Moderation Flashcards
What is effect modification?
Effect modification, or interaction, occurs when the relationship between an independent variable (X1) and a dependent variable (Y) changes depending on the level of a third variable (Z)
This concept highlights heterogeneity in relationships and provides insights into subgroup-specific effects.
Give an example of effect modification.
The relationship between poverty and crime rates may differ based on urbanization levels
This illustrates how one independent variable’s effect can be altered by another variable.
How are dummy variables used in effect modification?
Dummy variables must be created for categorical variables with more than two levels
This allows for the inclusion of categorical variables in regression analysis.
What is a continuous × continuous interaction?
An interaction where two continuous variables affect the dependent variable together
This type of interaction is often analyzed in regression models.
What is the graphical format for presenting interactions?
The effect of one variable is plotted as a function of the other
For example, the effect of height decreases as reading scores increase.
Define an outlier.
An outlier is an observation that lies an abnormal distance from other values in a dataset
For example, a murder rate of 78.5 in Washington, DC is considered an outlier compared to other states.
What is an influential point?
An influential point is an outlier that significantly affects the results of statistical analysis, such as regression coefficients
Not all outliers are influential, but influential points distort the model’s relationship.
What methods can be used to identify outliers?
Graphical methods:
* Boxplots
* Scatterplots
* Histograms
These methods help visualize the relationship between variables and highlight anomalies.
What is Tukey’s method for detecting outliers?
Uses the interquartile range (IQR) to detect outliers:
* IQR = Q3 - Q1
* Lower Outer Fence = Q1 - (3 × IQR)
* Upper Outer Fence = Q3 + (3 × IQR)
This method identifies mild and extreme outliers based on fences calculated from the IQR.
How are outliers flagged using standard deviation?
Outliers are flagged when their distance from the mean exceeds 2–3 standard deviations
68%, 95%, and 99.7% of values in a normal distribution fall within 1, 2, and 3 standard deviations from the mean.
What should be done with outliers in analysis?
Decision framework:
* Fix or remove measurement errors
* Exclude non-population data
* Retain natural part of population
Justify any exclusion with proper documentation.
What are standardized residuals?
Standardized residuals quantify how far a residual deviates from zero in standard deviation units
This helps identify influential points in regression analysis.
True or False: All outliers are influential.
False
While all influential points are outliers, not all outliers have a significant impact on the model.
What is the impact of outliers on statistical analysis?
Outliers can increase error variance and distort parameter estimates, leading to Type I or II error
This reduces the overall power of statistical tests.
