To apply the probability formula's on real data we have to count quite a bit. And for that purpose, the command table() is quite handy. Until now we have only applied it to make a frequency distribution for a single variable. But it can also make counts over two variables and show the result in a contingency table (i.e. frequency table with 2 dimensions).

For example, to look at the distribution of the passenger class for the different sexes, you can create a contingency table for the two variables sex and pclass with the command:

table(titanic$sex,titanic$pclass)

Notice that the categories from the first argument in the table() command (titanic$sex) become the rows in the contingency table, and the categories from the second argument (titanic$pclass) become the columns.

If you would like the rows and columns switched, you can simply change the order of the input-arguments:

table(titanic$pclass,titanic$sex)

You can also add the variable names to the table to remember which is which and make the interpretation easier:

table(pclass = titanic$pclass, sex = titanic$sex)

table(titanic$ pclass, titanic$ survived)

To turn a table with frequencies into a table with probabilities, we'd have to divide each cell in this table by the total number of passengers (i.e. the total number of observations: #1309#). This can be achieved via the following commands:

gender_pclass <- table(titanic$sex,titanic$pclass)
gender_pclass/sum(gender_pclass)

You can also use the command prop.table() to do the same in a slightly easier way.

prop.table( table(titanic$sex,titanic$pclass) )

prop.table(table(titanic$ sex, titanic$ survived))

prop.table() has an additional useful option: it can calculate proportions per row or per column. For this task a second input argument is used. For example, to calculate the distribution over the three classes within each gender, you should use:

prop.table( table(titanic$sex,titanic$pclass), margin=1 )

And to calculate the distribution over gender within each passenger class, the following command should be used:

prop.table( table(titanic$sex,titanic$pclass), margin=2 )

For the last two examples, you can see how for margin=1 the proportions per row sum to 1, and for margin=2 the proportions per column.

Note that if you would change the order of the input arguments (titanic$sex and titanic$pclass in the example above), then the numbers to be used for margin should also be changed to get the same result. In other words: the proportions in the following tables are the same (they only have rows and columns interchanged).

prop.table( table(titanic$pclass,titanic$sex), margin=1 )

prop.table( table(titanic$sex,titanic$pclass), margin=2 )

prop.table(table(titanic$ sex, titanic$ pclass), margin = 1)