PSC 041 Chapter 9: Multivariate Correlational Research

Correlational Studies purpose & types

-early step to establish a casual relationship

-longitudinal design, multiple-regression analysis, & "pattern & parsimony" approach

-variables are all measured, not manipulated

longitudinal designs (which casual criteria?)

temporal precedence

multiple-regression analysis (which casual criteria?)

eliminates third variable explanations (internal validity)

pattern and parsimony

combines correlational studies

multivariate designs

a study designed to test an association involving more than two measured variables

longitudinal designs

a study in which the same variables are measured in the same people at different points in time

-multivariate because different variable's levels differ at each point in time (ex: score time 1, score time 2, etc.)

-allows researchers to establish temporal precedence in their data

cross-sectional correlations

in a longitudinal design, a correlation between two variables that are measured at the same time

-can't establish temporal precedence; either variable could have caused the other

autocorrelations

In a longitudinal design, the correlation of one variable with itself, measured at two different times.

-extroversion at time 1, extroversion at time 2

cross-lag correlations

in a longitudinal design, a correlation between an earlier measure of one variable and a later measure of another variable

-can address the directionality problem and help establish temporal precedence

-"cross" = two different variables; "lag" = two different times

possible problems for cross-leg correlations

-A causes B

-B causes A

-A & B are mutually reenforcing

longitudinal designs and the 2 criteria for causation

1. covariance

-when 2 variables are correlated & CIs don't contain zero

2. temporal precedence

-comparing cross-lag correlations & the statistical significance of each

3. internal validity

-don't rule out 3rd variables

-can take steps to prevent

Why use a correlational study to help establish causation when you could use an experiment?

sometimes people can't be randomly assigned a causal variable of interest because it is unethical

-smoking, abusive childhood, etc.

multiple regression (multivariate regression)

a statistical technique that computes the relationship between a predictor variable and a criterion variable, controlling for other predictor variables

-By conducting a multivariate design, researchers can evaluate whether a relationship between two key variables still holds when they control for another variable. (from your textbook)

-The analysis tells you about the impact of each predictor variable, given that the other one is also measured.

control for

holding a potential third variable at a constant level while investigating the association between two other variables

Ruling Out Third Variables With Multiple Regression Analysis

see if a pattern/trend holds true for subgroups

-if it does, then likely no third variable, if it doesn't then what ever subcategory that divided the groups (age, socioeconomic status, etc.) may be a third variable

criterion variable

dependent variable; the variable in a multiple-regression analysis that the researchers are most interested in understanding or predicting

predictor variable

independent variable; a variable in a multiple-regression analysis that is used to explain variance in the criterion variable

Beta (β)

-similar to r in that they describe the direction and strength of a relationship; & can be used to compare relationships

-+/- β= +/- relationship when other predictor variables are controlled for

β vs b

-b = unstandardized & in original units; can't be used to compare to other bs

-β= standardized & can be used for comparison

CIs for βs

-statistically significant: p value < 0.05, meaning that the CI does not contain zero

-not statistically significant: p values > 0.05, meaning that the CI does contain zero

Why add several predictors to a regression?

-control for several 3rd variables

-find other predictors

Regression terms in popular media

-"controlled for"

-"adjusting for"

-"considering"

Regression does not establish causation

-cannot always establish temporal precedence

-researchers can't control for variables that they did not measure

-The third variable problem is why experiments are more convincing in establishing causation (not always feasible)

parsimony

The degree to which a theory provides the simplest explanation of some phenomenon. In the context of investigating a claim, the simplest explanation of a pattern of data; the best explanation that requires making the fewest exceptions or qualifications.

-diversity of empirical findings can make it harder to find 3rd variable explanations

-Not a statistical correction but a collection of evidence based on hypothesis testing around theories (replication, open science practices)

-Build a theory of causation with a variety of studies that account for different third variables and temporal precedence

parsimony in popular media

journalists may leave out past studies that show the pattern of patrimony

-selectively present the scientific process (mislead)

-easier to argue against a single case than a pattern

-may seem to overturn decades of research--wrong impression

mediator

a variable that helps explain the relationship between two other variables

-correlational or experimental

testing for mediators

-use multiple regression analysis or structural equation modeling with or without bootstrapping

mediation hypotheses are ____________

casual

-need temporal precedence

mediators vs third variables

-3rd variables are external to the 2 variables in the original bivariate correlation; accident & not of central interest to the researchers

-mediation hypotheses are theoretically meaningful, step-by-step stories that are of direct interest to the researchers; not a nuisance

mediators vs moderators

Mediators indicate why (or how) variables are related. Explain for everyone.

Moderators indicate when or for whom variables are related. They can often be thought of as boundary conditions for an association. What groups or situations change the intensity of the relationship? Explain for some people.

mediation= come in the middle of the 2 other variables; moderating = "to change" the intensity of the relationship

Multivariate Designs and the Four Validities

-must interrogate construct validity (how well each variable was measured)

-can also interrogate the external validity (generalizability/sampling)

-statistical validity (point estimates, CIs and replication, betas, outliers, curvilinear associations)