Conditional and Marginal frequencies

The methodological analysis is divided in:
1) choose a population,
2) decide the variable/attribute to observe and relative scale of measurement,
3) create a dataset with a survey,
4) analyze distributions (using the conditional frequency).

The conditional frequency indicates how many members of a group have a particular mode of a character.

For example in the two-way table, If we set the value xi for the variable X and examine the distribution of Y limited to the observations that have assumed the i-th mode of the X, then we obtain the conditional distribution of the Y given xi.

Formally we will indicate with (Y | X = xi) the conditioned variable Y.

For example, the following table shows the relationships between the categories “sex” and “genre of movies preferred”. We fix the mode of the X=women, and we analyze the Y, the result will be the distribution of the chosen variable Y relative to the women.

	Musical	Action	Horror	Total
Men	6	16	8	30
Women	12	14	4	30
Total	18	30	12	60

Column and row called total there the marginal frequency and at the cross of each column and row there is the joint frequency.