A two-way table sorts every individual by two categorical variables at once.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Inside and edges
The inner cells give joint counts. The row and column totals in the margins give each variable alone.
Relative frequency
Dividing a cell by a total turns counts into proportions, which is what makes groups comparable.
Which total to divide by
Dividing by the grand total gives an overall proportion. Dividing by a row total gives a proportion within that row.
Judging association
Compare row proportions across rows. Similar proportions mean no association; different ones mean there is.
Never compare raw counts
Groups are rarely the same size, so a bigger count can simply mean a bigger group.
Two categorical variables at once
Each cell counts individuals in both categories, and the margins give the totals for each variable separately. The margins should sum to the grand total both ways, which is a built-in check.
Percentages need a stated base
A percentage can be of the whole table, of a row, or of a column, and the three answer different questions. Saying which was used is not pedantry — without it the number is ambiguous.
Comparing conditional percentages
If the percentage in a category differs substantially across rows, the variables are associated. Comparing row percentages is how association is detected in categorical data.
Association is not causation
A table can show that two variables move together. Whether one causes the other depends on how the data were collected, and an observational table cannot settle it.
Step 2: Try It Yourself
Tap and try it out.
Group 1 yes
Group 1 no
Group 2 yes
Group 2 no
Group 1 yes has the most. It has 25 more than Group 2 no.
Step 3: Watch an Example
One step at a time.
Watch Sana Compare Two Rows
Group 1 has 30 yes out of 50. Group 2 has 15 yes out of 20.
- Step 1
The raw counts, 30 against 15, suggest Group 1 is keener.
Step 4: Your Turn
Practice makes it stick.
The Proportion
Problem 1 of 2
30 yes out of 50. What proportion, as a decimal?
The Other Row
Problem 2 of 2
15 yes out of 20. What proportion, as a decimal?
Read the Table
1 of 8
12 yes out of 48. Proportion as a decimal?
2 of 8
Cells 20, 30, 25 and 25. Grand total?
3 of 8
A row has 20 yes and 30 no. Row total?
4 of 8
That row: proportion saying yes, as a decimal?
5 of 8
Row proportions 0.5 and 0.5. Is there association? 1 yes, 0 no.
6 of 8
Row proportions 0.2 and 0.8. Is there association? 1 yes, 0 no.
7 of 8
Match each figure with where it comes from.
Tap a card on the left to start.
8 of 8
18 yes out of 24. Proportion as a decimal?
Step 5: Quick Check
Show what you know.
Question 1 of 2
9 yes out of 36. What proportion, as a decimal?
Question 2 of 2
Why compare proportions rather than counts?
What You Learned
- A two-way table cross-classifies by two categorical variables.
- Inner cells are joint counts; margins give each variable alone.
- Compare row proportions, never raw counts, to judge association.