Data sets with two categorical variables

Bivariate categorical data sets are usually summarised with a contingency table.

For example, a study examined 686 tourists and classified each by educational level and by whether they were 'information seekers' (who requested destination-specific literature from travel agents) or 'non-seekers':

  Information seeker?  
Education     Yes         No        Total   
  Some high school 013 027 40
  High school degree    064 118 182
  Some college    100 123 223
  College degree    059 069 128
  Graduate degree    067 046 113
Total 303 383 686

Joint probabilities

Bivariate categorical data can be modelled as a random sample from an underlying population of pairs of categorical values. The population proportion for each pair (xy) is denoted by pxy and is called the joint probability for (xy).

In games of chance, we can often work out the joint probabilities. For example, if a gambler draws a card from a shuffled deck and also tosses a coin, there are eight possible combinations,