Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Dichotomous Features

Variables at the nominal level of measurement exhibit only a limited number of categories. If the number of different categories is restricted to two, we talk of a dichotomous or binary variable.

When looking at dichotomous variables we may distinguish between artificial and natural dichotomy. While natural dichotomy occurs with variables which "naturally" may assume only two possible states (e.g. gender or pregnancy), artificial dichotomy can be created simply by comparing an interval scaled variable to a threshold (for example, all folks being older than 40 years will get assigned a value of 1, all other people a value of 0).

Another example for an artifical dichotomy is the state of a warning light which switches on if a certain threshold of a variable is exceeded. For example, a warning light may indicate a dangerous overpressure in a reactor of an industrial facility. In this case the continuously measured pressure is reduced to a binary state (warning light on or off).

The dichotomization of a variable is an often used approach to classify data or events. The response of such a classifier is the result of the comparison of the continuous estimator to a threshold (see discriminant analysis and logistic regression).