Factorial experiments for two factors
A factorial experiment is the most efficient way to estimate the separate effects of two factors on a response. Usually factorial experiments are designed with the same number of experimental units used for each combination of factor levels. Using the terminology of experimental design, this is expressed as the same number of replicates for each treatment.
The design of factorial experiments should also include random allocation of the treatments (factor combinations) to the pool of experimental units.
When designing experiments, never forget to randomise the allocation of treatments.
A few examples of data from factorial experiments are given below.
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 for each of the 16 treatments. 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 layout of the data in the table does not correspond to the layout of the plots in the field — the treatments were randomly allocated to the plots.
Television screen brightness
An experiment was conducted to study the effect of glass type and phosphor type on the brightness of a television screen. The variable measured is the current in microampleres necessary to produce a certain brightness; the larger this current, the poorer the screen characteristics.
Phosphor type | |||
---|---|---|---|
Glass type | A | B | C |
Type 1 | 280 290 285 |
300 310 295 |
270 285 290 |
Type 2 | 230 235 240 |
260 240 235 |
220 225 230 |
The 18 screen samples were tested in random order.