Have you ever noticed how mobile users behave differently from desktop users? It’s not just a feeling — it’s a relationship between two categorical variables. The variable “device” (mobile or desktop) and the variable “converted” (yes or no) — when we cross them in a table, we can see if there’s a systematic link.
Contingency tables (also called two-way tables or cross-tabulations) are the basic tool for this. They allow us to evaluate the interaction between two categorical variables and to quantify conditional probability — how likely an event is “given that” another has occurred.
The question about mobile vs desktop differences, for example, translates into a conditional probability: is P(conversion | device = mobile) different from P(conversion | device = desktop)? If yes, there’s a relationship. If not, the two variables are independent.
Let’s see how this works, starting with a deliberately light-hearted example.
Continue reading “Contingency Tables and Conditional Probability”