Yates Analysis

Yates Analysis
Yates Analysis

Yates Analysis. Photo by Simon Cunningham

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
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.
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