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The analysis that is used to assess the relationship between a factor predictor variable and a binary target variable involves evaluating the mean probabilities and counts of observations. This approach provides insights into how the different levels of the factor predictor correspond to the likelihood of the binary outcome occurring.

By constructing a table that organizes the counts and calculates the probabilities of the target variable for each category of the predictor, you can effectively illustrate the relationship. This method allows for a clear comparison across the different categories of the factor, enabling an understanding of how each level affects the outcome. It is particularly useful when dealing with categorical data and binary outcomes, making it a critical tool in statistical analysis for this type of relationship.

Other methods, such as scatter plots or bar charts, do not convey the same level of detail in terms of probabilities and direct association with a binary outcome as the table provides. Scatter plots, while helpful in showing relationships for continuous variables, are less effective for categorical predictors with binary targets. Bar charts can visualize counts but may lack the detailed probability assessment that a well-structured table can provide. Box plots, typically used for continuous data, would not be appropriate for examining the relationship between a factor variable and a binary outcome.