Independence in Two Way or Contingency Tables
The two way table below contains some completely fictitious data on the the types of computers favoured by men and women.
| Laptop | Desktop | Tablet | Total |
Men | 31 | 17 | 40 | 88 |
Women | 12 | 42 | 17 | 71 |
Total | 43 | 59 | 57 | 159 |
Events A and B are independent if
(1)
For the table above take A as 'a person picked at random favours a desktop', and event B as 'a person picked at random is a woman'.
The probability that a person picked at random favours desktops is
and the probability that a person picked at random is a woman is
The number of women who favour desktops is 42 out of a total of 159, so the probability that a person picked at random is a woman favouring a desktop is
These probabilities do not satisfy condition (1) for indepence since