Interpret two-way tables
Theory
A two-way table sorts each result by two things at once, so every cell counts results in one row group and one column group. Row totals and column totals both add to the grand total.
A two-way table sorts each result by two things at once — one down the rows, one across the columns.
Each cell counts the results that fit both its row group and its column group.
A row total adds every cell across a row; a column total adds every cell down a column.
The bottom-right grand total is every result counted once.
The row totals and the column totals must agree.
| Group | Ate | Skipped | Total |
|---|---|---|---|
| Girls | 16 | 4 | 20 |
| Boys | 14 | 6 | 20 |
| Total | 30 | 10 | 40 |
How to read a two-way table
- Pick a row group and a column group.
- Cross them — the cell where they meet is the count for both.
- Add across a row, or down a column, for a total.
- Check that the row totals and column totals reach the same grand total.
Cross the Girls row with the Ate column.
| Girls who ate | \(=\) | \(16\) |
Add across the Boys row.
| \(14+6\) | \(=\) | \(20\) |
Add down the Skipped column.
| \(4+6\) | \(=\) | \(10\) |
Add the row totals (or the column totals).
| \(20+20\) | \(=\) | \(40\) |
Common pitfalls
Frequently asked questions
What does each cell in a two-way table mean?
A cell counts the results that fit both its row group and its column group at the same time, such as girls who ate breakfast.
How do I find a row total?
Add every cell across that row. It counts all the results in that row group, whatever the column.
How do I find a column total?
Add every cell down that column. It counts all the results in that column group across both rows.
What is the grand total?
The number in the bottom-right corner. It counts every result once, and both the row totals and the column totals add up to it.
How can I check my totals?
Add the row totals and add the column totals separately. Both should reach the same grand total; if not, a cell has been misread.