Factorial design
An efficient design for experiments with two or more factors uses each possible combination of factor levels (called treatments) in the same number of experimental units. The repeat measurements for each treatment are called replicates and the design is called a factorial design.
The design on the previous page was an example of a factorial design for two factors but similar designs are also used for three or more factors.
Soybean yield and trace elements
An experiment was conducted to assess how different applications of manganese (Mn) and copper (Cu) affect the yield of soybeans.
In the experiment, a large field was subdivided into 32 plots and two were randomly allocated to each combination of Mn rate and Cu rate — i.e. there were 2 replicates. Soybeans were planted in rows 1 metre apart and the yield of soybeans (in kg per hectare) was recorded from each plot.
Rate of Mn | ||||
---|---|---|---|---|
Rate of Cu | 20 | 50 | 80 | 110 |
1 | 1558 1578 |
2003 2033 |
2490 2470 |
2830 2810 |
2 | 1590 1610 |
2020 2051 |
2620 2632 |
2841 2841 |
5 | 1558 1550 |
2003 2010 |
2490 2690 |
2830 2910 |
7 | 1328 1427 |
2010 2031 |
2887 2832 |
2960 2941 |
Note that the rates of application of the two trace elements are numerical not categorical. However when only a few values are used, such factors can be treated as categorical for analysis purposes.
Legume germination
A greenhouse experiment was conducted to determine the rate of emergence of seeds of three species of legumes, treated and not treated with a fungicide, and planted in three soil types. The responses in the table below are the number of plants emerging out of 300 seeds.
No fungicide | Fungicide | ||||||
---|---|---|---|---|---|---|---|
Legume species | Silt loam | Sand | Clay | Silt loam | Sand | Clay | |
Alfalfa | 266 | 286 | 66 | 276 | 271 | 215 | |
Red clover | 252 | 298 | 167 | 275 | 292 | 203 | |
Sweet clover | 152 | 197 | 52 | 178 | 219 | 121 |