Many subjects are collected under the term methodology. One of them is variables, or in this article especially binary variables. They can describe anything that has only two options or outcomes, whether it is a question with “yes” or “no” as answers, computer code with 1 and 0, or a simple success or failure experiment. The following article will explain everything you need to know about binary variables.
Binary variable in a nutshell
Binary variables are variables with only two outcomes, mostly defined as “success” or “failure.”
Definition: Binary variable
Binary variables, sometimes also called binomial random variables or dichotomous variables, are a type of categorical variable with only two possible outcomes. It is mostly used in binomial distributions, but also in programming, medical tests, or everyday speech. Every experiment can be defined by binomial variables, by splitting the results into two groups.
The word “binomial” originates from Latin, meaning twofold, double, or dual, which fits the definition perfectly as binary variables are characterized by two options. If you want to find out more about the etymology and the root word “bi,” click on the button below.
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Examples
The following examples will show you the usage of this type of variable in different fields. If we have the outcomes 0 or 1, then it is also called a numerical variable because it is defined by numbers.
Examples
- Binomial distribution: success or failure
- Programming: 1 or 0, true or false
- Medical tests: positive or negative
- Everyday speech: yes or no, underage or adult
Types
There are generally two different types of binary variables, opposite and conjunct ones.
Opposite binary variables
Opposite binary variables are, as the name suggests, opposites. This means they exclude each other.
Examples
- Yes or no
- 1 or 0
- Open or closed
- On or off
Conjunct binary variables
Conjunct binary variables cover a gray area and do not always exactly mean opposites.
Examples
- Cat person or dog person. Many people can choose one, but in reality, they might like both, neither, or it depends on the individual animal.
- Political orientation in America. People can be divided into Democrats and Republicans, but in reality, some people are on neither side nor like the approaches of both sides.
Dummy variables
Dummy variables are variables that have no relationship to the object they are referring to, for example, if you number the US states randomly. If there are only two dummy variables, then they are also binary variables.
Binomial distribution
A binomial distribution is an experiment with independent trials and only two outcomes per trial; “success” and “failure.” The following four rules will show you how a binomial distribution works.
- There has to be a fixed number (n) of trials.
- Each trial has only two outcomes; success or failure.
- The probability of success remains the same every trial and is called p or sometimes π.
→ The probability of failure q is thus q=1-p. - All trials are independent. This means that the result of the prior trial does not affect the next one.
Example
You are writing an exam with 10 exercises, where you have to tick whether the given statement is right or wrong. In this case, your answer to the previous question has no impact on the next one. Thus, the events of ticking the boxes are independent.
FAQs
Binary variables are variables with only two options, for example, yes/no, open/closed, on/off, or success/failure.
Binary variables can be used in many different ways. The most common example is a binomial distribution; however, they are also used in programming codes or even everyday speech, considering “yes” and “no” are also binary variables.
Not exactly. A binary variable always consists of two options. Dummy variables can also have two absolute values, but mostly they contain more than two. This means that dummy variables with two outcomes are binary variables, but if they have more outcomes, they are not.
