In the context of statistics and data display, the term "two-way" in a two-way table refers to the fact that the table organizes data based on two distinct categories simultaneously.
A two-way table is a visual tool used to summarize and display the frequencies or counts of data points according to two different categorical variables. As the reference states, a two-way table is one way to display frequencies for two different categories collected from a single group of people.
How "Two-Way" is Represented
The "two-way" nature is visually represented by the structure of the table itself:
- Category 1: One category's different values or levels are used to define the rows of the table.
- Category 2: The other category's different values or levels are used to define the columns of the table.
Each cell within the table's grid then shows the frequency (or count) of observations that fall into the specific combination of the row category and the column category.
Displaying Frequencies
The primary purpose of this two-way classification is to easily see how frequencies are distributed across the combinations of the two categories for the single group being studied. This allows for comparisons and the identification of potential relationships between the two categories.
Practical Example
Imagine you surveyed a group of students about their favorite subject (Math or Science) and their grade level (9th or 10th). A two-way table would display the results based on these two categories: Subject (rows) and Grade Level (columns).
| Favorite Subject | 9th Grade | 10th Grade | Total |
|---|---|---|---|
| Math | 30 | 25 | 55 |
| Science | 20 | 35 | 55 |
| Total | 50 | 60 | 110 |
In this example:
- The first category is "Favorite Subject" (Math, Science). These form the rows.
- The second category is "Grade Level" (9th Grade, 10th Grade). These form the columns.
- Each number in the grid (e.g., 30) represents the frequency of students who belong to both the specific row category (Math) and the specific column category (9th Grade).
This simple structure clearly shows how the data is classified in two directions simultaneously, giving the table its name: "two-way".
