Probabilities for a single variable
A model for two categorical variables is characterised by the joint probabilities pxy.
The marginal probability, px, for a variable X is the proportion of (x, y) pairs in the population with X = x . This can be found by adding all joint probabilities for pairs with this x-value.
There is a similar formula for the marginal probabilities of the other variable,
Example
In the following example, the marginal probabilities for X are the row of totals under the table, and the marginal probabilities for Y are the column of totals on the right.
Variable X | ||||
---|---|---|---|---|
Variable Y | X = A | X = B | X = C | Total |
Y = 1 | 0.2576 | 0.1364 | 0.1212 | 0.5152 |
Y = 2 | 0.0909 | 0.0758 | 0.0152 | 0.1818 |
Y = 3 | 0.0455 | 0.0758 | 0.0606 | 0.1818 |
Y = 4 | 0.0152 | 0.0303 | 0.0758 | 0.1212 |
Total | 0.4091 | 0.3182 | 0.2727 | 1.0000 |