3. Two-Way Tables and Probability
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When do we use a two-way table?
See solution.
We use two-way tables when we want to display information about two different categories taken from the same source or population. Let's use an example to illustrate how to construct a two-way table.
We asked 40 high school students if they play a musical instrument. We also asked them if they paint regularly. Let's make a two-way table using the possible answers of these questions as the headers.
| Plays an Instrument | Does Not Play an Instrument | |
|---|---|---|
| Paints Regularly | ||
| Does Not Paint Regularly |
We can see that each column represents one possible outcome of the first question and each row represents one possible outcome of the second question. We recorded the following responses from our questions.
Each entry of the table, called a joint frequency, is the intersection of a column and a row. The value of each entry is the number of times — the frequency — that the outcomes from that row and column were achieved at the same time. Let's insert the values we have into the table!
| Plays an Instrument | Does Not Play an Instrument | |
|---|---|---|
| Paints Regularly | 14 | 11 |
| Does Not Paint Regularly | 8 | 7 |
Looking at a two-way table, we are able to identify the potential outcomes of the categories of interest from the headers and we can find the joint frequencies of these outcomes in the individual cells.