A manufacturer was considering marketing crackers high in a certain kind of edible fiber as a dieting aid. Dieters would consume some crackers before a meal, filling their stomachs so that they would feel less hungry and eat less. A laboratory studied whether people would in fact eat less in this way.
Overweight female subjects ate crackers with different types of fiber (bran fiber, gum fiber, both, and a control cracker) and were then allowed to eat as much as they wished from a prepared menu. The amount of food they consumed and their weight were monitored, along with any side effects they reported. Unfortunately, some subjects developed uncomfortable bloating and gastric upset from some of the fiber crackers. A contingency table of "Cracker" versus "Bloat" shows the relationship between the four different types of cracker and the four levels of severity of bloating as reported by the subjects.
A Chi-Square test can be used to test whether Bloating is independent of Cracker (the type of fiber eaten).