# The alias concept

An alias is the fact that, between two factors, the factors have the same level for the totality of experiments in a design of experiments.

For example, suppose that the following design of experiments was carried out:

A |
B |
Y |

1 |
1 | 5 |

1 |
1 | 5 |

2 |
2 | 10 |

2 |
2 | 10 |

Factors A and B vary at the same time, so it is not possible to differentiate factors A and B nor is it possible to say which of the two causes the variance of Y from 5 to 10 when it moves from 1 to 2.

These two factors are called aliases.

Obviously, when building a design of experiments, the tests are carefully chosen so that each factor does not become an alias of another factor. However, it is still possible for a factor to become the alias of an interaction.Let us take the following example:

In this example we have built a plan with three factors using the table L4. In the alias table the following is observed:

- Factor a is an alias to the b*c interaction
- Factor b is an alias to the a*c interaction
- Factor c is an alias to the a*b interaction

Similarly, if two factors are aliases then it is not possible to say, at the end of the design of experiments, whether the observed effect is due to factor a at the b*c interaction or the sum of the two. We therefore assume that the b*c interaction is null, though it must be verified experimentally.

To avoid this type of problem, design of experiments are generally chosen where none of the factors is alias to an interaction. In the preceding example we could have chose the L8 plan where none of the factors is alias to an interaction.