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Dependent Variable: Measuring the Outcome

A dependant variable is an entity whose observed value will change in response to another variable’s observed value. This measure, often called the response variable, is commonly visualized on the Y-axis of charts, graphs, plots, and other visual tools.

The dependent variable is a measure of dependency related to one or more independent variables. In other words; a measure of how much the observed value variable will change in response to a change in observed value for one or more variables.

Visualizing the Dependent Variable

To better illustrate the role of dependent (response) variables, consider a hypothetical study that observes the change in a person’s weight based on the type of diet chosen. In this scenario, the measure of a person’s weight is the dependent variable and the chosen diet is the independent variable. The chart below also illustrates the relationship between response and explanatory variables.

indpendent vs dependent variables histogram sample
This chart illustrates an independent variable on the x-axis and a dependent value on the y-axis

Naming Conventions

Statistical terminology is notoriously convoluted—the same concepts are often named differently based on the field of application. The dependent variable is one of the most commonly co-opted terms that, depending on the context of its use, may be referred to as any of the following forms (Upton, 2014):

  • Response variable
  • Outcome variable
  • Predicted Variable
  • Experimental variable
  • Explained variable
  • Output
  • Regressand
  • Criterion
  • Measured variable
  • Target Variable
  • Label

These are but some of the many forms to which the dependent variable is referred. As an example, machine-learning applications often use the terms label; clinical studies often use experimental variable; regression analysis often elects to use regressand—all referring to the same dependent variable.

Products of Functions

In mathematics, dependant and independent variables are models in the simplest form as functions. The function takes an input value (independent variable) and generates an output value (dependant variable) based on an algorithm. Consider the general formula below:

function formula
The canonical representation of a mathematical function that takes a value as an argument and generates and output value

This notation is the most basic form where x is the independent variable and f represents the function that generates the output. Functions can be used to calculate the result of formulas. Consider the formula for a linear equation: y = mx + b. A function is a mapping of one thing into another such that this equation can be represented as such:

function independant variables 1
The linear equation is mapped to a custom function “f” where x, m, and b are independent variables and the output is the dependent variable

Understanding the difference between dependent variables and independent variables is essential in drawing meaningful conclusions from data. Whether they’re being referred to as an experimental value, the output of a function, or the response variable—they illustrate the results of events in many cases and the focus of statistical analysis.

References

  1. Upton, Graham, and Ian Cook. A Dictionary of Statistics 3e. Oxford, United Kingdom, Oxford University Press, 2014.