Chapter 9- Multivariate correlational research Flashcards
Multivariate designs definition
Involve more than 2 measured variables. These techniques can be used to get closer to a causal claim without setting up an experiment.
Multivariate designs (3)
longitudinal designs, multiple-regression designs, and the pattern and parsimony approach.
3 criteria for establishing causation
covariance, temporal precedence, and internal validity.
Narcissism
A personality trait in which people feel superior to others, believe they deserve special treatment, and respond strongly when others put them down. Childhood narcissism is different from high self esteem.
Longitudinal designs
Measure the same variables in the same people at several points in time. It is used to study changes in a trait or ability as a person grows older.
How can results from longitudinal studies be interpreted? (3)
- Cross lag correlations
- Cross sectional correlations
- Autocorrelations
Cross-sectional correlations
Test to see whether 2 variables that were measured at the same point in time are correlated. Example- the correlation between mothers’ overvaluation and children’s narcissism at time 4 was r= .099. This is consistent with the hypothesis. However, this result can’t establish temporal precedence since the variables were measured at the same time.
Autocorrelations
Autocorrelations determine the correlation of one variable with itself, measured on 2 different occasions. For example, researchers asking whether mothers’ overvaluation at time 1 was associated with mothers’ overvaluation at time 2, 3, and 4.
Cross-lag correlations
Show whether the earlier measure of one variable is associated with the later measure of the other variable. They are the primary area of interest because they address the directionality problem and help to establish temporal precedence. Example- investigating whether mothers’ overvaluation at time 1 is correlated with child narcissism later on (time 2, etc).
A correlation is statistically significant if
The 95% confidence interval does not include zero.
What does it mean when a cross lag correlation is not significant?
The cross-lag correlations from mothers to children (time 1 to time 2, time 2 to time 3, etc) were significant. The correlations from children to mothers were not. This means that the mothers who overvalued their children at one time had children who were higher in narcissism 6 months later. However, children who were higher in narcissism at a particular time didn’t have mothers who overvalued them 6 months later. These correlations together suggest that the overvaluation, not the narcissism, came first. Establishes temporal precedence
3 possible patterns from a cross-lag study
- The pattern observed above- overvaluation came before narcissism
- Narcissism at earlier times was correlated with overpraise later- this would mean that childhood narcissistic tendency came first, leading parents to change their praise later.
- Overpraise predicted narcissism later, and narcissism predicted overpraise later- this means the two variables are mutually reinforcing. There is a cycle in which overpraise leads to narcissism, which leads parents to overpraise, and so on.
How do longitudinal designs establish covariance?
Statistical relationships in longitudinal designs help establish covariance. When two variables are correlated and their 95% CIs do not contain zero (as in the cross-lag correlations) there is covariance.
How do longitudinal designs establish temporal precedence?
Longitudinal designs can help researchers make inferences about temporal precedence. Each variable is measured at different points in time, so they know which one came first. By comparing the relative strength of the two cross-lag correlations, the researchers can see which path is stronger. If only one is statistically significant, the researchers are closer to establishing causation.
Can longitudinal studies establish internal validity?
If longitudinal studies only measure two key variables, they might not help rule out third variables. For example, high income parents might be more likely to overpraise their children and these children might also think they’re better than other kids. Gender is also a possible third variable, but the researchers were also able to study the longitudinal patterns of boys and girls separately and rule it out.
Why not just do an experiment?
For the Brummelman study, it’s too difficult to manipulate the variables. You can’t manipulate personality traits, and it’s difficult to assign parents to daily parenting styles. It can also be unethical to manipulate certain variables. If we suspect certain types of praise can cause narcissism, it would be unethical to assign children to receive this praise.
Multiple regression
A statistical technique that can help rule out some third variables, addressing some internal validity concerns.
Chandra et al. 2008
Participants reported how often they watched 23 programs popular with teens. Coders watched 14 episodes of each show, and counted how many scenes involved sex. Girls were asked if they had ever gotten pregnant, and boys were asked if they had ever gotten a girl pregnant. Researchers also measured the total amount of time teenage participants spent watching any kind of TV, their age, their academic grades, and whether they lived with both parents. This makes the study a multivariate correlational study.
How can multivariate designs control for third variables?
For example, age is a third variable correlated with both of the other variables, so researchers want to know what happens when they control for age. To control for this, researchers can hold age constant and see if the correlation still holds by analyzing each subgroup. Are watching sex on TV and pregnancy still correlated in 16 year old participants, in 18 year old participants, and 20 year old participants?
2 possible outcomes of subgroup analysis
- By graphing the data, we see that the relationship holds constant even within age subgroups.
- The relationship does not hold when only looking at 16 year olds or only 20 year olds, even though the relationship is positive overall. This would mean that the association goes away when we control for age, and that the third variable (age) was responsible for the relationship.
When researchers use regression, they are testing
Whether some key relationship holds true even when a suspected third variable is statistically controlled for.
Criterion/dependent variable
Researchers choose the variable they are most interested in understanding or predicting. In the Chandra study, this was pregnancy.
Predictor/independent variables
The rest of the variables (sexual content of the TV shows, age of each teen).
How is the beta value similar to r?
