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Correlational Research
Association Claims
• Correlational research: Assess
relationships among naturally occurring
variables.
Attitudes, preferences, intelligence, personality
traits, feelings, age, sex
A Study with All Measured
Variables Is Correlational
• What makes a study correlational?
– Having two measured variables
Introducing Bivariate Correlations
• Describing associations between two
quantitative variables
• Describing associations with categorical
data
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The Correlation Coefficient
© 2002 John Wiley & Sons, Inc.
Describing Associations Between
Two Quantitative Variables
Analyzing Associations
When One Variable Is Categorical
• t test: a statistic to test the difference
between two group averages
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10152025303540
Extern
aliz
atio
n
Inte
rnal
izat
ion
Dep
ress
ion
Life E
vents
Stress
Dating Violence Males No Dating Violence Males
05
1015202530354045
Extern
aliza
tion
Inte
rnali
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Depre
ssion
Life E
vents
Stress
Dating Violent Females No Dating Violence Females
Adolescents
Interrogating Association Claims
• Construct validity: How well was each variable
measured?
• Statistical validity: How well do the data support
the conclusion?
• Internal validity: Can we make a causal
inference from association?
• External validity: To whom can the association
be generalized?
Construct Validity
• Ask about the construct validity of each
variable.
– How well was each of the variables measured?
– Does the measure have good reliability?
– Is it measuring what it’s intended to measure?
– What is the evidence for its face validity, for its
concurrent validity, and for its discriminant and
convergent validity?
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Statistical Validity
• What is the effect size?
• Is the correlation statistically significant?
• Could outliers be affecting the association?
• Is there restriction of range?
• Is the association curvilinear?
What Is the Effect Size?
• Effect size:
describes the
strength of an
association
Larger Effect Sizes Give
More Accurate Predictions
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Larger Effect Sizes Give
More Accurate Predictions
• When everything else
is equal, a larger
effect size is usually
considered more
important than a
small one. But there
are some exceptions.
Is the Correlation
Statistically Significant?
• Statistical significance
• The logic of statistical inference
• What does a statistically significant result
mean?
• What does a nonsignificant result mean?
• Effect size, sample size, and significance
Is the Correlation
Statistically Significant?
• Reading about significance in journal
articles
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Could Outliers Be
Affecting the Association?
• Outlier
r = .37
r = .26
r =49
r =.15
Is There Restriction of Range?
r = .33 r = .57
SAT scores can range from 600 to 2,400
Is the Association Curvilinear?
• Curvilinear
association
r = .01
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Internal Validity
• Applying the three causal criteria
• More on internal validity: When is the
potential third variable a problem?
Correlational Research
• Correlation and Causality
– “Correlation does not imply causation.”
– Spurious relationship
Applying the Three Causal Criteria
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External Validity
• How important is external validity?
• Moderating variables
Correlational Research Designs
• A research design is a plan for conducting a research project.
• 3 Types:
– cross-sectional
– successive independent samples (not in your book)
– longitudinal
• Successive Independent Samples Design:
Major goal is to describe changes in attitudes or
behavior within a population over time
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Percentage of High School Students Who Carried a Gun,* 1993-2015†
*On at least 1 day during the 30 days before the survey†Decreased 1993-2015, decreased 1993-1997, no change 1997-2015 [Based on linear and quadratic trend analyses using logistic
regression models controlling for sex, race/ethnicity, and grade (p < 0.05). Significant linear trends (if present) across all available
years are described first followed by linear changes in each segment of significant quadratic trends (if present).]
Note: This graph contains weighted results.
National Youth Risk Behavior Surveys, 1993-2015
Percentage of High School Students Who Ever Had Sexual Intercourse, 1991-2015*
*Decreased 1991-2015 [Based on linear and quadratic trend analyses using logistic regression models controlling for sex, race/ethnicity, and grade (p < 0.05). Significant linear trends (if present) across all
available years are described first followed by linear changes in each segment of significant quadratic
trends (if present).]
Note: This graph contains weighted results.
National Youth Risk Behavior Surveys, 1991-2015
• Longitudinal Research Designs
– The same sample of individuals completes
the measures at different points in time.
– Allows researchers to assess how individuals
change over time.
– The sample of respondents is used to
represent how individuals in the population
change over time.
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Reviewing the Three Causal Criteria
• Multivariate designs involve more than
two measured variables.
