Yates analysis is a method of analyzing data from full and partial factorial design experiments. It requires two levels for each factor in the experiment – these are commonly referred to as ‘high’ and ‘low’ levels, and are represented by + and – signs respectively.

## Yates order

‘Yates order’ refers to a specific arrangement of experiment data needed for Yates analysis. To get your data into Yates order, experiments should be arranged so that, with *k* number of factors, each factor in its own column, *2 ^{(k-1)} *minus signs in a column (low levels) should be followed by the same number of plus signs (high levels), as a pattern down the height of the column. It sounds complicated, but let’s look at a simple example with 3 factors, already in Yates order:

Trial | Factor 1 | Factor 2 | Factor 3 | Data |
---|---|---|---|---|

1 | – | – | – | |

2 | + | – | – | |

3 | – | + | – | |

4 | + | + | – | |

5 | – | – | + | |

6 | + | – | + | |

7 | – | + | + | |

8 | + | + | + | |

For the first column in the table above, *k* = 1. According to Yates order, there should be a pattern of 2^{(1-1)} minus signs followed by 2^{(1-1)} plus signs in this column – or 1 minus sign and 1 plus sign. A quick look at the table will tell you this is the case. For the second factor in the table, Yates order dictates a pattern of 2^{(2-1)} minus signs followed by 2^{(2-1)} plus signs.

## Yates analysis output

Most Yates analysis is performed using analysis software. The output consists of:

**Factor identifier.**The notation varies depending on the software, but it generally looks like the notation we talk about in the Partial/Fractional Factorial Design topic. Sometimes you’ll see numbers used rather than letters.**Ranked factor list.**This uses least squares to determine the most significant factors – ie, the ones that had most effect on the results. For each factor,- t-value for each factor.
- residual standard deviation for that factor alone.
- cumulative residual standard deviation for factors up to and including that factor.