ch9 Flashcards
Multivariate designs
involve more than two measured variables
two types of multivariate design
- Longitudinal designs
- Multiple-regression
Longitudinal designs
provides evidence for temporal precedence by measuring the same variable in the same people at several different times
types of correlations from longitudinal designs
- Cross-sectional correlations
- Autocorrelations
- Cross-lag correlations
Cross-sectional correlations
tell us whether two variables measured at the same time are correlated
Autocorrelations
when a variable correlates with itself across time
Cross-lag correlations
- show whether an earlier measure of one variable is associated with a later measure of the other variable
- helps establish temporal precedence/ directionality problem
how do you know which variable comes first from a cross-lag correlation?
If earlier variable A’s correlation to B’s later on is statistically significant and earlier B’s correlation to A’s later on isn’t, we can know that A comes before B
whichever relationship is statistically significant is the direction of the relationship
Three possible patterns for cross-lag correlations
- A comes before B
- B comes before A
- Mutually reinforcing: both correlations are statistically significant, indicating a cycle in which each variable reinforces the other continuously
do longitudinal studies address the third variable problem?
- hen conducted simply, longitudinal studies only measure the two key variables and can’t rule out a third variable
- Might be able to design their studies in particular ways or do statistical analyses to address some third variables
Multiple regression (multivariate regression)
a statistical technique to help rule out some third variables, addressing internal validity concerns
Criterion variable
-dependent variable
- the variable in multiple regression they are most interested in understanding or predicting/ outcome of interest
- Specified in either top row or title of regression table
Predictor variables
-independent variables
- the rest of the variables measured in a regression analysis that may cause the criterion variable
-Although it is considered an independent variable, it isn’t manipulated, and causation cannot be inferred
Beta
- similar to r, in that it denotes direction and strength of relationships. Represents the relationship between the criterion variable and the predictor variable
direction of beta
- Positive beta means a positive relationship when other predictor variables are statistically controlled for, and vice versa
- A beta that is zero or not statistically different from zero represents no relationship when other predictors are statistically controlled for
can you compare betas on different regression tables?
Within a single regression table, we can usually compare predictor variables but not across different regression tables
- No absolutes for effect sizes (like cohen’s for r)
how do you measure effect sizes of beta?
R squared is a measure of effect size- regression analyses (software) often includes measure of r squared- gives you information about effect size for each of the predictor variables
The coefficient b
The coefficient b
same as beta except it hasn’t been standardized to a scale (between 1 and -1)
- so it can’t be compared even within same table
Statistical significance of beta
Show us whether or not the results are due to chance/sampling error- whether or not they actually come from a population where the relationship is zero
how is statistical significance marked on a regression table? what values
Regression tables have column labeled sig or p, or asterisked footnote with p value for each beta
Less than .05 = statistically significant
If more than .05 data isn’t significant
what does adding more predictors to a regression table do? (2)
- Can help control for several third variables at once (closer to causal claim)
- Examines the betas for all the other predictor variables to get a sense of which factors most strongly predict chance of our criterion variable
when can beta exceed an absolute value of 1?
- Multicollinearity- where predictors are so strongly correlated that you can’t separate the contribution of each
- Or when variables aren’t continuous variables/ or dichotomous yes or no variables
Multicollinearity
where predictors are so strongly correlated that you can’t separate the contribution of each
R squared
measure of effect size- regression analyses (software) often includes measure of r squared- gives you information about effect size for each of the predictor variables
Phrases to detect if regression analysis was used in media
- “Controlled for”
- “Taking into account”
- “Correcting for” or “adjusting for’
Regression doesn’t establish causation- Even if a large # of variables are controlled for, two problems
- Temporal precedence isn’t always established
- Even when a study takes place over time (longitudinally,) can’t control for unknown third variables- variables they didn’t think to measure
why are experiments more convincing than multiple-regression in terms of internal validity?
random assignment makes two groups likely to be equal on any third variable the researchers don’t think to measure
Parsimony (in causal claims)
the simplest explanation of a pattern of data- the theory that requires making the fewest exceptions
“Pattern and parsimony” approach
- investigate causality by using a variety of correlational studies that all point in a single, causal direction
- includes making and testing a series of questions based off/ all can be explained by a simple theory
Mediators (mediating variables)
a variable that serves as an explanation for a connection between variables
5 steps of mediation
- Test relationship c (the original correlation or causation)
- Test relationship a ( the relationship between the first variable and the mediator
- Test relationship b ( relationship between third variable and mediator
- Run a regression test using the first variable and the mediator as predictors of the third variable
- the relationship between the first and third variables should drop when the mediator is controlled for - Temporal precedence: mediation is definitively established only when the proposed causal variable is measured or manipulated first in a study, followed later by the mediating variable, followed by the proposed outcome variable
similarities and differences of mediators and third variables
Similarities:
- Multivariate research designs
- Detected using multiple regression
Differences:
- third variables are external to the bivariate correlation (problematic “lurking variable”)
- mediators are internal to the causal variable, meaning they work directly as a step within the relationship and aren’t problematic
Mediators vs moderators
- Mediators ask “why”, come between two variables
- Moderators ask “for whom” or “when”- does it work in every situation- is it different based on the level of the variable?
statistical validity in multivariate designs
- Effect size of beta (compare within table)
- and the statistical significance
Also look for
- Subgroups
- Outliers
- Curvilinear associations
