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 ID: 646528
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Slide1
Chapter 9: Correlational ResearchSlide2
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 correlationSlide3
Correlation and Regression: The Basics
Positive correlation
Higher scores on one variable associated with higher scores on a second variableSlide4
Correlation and Regression: The Basics
Negative correlation
Higher scores on one variable associated with lower scores on a second variableSlide5
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 NegativeSlide6
Correlation and Regression: The Basics
Scatterplots
Graphic representations of data from your two variables
One variable on X-axis, one on Y-axis
Examples:Slide7
Correlation and Regression: The Basics
Scatterplots
Creating a scatterplot from data
Each point represents an individual subjectSlide8
Correlation and Regression: The Basics
Scatterplots from the hypothetical GPA data for positive (top) and negative (bottom) correlationsSlide9
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 negativeSlide10
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 factorsSlide11
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)Slide12
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 2.1Slide13
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
variablesSlide14Slide15
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 damageSlide16
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
likelihood to anthropomorphizeSlide17
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 affectSlide18
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