maths world

Binary Variables

A binary variable is a categorical variable that can only take one of two values, usually represented as a Boolean — True or False — or an integer variable — 0 or 1 — where $0$ typically indicates that the attribute is absent, and $1$ indicates that it is present.

Some examples of binary variables, i.e. attributes, are:

Smoking is a binary variable with only two possible values: yes or no
A medical test has two possible outcomes: positive or negative
Gender is traditionally described as male or female
Health status can be defined as diseased or healthy
Company types may have two values: private or public
E-mails can be assigned into two categories: spam or not
Credit card transactions can be fraud or not

In some applications, it may be useful to construct a binary variable from other types of data. If you can turn a non-binary attribute into only two categories, you have a binary variable. For example, the numerical variable of age can be divided into two groups: 'less than 30' or 'equal or greater than 30'.

Datasets used in machine learning applications have more likely binary variables. Some applications such as medical diagnoses, spam analysis, facial recognition, and financial fraud detection have binary variables.

Although binary variables are commonly used in statistics (i.e. for the binomial distribution), the term “binary variable” is seldom used. This may be in part because it’s rare to come across a variable that only has two choices outside of a Bernoulli distribution.

BINARY VARIABLES AND DICHOTOMOUS VARIABLES

Binomial variables are also same as dichotomous variables ,because it also take two values.

BINARY VARIBLES AND DUMMY VARIABLES

The terms dummy variable and binary variable are sometimes used interchangeably. However, they are not exactly the same thing. A dummy variable is used in regression analysis to quantify categorical variables that don’t have any relationship. For example, you could code 1 as Caucasian, 2 as African American, 3 as Asian etc. If your dummy variable has only two options, like 1=Male and 2=female, then that dummy variable is also a binary variable.

Types of binary variables .

Opposite binary variables
Conduct binary variables

OPPOSITE BINARY VARIABLES

Opposite binary variables are polar opposite, like “Success” and “Failure.” Something either works, or it doesn’t. There’s no middle ground.

Examples are,

1 / 0.
Yes / No.
Success / Failure.
Male / Female.
Black / White

binary variable

Take the red pill, or the blue pill?

CONJUNCT BINARY VARIABLES

Conjunct binary variables aren’t opposites of each other. They have more of a grey area.

For example, in the United States you can be affiliated with the Democrat or Republican parties. In real life though, most people aren’t staunchly republican or staunchly democrat. It’s common for people to flip flop between parties, agree with 20% of what the other party says (making them 20% of one party and 80% of the other) or even to identify as another party entirely, like the Green Party.

REFFERENCE
https://www.statisticshowto.com/binary-variable-2/

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