Contingency Tables are one way to organise data. Here is a data summary of computer users in a group.
| PC | Mac | Row Totals | |
| Male | 45 | 38 | 83 |
| Female | 40 | 55 | 95 |
| Column Totals | 85 | 93 | 178 |
The intersection between the row and column defines one piece of information. For example, The intersection of PC and Male, 45, is the number of males (who participated in the survey) who use a PC at work, the junction between row total and females (95) is the total number of females in the survey, and a total of 178 people in the study, etc.
Marginal, Joint, and conditional probabilities
Before we get into the calculations, a gentle reminder on probability.
P(event) = # Events / # Outcomes.
Marginal probabilities are the probabilities for single events without counting the other events in the table.
P(Female) = # Females / # Grand Total = 95 / 178 = 0.53.
P(Mac sold) = # Mac / # Grand Total = 93/178 = 0.52.
Let’s redraw the contingency table with marginal probabilities now.
| PC | Mac | Row Totals | |
| Male | 83/178 0.47 | ||
| Female | 95/178 0.53 | ||
| Column Totals | 85/178 0.48 | 93/178 0.52 | 178/178 1.0 |
Clearly, the numbers are all sitting on the margins, hence the name.
We’ll see the other two probabilities in the next post.
Reference
Statistics By Jim: Page
