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Chapter 9: Correlational Research
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
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
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
Correlation and Regression: The Basics
Positive correlation Higher scores on one
variable associated with higher scores on a second variable
Correlation and Regression: The Basics
Negative correlation Higher scores on one
variable associated with lower scores on a second variable
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
Correlation and Regression: The Basics
Scatterplots Graphic representations of data from your two variables One variable on X-axis, one on Y-axis Examples:
Correlation and Regression: The Basics
Scatterplots Creating a scatterplot from data
• Each point represents an individual subject
Correlation and Regression: The Basics
Scatterplots from the hypothetical GPA data for positive (top) and negative (bottom) correlations
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
Correlation and Regression: The Basics
Coefficient of determination Equals value of Pearson’s r2
• 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 r2 = .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
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)
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
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
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
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• IVstudy1 = [false] personality feedback (will be lonely, will have many
connections with others)• DVstudy1 = degree of belief in supernatural beings (e.g., God, Devil,
ghosts)• IVstudy2 = induce feeling of connection or disconnection
• DVstudy1 = anthropomorphic ratings of own pets and others’ pets
• Results feelings of disconnection (loneliness) increased Ss likelihood to anthropomorphize
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
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