Marginal RF: Proportion within a category, ignoring others. | Conditional RF: Proportion within a category, given another category.

Association: Conditional relative frequencies differ. | Independence: Conditional relative frequencies are the same.

Side-by-side: Compares groups using separate bars for each category. | Segmented: Shows distribution within each group using segments in a bar.

Relative frequencies (joint, marginal, conditional) help reveal patterns and relationships between categorical variables in a two-way table.

Compare conditional relative frequencies to see if they differ significantly across categories. If they do, the variables are associated; if they are roughly equal, they are independent.

Side-by-side bar graphs visually compare the distributions of a categorical variable across different groups or categories of another variable.

Segmented bar graphs show the distribution of a categorical variable within each group or category of another variable, displayed as segments within a single bar.

Mosaic plots visualize the relationship between two categorical variables, where the area of each rectangle is proportional to the joint relative frequency of the categories.

$\frac{\text{Row or Column Total}}{\text{Grand Total}}$

$\frac{\text{Frequency of Intersection}}{\text{Total Frequency of Given Category}}$