5) Relationships in Categorical Data

Two-Way Tables

Summarize data about two categorical variables (factors) collected on the same set of individuals.

If a row variable has “r” levels and the column variable has “c” levels, then it is called an “r by c” table.

Marginal Distribution

One of the categorical variables in a two-way table of counts which represents the distribution of that variable among all individuals described by the table.

Relative frequencies or percentages of individual variables in a two-way table. The “total” for one variable (row or column).

Marginal Distribution Formula

Found by taking the marginal frequency and dividing by the grand total, then multiplying by 100%.

(Total of one column / total of all columns) × 100%

Conditional Distribution

The distribution of one factor for each level of the other factor.

Distribution of values of that variable among only individuals who have a given value of the other variable.

Conditional Distribution Formula

A count within a single row / column divided by the total of that row / column.

“Conditional”

“Conditioned on”

“If”

“Given”

Simpson’s Paradox

Confounding or lurking variables are always a problem for interpretation, but their impact can be even more drastic when dealing with categorical data.

An association that holds for all of several groups can reverse direction when the data are combined to form a single group.