Two-way tables
Every person answered two questions with a few possible answers each. How do you count them so you can tell whether the answers go together?
Where you are 3 inside
What this area is about
A two-way table counts one group of individuals by two categorical variables at once: one row per category of one variable, one column per category of the other, and each cell counts the individuals with both. It keeps which answers came from the same person, which two separate frequency tables lose. Turning its counts into shares of the right total is what lets you say whether the two variables are associated in that data.
How these fit together
Definitions. Joint and marginal frequencies name the parts: a joint frequency is one cell, and the marginal frequencies are the row and column totals, each describing one variable on its own.
A procedure. Conditional relative frequencies divide a cell by its row total or its column total, the group the question narrows to. The two choices answer different questions and usually give different numbers.
A definition built on them. Association in a two-way table calls the variables associated in the data when the conditional shares differ noticeably from row to row, and draws those shares as a segmented bar graph.
A path through it
Joint and marginal frequencies, then conditional relative frequencies, then association.
Finish here and you can read joint and marginal probabilities and conditional probability from a table, and later test an association with a chi-square test for independence.