There is one beta value for each predictor variable. Like r, a positive/negative beta indicates a positive/negative relationship between the predictor and criterion variable. A zero value represents no relationship. The higher/lower the beta, the stronger/weaker the relationship
Which beta values can be compared?
Beta values can be compared to other betas in a single regression table. We can say that the beta for the age predictor appears to be stronger than the beta for the exposure to sex on TV predictor. However, we can’t compare the beta value on one regression table to a beta value on another regression table. Betas change based on which variables are controlled for the regression.
b value
Some regression tables will use a b symbol instead of beta. We can’t compare two b values within the same table to each other. A large b value might not indicate a stronger relationship between variables
What does a positive beta value indicate?
For example, a beta of .25 indicates a positive relationship- higher levels of sex on TV go with higher pregnancy risk even when we statistically control for other variables, like age. The other beta for the age predictor variable is also positive. This means that older age is associated with higher pregnancy rates, even when sex on TV is controlled for.
p value
A p value of .05 complements the .95 from a 95% CI. When a p value is less than .05, we can infer that the 95% CI for the beta doesn’t contain 0 and is statistically significant. CIs are more informative because they give the precision of the beta estimate.
What does a beta value of zero mean?
This means that when controlling for parental involvement, the relationship between the two variables has a CI containing zero (it’s not significant). The relationship between family meal frequency and child academic success can likely be explained by the third variable of parental involvement.
Adding several predictors to a regression analysis can answer 2 questions
- It helps control for several third variables at once. This helps researchers to get closer to making a causal claim.
- By looking at the betas for all the other predictor variables, we can get a sense of which other factors predict the chance of pregnancy.
“Controlled for” means
This phrase is a common sign of a regression analysis
“Adjusting for” means
If researchers are said to have adjusted for multiple variables, it means that the researchers conducted multiple regression analyses.
“Considering”
The phrase “even when other factors were considered” indicates the researchers used multiple regression.
If you can’t tell from the news story what the researchers controlled for, it’s reasonable to suspect
That certain third variables cannot be ruled out.
Why can’t regression establish causation? (3)
- Multivariate designs analyzed with regression can control for third variables, but they can’t establish temporal precedence.
2/ Even with longitudinal studies, researchers can’t control for third variables that they don’t measure (level of religiosity, etc). - It’s also possible that certain types of teens are more likely to watch sexual TV content and these same teens are also more likely to be sexually active
Parsimony
The degree to which a scientific theory provides the simplest explanation of some phenomenon. With causal claims, it means the simplest explanation of a pattern of data- the theory that requires making the fewest exceptions or qualifications.
Parsimony example
The best example of this is the relationship between smoking and lung cancer. There are many possible third variables for this relationship, and an experiment would be unethical. To solve this problem, a mechanism was specified for the causal path. In the case of cigarettes, researchers proposed that cigarette smoke contains chemicals that are toxic when they come into contact with human tissue. The more contact a person has with these chemicals, the greater the toxicity exposure. This theory leads to a set of predictions, which can be explained by the simple parsimonious theory that cause cancer- the longer a person has smoked cigarettes, the greater their chance of getting cancer, and others
How are parsimonious predictions evaluated to confirm the theory?
Converging evidence from several individual studies conducted by medical researchers has supported each of these separate predictions. All five of these diverse predictions are tied back to one central principle (the toxicity of chemicals in cigarette smoke), there is a strong case for parsimony. The diversity of these findings makes it hard to raise third variable explanations that would explain each finding.
Mediation
Once researchers have established a relationship between two variables, they might want to ask why the relationship occurs. Correlation and experimental studies can test mediators. Mediation hypotheses are causal claims, so mediation can only be definitively established in conjunction with temporal precedence. The proposed causal variable comes first, then the mediator, then the proposed outcome variable.
Example of mediation
Example- there’s an association between having deep conversations and feelings of well being. One mediator could be social ties- deeper conversations might help build social connections, which in turn lead to increased well being. Therefore, there is a relationship between the two variables, but only because 2 other relationships (deep talk and social ties, and social ties and well being) exist simultaneously.
How are third variables different from mediators?
Third variables are external to the two variables in the original bivariate correlation. It might be seen as an accident that distracts from the relationship of interest. If education was a third variable, we would be saying that deep talk and well-being are correlated with each other only because each one is correlated separately with education. In contrast, mediators are of direct interest to researchers.
Moderators
When researchers test for moderators (chapter 8) they ask, are these two variables linked the same way for everyone, or in every situation? Who is most vulnerable, and for whom is the association the strongest? Moderators can change the relationship between 2 variables.
Why is the difference between mediators and moderators?
While a mediation hypothesis could propose that medical compliance is the reason conscientiousness is related to better health, a moderation hypothesis could propose that the link between conscientiousness and good health is strongest among older people (whose health is more vulnerable) and weakest among younger people.
How is the construct validity of a multivariate design interrogated?
For any multivariate design, it’s appropriate to interrogate the construct validity of the variables in the study by asking how well each variable was measured.
How is the statistical validity of a multivariate design interrogated?
For a multivariate correlational study, we can interrogate the statistical validity by asking about point estimates and confidence intervals and ask whether the study has been replicated.
How is the external validity of a multivariate design interrogated?
We can also interrogate the external validity of a multivariate design. For the sexual TV content and pregnancy study, we can ask whether the teenagers were sampled randomly and from what kind of population.
