This worksheet teaches students to read and construct two-way tables for categorical variables, calculate conditional proportions, and discuss whether two variables appear to be related. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A two-way table displays the counts for two categorical variables at once — one variable's categories as rows, the other's as columns.
- The row total and column total are the sums along each row/column; the grand total is the sum of everything.
- A conditional proportion (e.g. "of house dwellers, what proportion own a pet") divides a cell by its row or column total — always be clear about which total is being used.
- If two variables are not related (independent), the conditional proportion should be roughly the same across every category of the other variable.
- The expected count for a cell under "no relationship" (independence) is (row total × column total) ÷ grand total — comparing this to the observed count reveals whether a relationship might exist.
What your child will practise:
- Reading row, column and grand totals from a two-way table.
- Calculating a conditional proportion within a specific row or column.
- Comparing conditional proportions across categories to assess whether a relationship appears to exist.
- Calculating the expected count for a cell under independence, and compare it to the observed count.
- Identifying which pair of categories shows the largest apparent difference/relationship in a multi-category table.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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