• Three criteria for establishing causation
– Covariance
– Temporal precedence
– Internal validity
Establishing Temporal Precedence
with Longitudinal Designs
• Interpreting results from longitudinal
designs
• Longitudinal studies and the three criteria
for causation
• Why not just do an experiment?
Stability of Attachment Classifications from Infancy to
Adulthood
20 2 3
6 8 2
3 2 4
Secure Avoidant Resistant
Secure
Dismissing
Preoccupied
3 Groups Secure/Insecure
64% stayed the same 72% stayed the same
72% if no significant life events 78% if no significant life events
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Interpreting Results from
Longitudinal Designs
• Cross-sectional correlations
• Autocorrelations
• Cross-lag correlations
Cross-Sectional Correlations
Autocorrelations
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Cross-Lag Correlations
Insert Figure 9.3 from p. 241
2 Threats to Internal Validity in
Longitudinal designs
• Instrumentation- measurement equivalency and cultural change
• Mortality or attrition of subjects is a major threat to a lengthy longitudinal study since the sample remaining at the end of the study is unlikely to be comparable to the initial sample. For example, the surviving sample is likely to be healthier, more stable in lifestyle and so forth.
Longitudinal Studies and the
Three Criteria for Causation
• Longitudinal designs
can provide some
evidence for causation
by fulfilling three criteria
– Covariance
– Temporal precedence
– Internal validity
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Measuring More Than Two Variables
Using Statistics to
Control for Third Variables
• Control for
Why Not Just Do an Experiment?
• In many cases participants cannot be
randomly assigned to a variable.
– Cannot be assigned to preferences
– Unethical to assign participants
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Ruling Out Third Variables with
Multiple-Regression Analyses
• Measuring more than two variables
• Regression results indicate if a third
variable affects the relationship
• Adding more predictors to a regression
• Regression in popular press articles
• Regression does not establish causation
Regression Results Indicate If a Third
Variable Affects the Relationship
• Criterion variables and predictor
variables
• Using beta to test for third variables
Criterion Variables and Predictor
Variables
• Criterion variable: dependent variable
• Predictor variables: independent variables
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Using Beta to Test for Third Variables
• Beta basics
• Interpreting beta
Using Beta to Test for Third Variables
• Statistical significance of beta
Using Beta to Test for Third Variables
• What if beta is not
significant?
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Adding More Predictors to a Regression
Regression in
Popular Press Articles
• “Controlled for”
• “Taking into account”
• “Correcting for” or “Adjusting for”
Regression Does Not
Establish Causation
• Multiple regression is not a foolproof
way to rule out all kinds of third
variables.
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Getting at Causality with
Pattern and Parsimony
1. The longer a person has smoked
cigarettes, the greater are the chances of
getting cancer.
2. People who stop smoking have lower
cancer rates than people who continue
smoking.
3. Smokers’ cancers tend to be in the lungs
and of a particular type.
4. Smokers who use filtered cigarettes
have a somewhat lower rate of cancer than
smokers of unfiltered cigarettes.
5. People who live with smokers would
have higher rates of cancer, too, because
of their passive exposure to the same
chemicals.
Pattern, Parsimony,
and the Popular Press
• Journalists do not always fairly represent
pattern and parsimony.
• When journalists report only one study at a
time, they are selectively presenting only
part of the scientific process.
Mediation
• Mediators vs. third variables
• Mediators vs. moderators
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High School Students: Non Virgins
Discussion
Parents
Parental
Approval
Discussion
Friends
Friends’
Approval
Attitudes
about
Premarital
Sex
Sexual
Behavior
.20
.21
.24
.55
Contraceptive
Use
Contraceptive
knowledge
.16
.25
.28
Mediators vs. Third Variables
• Similarities
– Both involve multivariate
research designs.
– Both can be detected using
multiple regression.
• Differences
– Third variables are external to
the bivariate correlation
(problematic).
– Mediators are internal to the
causal variable (not
problematic).
Mediators vs. Moderators
• Mediators ask “why,” and moderators ask
“for whom” or “when.”
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Multivariate Designs and
the Four Validities
• Internal validity
(already discussed)
• Construct validity
• External validity
• Statistical validity
How Important Is External Validity?
O= Older adults
Y= Younger adults
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Moderating Variables
• Moderator
Moderating Variables
r = .29*
r = -.16