### Full Factorial Design

Full Factorial Design allows for experiments to include at least one test in all combinations of variables and levels. It is impossible to miss interactions with this exhaustive approach since all interactions between factors are taken into account. This exhaustive approach is time-consuming and expensive for experiments that involve multiple factors.

### Calculating the number of trials

The product of the factors’ levels determines the number of trials needed for a full-factorial experiment.

*No. of trials = F _{1} level count x F_{2} level count x … x F_{n} level count*

#### How many trials are there in a full factorial design?

Find the product by multiplying the number of levels multiplied by the number of factors.

Ex1. Ex1.

Ex 2. Ex 2. Three x two x five x four = 120 observations.

#### You can also see our Example of a Good Way to Start

Look at an experiment with 4 factors.

- There are two levels to the first factor.
- There are five levels to the second factor.
- Three levels are possible for the third factor.
- Six levels are possible for the fourth factor.

The experiment needs:

*No. of trials = 2 x 5 x 3 x 6 = 180 trials*

### Full Factorial Design Notes

- The full factorial design includes all combinations possible of each level and factor.
- It can take time to test out full factorial designs.
- It can be expensive to test out full factorial designs.
- Each combination of factors or levels requires at least one observation.
- Measures all possible interactions.
- Costly and time-consuming

### Why you would use partial or fractional factorial design instead

fractional Factorial Design can lead to the omission of important interactions.

The analysis of interactions is not possible with fractional factorials, such as Latin or GraecoLatin Squares. The interaction is confused with the other effects.

#### Partial Factorial Analysis: A Step Up from Full Factorial Analysis

- Trials will be reduced
- Confusion will ensue
- Resolution will decrease