Binary Data - in Statistics

In Statistics

In statistics, binary data is a statistical data type described by binary variables, which can take only two possible values. Binary data is used to represent the outcomes of Bernoulli trials, statistical experiments with only two possible outcomes. It is a type of categorical data, which more generally represents experiments with a fixed number of possible outcomes. The two values in a binary variable, despite being coded numerically as 0 and 1, are generally considered to exist on a nominal scale, meaning that they represent qualitatively different values that cannot be compared numerically. In this respect, also, binary data is similar to categorical data but distinct from count data or other types of numeric data. Often, binary data is used to represent one of two conceptually opposed values, e.g.

• the outcome of an experiment ("success" or "failure")
• the response to a yes-no question ("yes" or "no")
• presence or absence of some feature ("is present" or "is not present")
• the truth or falsehood of a proposition ("true" or "false", "correct" or "incorrect")

However, it can also be used for data that is assumed to have only two possible values, even if they are not conceptually opposed or conceptually represent all possible values in the space. For example, binary data is often used to represent the party choices of voters in elections in the United States, i.e. Republican or Democratic. In this case, there is no inherent reason why only two political parties should exist, and indeed, other parties do exist in the U.S., but they are so minor that they are generally simply ignored.

Binary variables that are random variables are distributed according to a Bernoulli distribution. Regression analysis on predicted outcomes that are binary variables is accomplished through logistic regression, probit regression or a related type of discrete choice model.