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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.
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.
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.
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 variable of this type is called a dummy variable. If the dependent variable is a dummy variable, then logistic regression or probit regression is commonly employed. In the case of regression analysis, a dummy variable can be used to represent subgroups of the sample in a study (e.g. the value 0 corresponding to a constituent of the control ...
The variable could take on a value of 1 for males and 0 for females (or vice versa). In machine learning this is known as one-hot encoding. Dummy variables are commonly used in regression analysis to represent categorical variables that have more than two levels, such as education level or occupation.
Some tests perform univariate analysis on a single sample with a single variable. Others compare two or more paired or unpaired samples. Unpaired samples are also called independent samples. Paired samples are also called dependent. Finally, there are some statistical tests that perform analysis of relationship between multiple variables like ...
Contrary to a widespread belief, a Guttman scale is not limited to dichotomous variables and does not necessarily determine an order among the variables. But if variables are all dichotomous, the variables are indeed ordered by their sensitivity in recording the assessed attribute, as illustrated by Example 1.