A two-way table sorts people by two things at once, such as year group and whether they walk to school.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The totals check the table
Each row adds to its row total, each column to its column total, and both reach the same grand total.
Compare proportions
A bigger group will have bigger counts. Divide by the group total before comparing.
What association means
If the proportions differ noticeably between rows, the two categories are associated.
Counting two categories at once
A two-way table cross-tabulates two categorical variables — say, whether someone has a pet against whether they have a garden. Each cell counts the individuals in both categories.
Row and column totals
The totals along the edges are the marginal frequencies: how many have a pet in total, regardless of garden. They should sum to the grand total both ways, which is a built-in arithmetic check on the table.
Percentages need a stated base
"60% have a pet" is ambiguous: 60% of everyone, or of those with gardens? Relative frequencies can be taken of the whole table, of a row, or of a column, and they answer different questions. Always say which.
Looking for association
If the percentage with a pet is much higher among those with gardens than without, the two variables are associated. Comparing row percentages across rows is how association is detected in categorical data.
Step 2: Try It Yourself
Tap and try it out.
Walk
Bus
There are 12 in all.
Walk has the most. It has 4 more than Bus.
Step 3: Watch an Example
One step at a time.
Watch Leo Compare Two Rows
Of 40 Year 7s, 30 walk. Of 20 Year 11s, 5 walk.
- Step 1
The counts are 30 and 5, but the groups are different sizes.
Step 4: Your Turn
Practice makes it stick.
The Row Total
Problem 1 of 2
A row has 12 and 18. What is the row total?
The Proportion
Problem 2 of 2
15 out of 60. What percent is that?
Read the Table
1 of 4
A row has 7 and 13. Row total?
2 of 4
20 out of 50. What percent?
3 of 4
Should counts be compared directly across differently sized groups? 1 for yes, 0 for no.
4 of 4
9 out of 12. What percent?
Step 5: Quick Check
Show what you know.
Question 1 of 1
18 out of 24. What percent?
What You Learned
- A two-way table sorts data by two categories at once.
- Rows, columns, and the grand total must all agree.
- Compare proportions rather than counts, because groups differ in size.