Two-way tables and conditional proportions — Data, 14–17 years
Compare groups fairly by asking “out of which group?” Data, 14–17 years.
What a two-way table does
A two-way table sorts observations by two categories at once, such as transport and punctuality. Each cell counts a combination, while row and column totals describe the groups. A conditional proportion compares a cell with the total of the group named in the question.
Why the denominator matters
The problem is that raw counts can make a large group look more successful simply because it has more people. Two-way tables grew from the need to compare categories while keeping the reference group clear. Asking “what fraction of bus users were late?” is different from asking “what fraction of late travellers used the bus?”
Reading the right fraction
In a class, 12 of 20 bus users were on time, and 8 were late. Among 10 cyclists, 9 were on time and 1 was late. The late rate for bus users is 8/20 = 40%; for cyclists it is 1/10 = 10%. The comparison uses each group’s own total.
The trap
A common mistake is to divide by the grand total every time. That is reasonable because the grand total is easy to spot, but it answers “what fraction of everyone is here?”, not “what fraction of this group is here?”. Read the wording first, then choose the matching row or column total.
Where it appears
Two-way tables help compare choices and outcomes in surveys, medical studies, transport reports and school data. A health researcher might compare a treatment group with a control group, while keeping the groups’ sizes visible. The table can show an association, but it does not by itself prove a cause.
Keep exploring
Other languages
Loading MyLeoNes™…