Complete design
In statistical test planning, a complete test plan ( full factorial design ) is a test plan that plays through all possible combinations of factors.
If, for example, four factors are to be investigated in an experiment, each of which should be set at two different levels in the experiment, a complete experiment plan requires a total of 2 4 = 16 test runs.
The disadvantage of complete test plans is that the number of test runs increases very quickly as the number of test factors increases. For example, examining six factors would require 2 6 = 64 trial runs. For this reason, if there are a large number of interesting factors, a partial factor plan is often used for reasons of economy , as long as it can be assumed that interactions can be neglected.
example
A farmer wants to find out the influence of irrigation and fertilization on the yield of his crops. The factor A measures the irrigation in the stages 1 ≙ "without artificial irrigation" and 2 ≙ "with artificial irrigation". Factor B measures the fertilization in the levels 1 ≙ "no fertilization", 2 ≙ "organic fertilization" and 3 ≙ "mineral fertilization". The complete test plan therefore contains a total of 2 · 3 = 6 factor level combinations. Each factor level combination should be examined a total of 4 times. For this the farmer grows his plants on 4 different fields. Each of these 4 fields is divided into 6 smaller areas, in each of which a factor level combination is examined. In total, the 4 fields (called blocks in the test plan) are therefore divided into 24 plots.
The design is shown in the following table:
| plot | block | A. | B. |
|---|---|---|---|
| 1 | 1 | 2 | 3 |
| 2 | 1 | 2 | 2 |
| 3 | 1 | 1 | 2 |
| 4th | 1 | 1 | 3 |
| 5 | 1 | 2 | 1 |
| 6th | 1 | 1 | 1 |
| 7th | 2 | 2 | 2 |
| 8th | 2 | 1 | 2 |
| 9 | 2 | 2 | 3 |
| 10 | 2 | 2 | 1 |
| 11 | 2 | 1 | 3 |
| 12 | 2 | 1 | 1 |
| 13 | 3 | 1 | 2 |
| 14th | 3 | 2 | 2 |
| 15th | 3 | 1 | 1 |
| 16 | 3 | 2 | 1 |
| 17th | 3 | 2 | 3 |
| 18th | 3 | 1 | 3 |
| 19th | 4th | 1 | 1 |
| 20th | 4th | 2 | 3 |
| 21st | 4th | 1 | 2 |
| 22nd | 4th | 2 | 1 |
| 23 | 4th | 1 | 3 |
| 24 | 4th | 2 | 2 |
The above test plan was created with the function design.ab from the R package agricolae . The factor level combinations are randomly assigned to the parcels under the secondary condition that each of the 6 factor level combinations occurs exactly once in each of the 4 blocks. Thanks to the complete test plan, interactions can be demonstrated in addition to the main effects. For example, mineral fertilized plants could benefit to different degrees from additional irrigation than organically fertilized plants.
Different location and soil conditions could prevail in the 4 blocks, which is taken into account by the block effect.
Individual evidence
- ^ A b Montgomery, Douglas C .: Design and Analysis of Experiments. John Wiley and Sons, 1991, ISBN 0-471-52994-X , p. 335
- ↑ Felipe de Mendiburu: agricolae: Statistical Procedures for Agricultural Research. June 12, 2016, accessed January 30, 2017 .