Segmented Bar Charts for Two Categorical Variables

Two-way tables hide comparisons because raw counts depend on group size. If 90 of 150 city respondents say yes and 40 of 100 rural respondents say yes, stacking raw counts into two bars makes the city bar taller just because the city group is bigger, not because city people say yes more often. You need rates, not counts.

To build the chart, take each column of the two-way table as one group, one bar. Find each group's total, then divide every category count in that column by the column total to get conditional relative frequencies. Stack those percentages inside the bar, so every bar reaches 100 percent no matter how many people were actually surveyed. Now segment height means rate within the group, and bars of equal height are directly comparable.

This is why normalizing to percent matters: for the city group, 90/150 = 60 percent yes; for the rural group, 40/100 = 40 percent yes. Even though city has more total respondents, the comparison that matters is 60 percent versus 40 percent, visible only once both bars are scaled to the same height. This idea sets up conditional probability and independence in the next topics: if the yes-rate were the same across groups, the segments would line up evenly, which is exactly the visual test for whether two categorical variables are associated.