counts the frequency of each possible combination of numbers of occurrences of the various categories. Regression analysis on categorical outcomes is accomplished through multinomial logistic regression, multinomial probit or a related type of discrete choice model. Categorical variables that have only two possible outcomes (e.g., "yes" vs. "no" or "success" vs. "failure") are known as binary variables (or Bernoulli variables). Because of their importance, these variables are often considered a separate category, with a separate distribution (the Bernoulli distribution) and separate regression models (logistic regression, probit regression, etc.). As a result, the term "categorical variable" is often reserved for cases with 3 or more outcomes, sometimes termed a multi-way variable in opposition to a binary variable. It is also possible to consider categorical variables where the number of categories is not fixed in advance. As an example, for a categorical variable describing a particular word, we might not know in advance the size of the vocabulary, and we would like to allow for the possibility of encountering words that we haven't already seen. Standard statistical models, such as those involving the categorical distribution and multinomial logistic regression, assume that the number of categories is known in advance, and changing the number of categories on the fly is tricky. In such cases, more advanced techniques must be used. An example is the Dirichlet process, which falls in the realm of nonparametric statistics. In such a case, it is logically assumed that an infinite number of categories exist, but at any one time most of them (in fact, all but a finite number) have never been seen. All formulas are phrased in terms of the number of categories actually seen so far rather than the (infinite) total number of potential categories in existence, and methods are created for incremental updating of statistical distributions, including adding "new" categories. Categorical variables and regression Categorical variables represent a qualitative method of scoring data (i.e. represents categories or group membership). These can be included as independent variables in a regression analysis or as dependent variables in logistic regression or probit regression, but must be converted to quantitative data in order to be able to analyze the data. One does so through the use of coding systems. Analyses are conducted such that only g -1 (g being the number of groups) are coded. This minimizes redundancy while still representing the complete data set as no additional information