Contingency Tables

$tiger$

~Note: These are tables displaying data in rows & columns

~Example:                        Titanic Mortality

                     Men        Women      Boys        Girls         Total
Survived      332           318              29             27            706
Died            1360           104              35             18          1517
Total           1692           422              64             45          2223

~How to find probabilities from the table~

~Note: the frequencies in the table are the actual numbers (Observed)

~Using the above contingency table, find the following:~

    P(a passenger was a man) = 1692/2223 = .76

    P(a passenger was a female) = (422+45)/2223 = .21

    P(a passenger was a survivor) = 706/2223 = .32

    P(a passenger was a boy or girl) = (64+45)/2223 = .05

    P(a passenger was a man and a survivor) = 332/2223 = .15

   P(a passenger was a woman or a survivor)=(422/2223) + (.32) - (318/2223)= .37

~Note: To test for independence of the row & column data, we need to calculate the Expected frequencies....we assume the cells are empty & we just know the totals of the rows & columns. In this case, the probabilities are calculated differently.

~Note: the Expected frequencies for each cell can be calculated by use of the formula:

Ex: for the cell that contains 332,
E =(2223)(706/2223)(1692/2223) =   537.360


Or, in short,
Expected frequency for each cell = (row total)(column total)
                                                                  (grand total)

~Note: The TI-83 will do this automatically when testing for
independence using chi-square (see discussion on my website)