Factorial design is a statistical technique where multiple treatments (or variables) are tested simultaneously. In other words, instead of testing each treatment individually, you test them together. This allows you to determine whether or not they interact with each other.

Factorial designs are commonly used in experiments because they allow researchers to examine interactions between independent variables.

For example, if you were conducting an experiment on the effects of different types of lights, humidity and soil type on plants, you could use a factorial design to test how these factors affect plant growth.

In this experiment, the factors would be the light type, humidity and soil type.

Typically, you assign two levels to each factor.

You might choose natural sunlight and electric bulb as two levels for the light type. For humidity, you might choose 20% and 60% levels, and for the soil type, you might consider sandy soil and clay soil.

You would conduct a full factorial design with eight runs using three factors and two levels for each factor. Each run represents a unique combination of a factor and a level.

**Factors and Levels**

The following table shows a typical factorial design with three factors and two levels for every factor.

- Sunlight + 20% Humidity + Sandy Soil
- Sunlight + 20% Humidity + Clay Soil
- Sunlight + 60% Humidity + Sandy Soil
- Sunlight + 60% Humidity + Clay Soil
- Bulb Light + 20% Humidity + Sandy Soil
- Bulb Light + 20% Humidity + Clay Soil
- Bulb Light + 60% Humidity + Sandy Soil
- Bulb Light + 60% Humidity + Clay Soil

## Calculating the number of runs

The number of runs required for a full factorial design can be calculated by the formula: Levels to the power factors.

With three factors and two levels, it will be 2 to power 3, which is 8.

## Definition of Factor

A factor is any independent variable that affects the outcome of your experiment, whose effect the experimenter wants to study.

## Definition of Level

Levels are the set of values assigned to the factors. They represent the conditions under which the runs will be conducted. Typically, you set two levels for each factor. However setting up more than two levels for a factor is also not unusual.