing the outcome variable, the correlation between the two variables does not provide support for this hypothesis

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 26 Alternative Explanations of a Correlation Reverse causation –The causal direction is opposite what has been hypothesized Reciprocal causation –The two variables cause each other

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 27 Alternative Explanations of a Correlation Common-causal variables –Variables not part of the research hypothesis cause both the predictor and the outcome variable Spurious relationship –The common-causal variable produces and “explains away” the relationship between the predictor and outcome variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 28 Alternative Explanations of a Correlation Extraneous variables –Variables other than the predictor cause the outcome variable but do not cause the predictor variable Mediating variables –Variables caused by the predictor variable in turn cause the outcome variable

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 29 Longitudinal Research Longitudinal research design –The same individuals are measured more than one time –The time period between the measurements is long enough that changes in the variables of interest could occur

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 30 Longitudinal Research Path analysis –An analysis technique for correlational data from longitudinal research designs Path diagram –A method for displaying the results of a path analysis –Represents the associations among a set of variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 31 Path Diagram

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 32 Longitudinal Research Longitudinal research designs take a long time to conduct. Cross-sectional research designs –Measure people from different age groups at the same time –Very limited in their ability to rule out reverse causation

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 33 Structural Equation Analysis Structural equation analysis –A statistical procedure that tests whether the observed relationships among a set of variables conform to the theoretical prediction about how those variables should be causally related Latent variables –The conceptual variables

Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 34 Structural Equation Model