Multivariate Correlational Designs

What are the 3 criteria for establishing causality

1. Covariance

2. Temporal Precedence

3. Internal Validity

1. Covariance

the results must show a correlation between the two variables

- how changes in one variable are associated with changes in another variable. For instance, if two variables tend to increase or decrease together, they exhibit positive covariance

FOR EXAMPLE:

researchers might examine the covariance between VIOLENT TELEVISION and CHILD ANGER/VIOLENCE. A positive covariance in this context would suggest that more violent a show is, the more anger/violence the child shows

Do the cause and effect co-occur?

Bivariate correlational design; Correlation vs T-test

1. CORRELATION

- TWO continuous variables

EX: scatterplot

2. T-test

- ONE categorical and one continuous variable

EX: Graph

2. Temporal precedence

The cause variable MUST come before the effect variable in time

Does the cause precede the effect?

TRUE or FALSE:

In a BIVARIATE correlational design, the two variables are measured at different times

FALSE!!!!

In a BIVARIATE correlational design, the two variables are measured at THE SAME TIME

What is the Directionality problem?

when we don't know which variable came first in time; i.e., the variables were measured at the same time

* Did watching violent TV shows come first? Or did aggression come first??

what are Longitudinal Designs?

studies where the SAME variables are measured over time

- To help establish temporal precedence

What are the 3 types of correlations?

1. Cross-sectional correlations

2. Autocorrelation

3. Cross-lagged correlation

1. Cross-sectional correlations

(what are they? What do they ask?)

The correlation between TWO variables measured at the SAME point in time

Q: are variables at the same time point correlated?

.

FOR INSTANCE:

- you measure stress and sleep quality among 200 people in 2025 → The correlation between stress and sleep quality (both in 2025) is a cross-sectional correlation.

- Tells you whether people who are more stressed right now also tend to sleep worse right now — but NOT which causes which.

2. AUTO correlation

(what are they? What do they ask?)

The correlation of THE SAME VARIABLE within itself overtime

Q:Are the variables STABLE overtime?

EX:

The correlation between stress in 2025 and stress in 2026 among the same participants.

- Shows how much individuals' stress levels are consistent across time.

3. Cross-lagged correlation

The correlation between one variable at Time 1 and a different variable at a later time (Time 2).

Q: Is the earlier measure of one variable associated with the later measure of another variable?

EX:

The correlation between stress in 2025 (Time 1) and sleep quality in 2026 (Time 2)

- If stress at Time 1 predicts later sleep quality (controlling for prior sleep quality), this suggests that stress might influence sleep over time.

What is a bidirectional relationship?

In the context of relationships, bidirectional relationships are characterized by the mutual influence between two parties. (one variable can affect the other, and vice versa)

EX:

A parent's behavior can influence a child's development, and a child's behavior can affect a parent's parenting style.

Longitudinal design: PRACTICE QUESTION

A child development researcher wants to test the theory that an authoritarian parenting style leads to conduct disorder in children and not the other way around. To test this theory, the researcher recruited 200 parents with children ages 4-5 (Time 1). The researcher interviewed the parents to determine their parenting styles and then interviewed the children to measure symptoms of conduct disorder. When the children turned 7-8 years old (Time 2), the researcher re-interviewed the parents to measure their parenting style and the children to measure their symptoms of conduct disorder.

(CHECK SLIDE 27 FOR DRAWING)

Q:

A) What conclusion should the researcher make about their theory?

Please explain which result(s) in the figure provide support for your

conclusion(s)

The researcher should conclude that there is evidence that authoritarian parenting predicts the development of conduct disorder in children because the cross-lagged correlation between authoritarian parenting and conduct disorder (.31) is statistically significant.

