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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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Life E

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Stress

Dating Violence Males No Dating Violence Males

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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