Yate's algorithm

Yate's algorithm

The Yate's algorithm is illustrated below for a 23 factorial experiment. Let us denote the three factors by A, B & C.

  1. Start with the results (with the average of the results in an experiment with replicates) in each run in standard order (first column in the table below).
  2. The first four entries in Column 1 (second column of the table below) are obtained by adding the pairs together. Thus 60 + 72 = 132, 54 + 68 = 122, etc.
  3. The second four entries in column 1 are obtained by subracting the top number from the bottom number of each pair (since effect is defined as high - low). Column 2 is obtained from column 1 in the same fashion. And similarly, column 3 from column 2.
  4. We stop the process when the first number in the column equals the sum of all the average results, here 514 (Or 3 columns since there are only 3 factors).

Table
Average Results Column 1 Column 2 Column 3 Divisor Estimates Variable
60 132 254 514 8 64.25 1 (Average)
72 122 260 92 4 23.0 A
54 135 26 -20 4 -5.0 B
68 125 66 6 4 1.5 AB
52 12 -10 6 4 1.5 C
83 14 -10 40 4 10.0 AC
45 31 2 0 4 0.0 BC
80 35 4 2 4 0.5 ABC

Check: Twice the sum of every second entry in column i is equal to the sum of the entries in column i +1. For example, the sum of every second entry in column 1 is 122 + 155 + 14 + 35 = 296, which when doubled, gives 592. This is equal to the sum of the entries in column 2.

Reference:

Box, George E. P., Hunter, William, G., and Hunter, Stuart J., "Statistics for Experimenters - An Introduction to Design, Data Analysis, and Model Building", John Wiley & Sons, New York, 1978.


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