Two-Way Tables and Relative Frequency

A two-way table (contingency table) displays data for two categorical variables. | | Coffee | Tea | Total | |---|---|---|---| | Male | 30 | 20 | 50 | | Female | 25 | 25 | 50 | | Total | 55 | 45 | 100 | Joint frequency: a specific cell (e.g., Males who drink coffee = 30) Marginal frequency: row or column total (e.g., Total males = 50) Grand total: bottom-right cell (100)

Example: Using the table above, what fraction of all people are females who drink tea?

Relative frequency = frac{text{frequency}}{text{total}} Three types: 1. Joint relative frequency: cell ÷ grand total ("what fraction of everyone...") 2. Marginal relative frequency: row/column total ÷ grand total 3. Conditional relative frequency: cell ÷ row or column total ("given that..., what fraction...") Conditional frequency answers questions like: "Of the males, what fraction drink coffe…

Example: Given that a person drinks coffee, what is the probability they are female?