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The values are ordered in a logical way and must be defined for each variable. Domains can be bigger or smaller. The smallest possible domains have those variables that can only have two values, also called binary (or dichotomous) variables. Bigger domains have non-dichotomous variables and the ones with a higher level of measurement.
A categorical variable that can take on exactly two values is termed a binary variable or a dichotomous variable; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called polytomous variables ; categorical variables are often assumed to be polytomous unless otherwise specified.
In statistics, dichotomous data may only exist at first two levels of measurement, namely at the nominal level of measurement (such as "British" vs "American" when measuring nationality) and at the ordinal level of measurement (such as "tall" vs "short", when measuring height). A variable measured dichotomously is called a dummy variable.
Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers in the integral data type, and continuous variables with the real data type involving floating point ...
A common measure of dichotomous thinking is the cliff effect. [1] A reason to avoid dichotomous thinking is that p-values and other statistics naturally change from study to study due to random variation alone; [2] [3] decisions about refutation or support of a scientific hypothesis based on a result from a single study are therefore not ...
The point biserial correlation coefficient (r pb) is a correlation coefficient used when one variable (e.g. Y) is dichotomous; Y can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable. In most situations it is not advisable to dichotomize variables artificially.
Dichotomous, where the respondent has two options. The dichotomous question is generally a "yes/no" close-ended question. This question is usually used in case of the need for necessary validation. It is the most natural form of a questionnaire. Nominal-polytomous, where the respondent has more than two unordered options.
In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or r φ) is a measure of association for two binary variables.. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975.