Types of Variables > Polychotomous Variable / Polytomous Variable
Contents:
- Definition
- Polychotomous Independent Variable
- Dichotomous vs. Polychotomous
- Polytomous vs. Polychotomous
What is a Polychotomous Variable?
A polychotomous variable (also called a polytomous variable) is a variable that can have more than two values (a variable with exactly two values is called a binary variable).
Polychotomous variables can be ordered, unordered, or sequential:
- Ordered polychotomous variables: variables that have some kind of order, like: “1” if you earn up to $25,000, “2” if you earn $25,001-$50,000 and “3” if you earn over $50,000.
- Unordered polychotomous variables: variables that don’t have an implied order, like: “1” for male, “2” for female “3” for trans gendered male and “4” for trans gendered female.
- Sequential polychotomous variables: variables with a sequence. For example: “1” for freshmen, “2” for sophomore, “3” for junior and “4” for senior.
Polychotomous variables are usually qualitative variables, but they can be quantitative variables as well. For example, if studying birth weight of children, you could have the categories of heavy smoker/smoker/light smoker or non-smoker. But it may be more useful to code the “number of cigarettes smoked per day during pregnancy” into categories:
- 0 cigarettes per day.
- up to 5 cigarettes per day.
- Between 6 and 20 cigarettes per day.
- Over 20 cigarettes per day.
Polychotomous Independent Variable
If your independent variable has more than two categories, then it’s a polychotomous independent variable. For example: race, country of origin, or school attended are all examples of independent variables that could have more than three categories.
Dichotomous vs. Polychotomous Variables
A dichotomous variable is the same as a binary variable, i.e. it has two possible values. So a dichotomous variable would have two values, a polychotomous variable would have more than two. In statistics, the term binary variable is preferred. The term dichotomous variable is used in psychometrics.
Polytomous vs. Polychotomous Variable
The two words mean the same thing. There’s some division in statistics about whether the term polytomous or polychotomous should be used. One Penn State professor [1] states that “The word [polychotomous] does not exist!”, although a quick check in the Mirriam-Webster dictionary says that it does: “dividing or marked by division into many parts, branches, or classes”.
Perhaps the confusion is that the two terms are used interchangeably, although in statistics (as a subject matter and for theoretical purposes), the more precise term is polytomous variable. As is the case with many precise terms in statistics though, it’s often the case that people use synonyms.
Fields that tend to use “polytomous variable”:
The term “polytomous variable” is more common in:
- Item Response Theory (IRT): Used in educational testing and psychometrics when describing multiple-choice questions with more than two possible answers.
- Biostatistics & Epidemiology: In logistic regression, “polytomous logistic regression” is a widely accepted term for models handling multiple categorical outcomes.
- General Statistical Literature: Many statistical textbooks and academic papers prefer “polytomous” over “polychotomous.”
Fields that tend to use “polychotomous variable”:
- Psychometrics & Survey Research: Used in questionnaires and scales where responses have multiple categories.
- Biostatistics & Epidemiology: Applied in medical and public health studies when classifying outcomes into multiple categories (e.g., types of diseases).
- Machine Learning & Data Science: Used when handling categorical variables in classification problems.
References
[1] Penn State. Stat504. Retrieved January 12, 2021 from: https://onlinecourses.science.psu.edu/stat504/node/172
Types of Variables > Polychotomous Variable / Polytomous Variable
What is a Polychotomous Variable?
A polychotomous variable (also called a polytomous variable) is a variable that can have more than two values (a variable with exactly two values is called a binary variable).
Polychotomous variables can be ordered, unordered, or sequential:
- Ordered polychotomous variables: variables that have some kind of order, like: “1” if you earn up to $25,000, “2” if you earn $25,001-$50,000 and “3” if you earn over $50,000.
- Unordered polychotomous variables: variables that don’t have an implied order, like: “1” for male, “2” for female “3” for trans gendered male and “4” for trans gendered female.
- Sequential polychotomous variables: variables with a sequence. For example: “1” for freshmen, “2” for sophomore, “3” for junior and “4” for senior.
Polychotomous variables are usually qualitative variables, but they can be quantitative variables as well. For example, if studying birth weight of children, you could have the categories of heavy smoker/smoker/light smoker or non-smoker. But it may be more useful to code the “number of cigarettes smoked per day during pregnancy” into categories:
- 0 cigarettes per day.
- up to 5 cigarettes per day.
- Between 6 and 20 cigarettes per day.
- Over 20 cigarettes per day.
Polychotomous Independent Variable
If your independent variable has more than two categories, then it’s a polychotomous independent variable. For example: race, country of origin, or school attended are all examples of independent variables that could have more than three categories.
Dichotomous vs. Polychotomous Variables
A dichotomous variable is the same as a binary variable, i.e. it has two possible values. So a dichotomous variable would have two values, a polychotomous variable would have more than two. In statistics, the term binary variable is preferred. The term dichotomous variable is used in psychometrics.
Polytomous Variable vs. Polychomotous
The two words mean the same thing. There’s some division in statistics about whether the term polytomous or polychotomous should be used. One Penn State professor [1] states that “The word [polychotomous] does not exist!”, although a quick check in the Mirriam-Webster dictionary says that it does: “dividing or marked by division into many parts, branches, or classes”.
Perhaps the confusion is that the two terms are used interchangeably, although in statistics (as a subject matter and for theoretical purposes), the more precise term is polytomous variable. As is the case with many precise terms in statistics though, it’s often the case that people use synonyms.
Fields that tend to use “polytomous variable”:
The term “polytomous variable” is more common in:
- Item Response Theory (IRT): Used in educational testing and psychometrics when describing multiple-choice questions with more than two possible answers.
- Biostatistics & Epidemiology: In logistic regression, “polytomous logistic regression” is a widely accepted term for models handling multiple categorical outcomes.
- General Statistical Literature: Many statistical textbooks and academic papers prefer “polytomous” over “polychotomous.”
Fields that tend to use “polychotomous variable”:
- Psychometrics & Survey Research: Used in questionnaires and scales where responses have multiple categories.
- Biostatistics & Epidemiology: Applied in medical and public health studies when classifying outcomes into multiple categories (e.g., types of diseases).
- Machine Learning & Data Science: Used when handling categorical variables in classification problems.
References
[1] Penn State. Stat504. Retrieved January 12, 2021 from: https://onlinecourses.science.psu.edu/stat504/node/172