Do older pupils prefer art?
A made-up school has two clubs, chess and art. Year 10 seems to love chess. Year 11 seems to love art. Is that a real link, or just luck in who turned up?
Chess and art are not numbers. They are categories. Correlation cannot help here. A different test can.
Key words
| Word | What it means | Example |
|---|---|---|
| Categorical variable | A variable whose values are groups, not amounts. | Club: chess or art |
| Association | A link between two variables: knowing one tells you something about the other. | Year group and club |
| Observed count | The number of people really counted in a cell of the table. | 30 Year 10 pupils in chess |
| Expected count | The number you would see in a cell if there were no link at all. | 20 |
| Chi-square | A number that says how far the observed counts are from the expected ones. Bigger means a stronger sign of a link. | 16.67 |
| Degrees of freedom | For a table: rows minus 1, times columns minus 1. | 1 for a two by two table |
| Critical value | The line the chi-square number must pass to count as evidence of a link. | 3.84 when degrees of freedom is 1 |
| Contingency table | A table that counts people in every combination of two categories. | Year group by club |
The cells students fill in are left blank in this preview.
By the end of this lesson
Note
I can say when to use a chi-square test, work one out on a small table, and decide if the result shows a link.
Starter: what you already know
Have a go
Starter: what you already know
3 questionsYour answers are marked here and are not kept. A college account keeps every student’s marks.
The idea: compare real with expected
Count the people in every combination of year and club. That is the observed table.
Now ask: what would the table look like if year and club had nothing to do with each other? That is the expected table. If the real counts sit far from the expected ones, there is a sign of a link.
Worked example: the observed table
| Chess | Art | Row total | |
|---|---|---|---|
| Year 10 | 30 | 10 | 40 |
| Year 11 | 20 | 40 | 60 |
| Column total | 50 | 50 | 100 |
The cells students fill in are left blank in this preview.
Check: read the observed table
Have a go
Check: read the observed table
3 questionsYour answers are marked here and are not kept. A college account keeps every student’s marks.