CHAPTER NINE Correlational Research Designs. Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 2 Study Questions What are correlational

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?


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?


Correlational Research Designs

• Correlational research designs – Used to search for and describe

relationships among measured variables


Associations AmongQuantitative Variables

A sample data set.


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


Regression Line

• Regression line – The straight line of “best fit” drawn through

the points on a scatterplot


Scatterplot

A scatterplot with regression line.


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


Patterns of RelationshipsBetween Two Variables

Examples of linear relationships.



Independent: When there is no relationship at all between the two variables



Curvilinear relationships: Relationships that change in direction


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 = -1.00 to r = +1.00


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


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 r2


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


Restriction of Range


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


Reporting Correlations andChi-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


Correlation Matrix

• Correlation matrix – A table showing the correlations of many

variables with each other


A Correlation Matrix

A correlation matrix reported in APA format.


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


Multiple Regression

The simultaneous impact of three measured independent variables as predictors of college GPA.


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


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


Alternative Explanationsof a Correlation

• Reverse causation– The causal direction is opposite what has

been hypothesized

• Reciprocal causation– The two variables cause each other



• 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



• 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


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



• 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


Path Diagram



• 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


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


Structural Equation Model

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CHAPTER NINE Correlational Research Designs. Copyright © Houghton Mifflin Company. All rights reserved.Chapter 9 | 2 Study Questions What are correlational