Longitudinal design: PRACTICE QUESTION

A child development researcher wants to test the theory that an authoritarian parenting style leads to conduct disorder in children and not the other way around. To test this theory, the researcher recruited 200 parents with children ages 4-5 (Time 1). The researcher interviewed the parents to determine their parenting styles and then interviewed the children to measure symptoms of conduct disorder. When the children turned 7-8 years old (Time 2), the researcher re-interviewed the parents to measure their parenting style and the children to measure their symptoms of conduct disorder.

(CHECK SLIDE 27 FOR DRAWING)

Q:

B) Is conduct disorder stable over time? Please indicate which result(s) in the figure support your answer and explain what these results mean in the context of this study.

Yes, there is evidence that conduct disorder is stable over time because the autocorrelation between conduct disorder at Time 1and conduct disorder at Time 2 is positive and statistically significant(.29).

Longitudinal design: PRACTICE QUESTION

A child development researcher wants to test the theory that an authoritarian parenting style leads to conduct disorder in children and not the other way around. To test this theory, the researcher recruited 200 parents with children ages 4-5 (Time 1). The researcher interviewed the parents to determine their parenting styles and then interviewed the children to measure symptoms of conduct disorder. When the children turned 7-8 years old (Time 2), the researcher re-interviewed the parents to measure their parenting style and the children to measure their symptoms of conduct disorder.

(CHECK SLIDE 27 FOR DRAWING)

Q:

c) Can the researcher claim that an authoritarian parenting style causes conduct disorder in children? Why or why not?

No, the researcher can't claim that there is a causal relationship between authoritarian parenting and conduct disorder because although the researcher has shown that the constructs co-vary and they have established temporal precedence by using a longitudinal design, they have not ruled out third variables (i.e., this is not an experiment and therefore there is no internal validity)

3. Internal Validity

Study design must rule out plausible alternative explanations for the relationship between the two variables

Have we ruled out third variables?

What are the reasons causal claims cant be made based on correlational validity?

Directionality problem

Third variable problem

Third Variable problem

Two variables are correlated, but only because they are both linked to a THIRD VARIABLE

EX: Ice-cream sales go up as well as shark attacks --> this can be due to a third variable (its summertime)

Ruling our third variables (2 ways) -->Way 1

1. Statistical Control

- use stats to hold construct constant in analyses to measure the unique effect of a variable

What does it mean to hold a construct constant?

Holding a variable constant means that the researcher is NOT interested in the effect of that variable on the outcome being measured.

- Instead, they are interested in the effect of the other variables in the model

This can be done through MULTIPLE REGRESSION:

Statistical analysis that can be used to rule out third variables

Multiple regression scenario:

A researcher wants to know whether watching violent TV is associated with child anger levels.

HOWEVER, they suspect that empathy might also play a role — children with LOWER empathy might BOTH (1) watch more violent TV and (2) show more anger.

Q: what does it mean when you "control for empathy" (The third variable)

You are asking:

"What is the relationship between TV violence and anger if all children had the SAME level of empathy?

- you REMOVE or hold CONSTANT the confound variable EMPATHY

- So instead of comparing children who differ both in how much violent TV they watch and in empathy, you compare them as if they had EQUAL EMPATHY

If you control for empathy and the relationship between violent tv and aggression persists, what would you predict regarding two people with the same level of empathy?

Given two people with the same amount of empathy, we would predict the person who watches more violent tv to be more aggressive

In more statistical terms (still regarding multiple regression) What does β represent?

The EFFECT of the predictor controlling for the other predictor

EX:

The relationship between physical health and relationship satisfaction, controlling for financial security

OVERALL, multiple regression answers the question...

Do we still see a link between thepredictor and outcome when controlling for a third variable?

HOWEVER

• Can't control for all potential third variables

• Not an experiment

• Still no internal validity

• Can't make causal claims

What is MODERATION?

- Is used to test if the direction and/or strength of an association between variables changes based on another variable

- It is a test of EXTERNAL validity

EX:

Does the relationship between studying an exam performance depend on the TYPE of studying?

What is MEDIATION?

Asks WHY two variables are related

- Test causal claims

EX:

WHY is studying related to better exam performance?

