Construct and interpret two-way frequency tables to investigate association between categorical variables.

What this dot point is asking

Bivariate data is not always numerical. When both variables are categorical, such as gender and preferred transport, you cannot draw a scatterplot or compute a correlation coefficient. Instead you organise the data in a two-way frequency table and look for patterns in the percentages.

Reading the table

The cells inside the table are the joint frequencies. The totals down the right edge and along the bottom are the marginal frequencies, and the single number in the bottom-right corner is the grand total. Always check that the row totals and the column totals each add up to the grand total before going further.

Judging association

To decide whether two categorical variables are associated, you compare the percentage breakdown of the response variable across each category of the explanatory variable. If those percentage breakdowns are noticeably different, the variables are associated. If they are about the same, there is no association.

Choosing the right percentages

The percentage direction must match the question. If sex is the explanatory variable and you want to know how drink preference depends on sex, calculate the percentages within each sex (so each sex column adds to 100 percent). Calculating the percentages the other way around answers a different question and usually hides the pattern you were asked about.

Describing the strength

You are not expected to run a formal significance test in this course. Instead, describe the association in words and quantify the gap. Phrases like a higher proportion of, compared with, and a difference of so many percentage points show the marker you have read the table correctly. A larger gap between the comparison groups suggests a stronger association.

When you report, state which variable you treated as explanatory, quote the comparison percentages, and finish with a plain-language conclusion about whether an association exists.

A complete answer converts the relevant cells to percentages on a common base, compares them across the explanatory categories, and concludes clearly about association rather than restating the original counts.