The word factor, in the context of Design of Experiments (DOE), has several other names. Let’s learn more about what a factor is and how it is used in DOE.

One of the most common formulas in statistics is Y = f(X) which states that Y is a function of X. If you define Y as the output, then the formula can be restated as the output is a function of the input where X is now defined as the input. When talking about Design of Experiments (DOE), X can also be called a factor. In DOE and linear regression, the factor can also be defined as a controllable, predictor, treatment or independent variable. They all mean the same thing.

## Overview: What is a factor?

The purpose of a DOE is to develop a prediction equation which allows you to estimate the response or dependent variable by manipulating the values of the independent variables or factors. Factors may be continuous variables or discrete variables

The values of the factors are set at different levels or settings and a combination of the factors and levels are used to record the impact on the response variable. If a factor is determined to be significant, it will be included in the final prediction equation. The relative impact of the factor will be calculated as a coefficient. The main effects of the factors alone as well as any interaction effects are calculated and commonly displayed in the output when using a statistical software program for your DOE.

## An industry example of a factor

An auto manufacturer wanted to test the fuel efficiency of its new model cars. They designed a DOE to test the effect or impact of certain driving variables on miles per gallon. One factor was the speed the car was driven. This was a continuous variable. They also chose the time of day, either morning or afternoon. This was a discrete factor.

Additional variables of tire pressure and octane rating of the gasoline were also selected as possible predictor variables or factors which might predict the response variable of miles per gallon.

### What is the difference between a factor and a level?

Factors are defined as the independent or predictor variables used in DOE or regression. Levels are the settings of the factors when you are using them during experimental runs. A 2-level experiment is the most common, where the levels would be a factor value designated as high and low.

### Is there a difference between a factor variable and a predictor variable?

No, they are used interchangeably, as is the term independent variable.

### Do factors need to be continuous data?

No, you can have continuous or discrete factors. For example, if time is a variable of interest then it would represent a continuous factor. If gender was another variable of interest, then it would be a binary discrete factor.