How to use two-way tables and segmented bar charts to examine relationships between categorical variables. Total row and Total column are called marginal frequencies or the marginal distribution. 2-way cross-classification tables & 2-way contingency tables. Two-way contingency tables show joint behavior (distribution) of two discrete variables.
You can probably guess that a two-way frequency table will deal with two variables (referred to as bivariate data). You may also see this term stated as row conditional relative frequency or column conditional relative frequency. Here we look at some examples of how to work with two way tables. There are a number of ways to get the marginal distributions using the margin.table command. Bivariate marginal and joint probabilities for discrete random variables are often displayed as two-way tables. Similarly for continuous random variables, the marginal probability density function can be written as pX(x).
When two variables are involved we call it a two-way table. When three categories are involved, we speak of a three-way table, and so on. For that task we turn to odds ratios, again. First, let’s get the distribution of attitudes conditional on education. The state space for is, and we can compute the probability distribution on this space as products of the individual coordinates’ distributions because the random variables Xi are independent. In general, when we build the joint distribution of two random variables we can make such a two-way table, of course, for more variables this is impossible.