Society of Actuaries (SOA) PA Practice Exam

What does the R code provided for creating a box plot enable?

1. Assessment of variance within a single factor

2. Comparison of means between two groups

3. Assessment of interaction between two factor variables

4. Visualization of correlation coefficients

The correct answer is: Assessment of interaction between two factor variables

The R code provided for creating a box plot effectively allows for the assessment of the distribution of data across different categories or groups, making it particularly useful for comparing the performance of different factors. When a box plot is generated for two or more factor variables, it visually represents the central tendency (medians) and variability (interquartile ranges) of the data. In the context of interaction effects between two factor variables, a box plot can show how the distribution of a continuous response variable changes across combinations of the factor levels. This is valuable in understanding whether the influence of one factor on the response variable varies depending on the level of the other factor, which is a key aspect of assessing interactions. The other concepts, while important, fall outside the primary capabilities of a box plot. For example, assessing variance within a single factor typically involves different statistical tests or visual methods such as ANOVA or variance plots. Comparing means between groups may often require additional statistical tests, such as t-tests, rather than simply using box plots alone. Lastly, visualization of correlation coefficients relies on scatter plots or heat maps rather than box plots.