- BECAUSE it leads to better UNDERSTANDING

What are the 4 steps of mediation? (PRACTICE DRAWING THIS) --> using studying, exam performance, and understanding

1. Establish that PREDICTOR is related to OUTCOME (path C -->)

2. Establish that PREDICTOR is ASSOCIATED with MEDIATOR (Path A -->)

3. Establish that MEDIATOR is associated with OUTCOME, CONTROLING for PREDICTOR

(Path B -->)

4. Establish that predictor is no longer related to outcome when controlling for mediator

(Path C -->)

MEDIATION - DONT FORGET TO...

ESTABLISH Temporal Precedence

Time 1 )- Studying

Time 2)- Understanding

Time 2 or later)- Exam result

Mediation equation

Total effect = direct effect + indirect effect

c = c' + ab

Complete mediation

X effects Y ONLY through M

>.80

Partial Mediation

X effects Y BOTH DIRECTLY and INDIRECTLY through M

<.80

MEDIATION: Practice

You think that a lack of sleep predicts relationship conflict because it diminishes people's ability to perspective-take.

A) What is the predictor, the mediator, and the outcome?

Predictor = sleep

Outcome = relationship conflict

Mediator = perspective-taking ability

MEDIATION: Practice

You think that a lack of sleep predicts relationship conflict because it diminishes people's ability to perspective-take.

B) Please draw out the mediation model.

MODEL HINT

MEDIATION: Practice

You think that a lack of sleep predicts relationship conflict because it diminishes people's ability to perspective-take.

C) In the context of this study, what do each of the following paths in the mediation model mean?

a =

b =

c =

ab =

c' =

a = the link between sleep and perspective taking ability

b = the link between perspective-taking ability and relationship conflict, controlling for sleep

c = the total effect of sleep on relationship conflict

ab = the indirect effect of sleep on relationship conflict (i.e., the effect of sleep on

relationship quality through perspective-taking)

c' = the direct effect of sleep on relationship conflict

MEDIATION: Practice

You think that a lack of sleep predicts relationship conflict because it diminishes people's ability to perspective-take.

D) You run a study to test this theory and find that 85% of the link between sleep and relationship conflict is explained by perspective-taking ability. What kind of mediation is this?

Complete Mediation

Identifying Multivariate Correlational DESIGNS:

For each of the following claims, identify the appropriate approach (longitudinal, multiple regression, moderation, or mediation)

1. The link between spending time in nature and wellbeing depends on the weather.

Moderation

Identifying Multivariate Correlational DESIGNS:

For each of the following claims, identify the appropriate approach (longitudinal, multiple regression, moderation, or mediation)

2. People who read regularly tend to be better writers because they have bigger imaginations.

Mediation

Identifying Multivariate Correlational DESIGNS:

For each of the following claims, identify the appropriate approach (longitudinal, multiple regression, moderation, or mediation)

3. The effect of smoking on lung health persists even when controlling for age.

Multiple regression

Identifying Multivariate Correlational DESIGNS:

For each of the following claims, identify the appropriate approach (longitudinal, multiple regression, moderation, or mediation)

4. Being extraverted is associated with being liked more by others; however, this effect is weaker for friends than for new acquaintances

Moderation

Identifying Multivariate Correlational DESIGNS:

For each of the following claims, identify the appropriate approach (longitudinal, multiple regression, moderation, or mediation)

5. Cross-lagged correlations suggest that stonewalling a romantic partner increases the chances of breaking up.

Longitudinal

OVERALL, HOW do we evaluate the VALIDITY of Multivariate Correlational Studies?

1. Construct validity

• How well have the constructs been measured?

2. External validity

• Does the association generalize to other groups and situations?

• Are there moderators?•

3. Statistical validity

• What is the effect size?• Factors that affect correlations

• How many people are in the sample?

NOT INTERNAL VALIDITY -> its not an experiment!