In the previous discussion we discussed the effect of a single treatment on certain responses . The single treatment is called the factor , and the level or level of the factor is called the level . The factor is symbolized by a capital letter while the level of the factor is symbolized by a lowercase letter . If we simultaneously observe the effect of several factors in the same study, the experiment is called a factorial experiment .
A factorial experiment is an experiment in which the treatment consists of all possible combinations of levels of several factors. Experiments using f factors with t levels for each factor are symbolized by the factorial experiment f t . For example, a 2 2 factorial experiment means that we use 2 factors and the level of each factor consists of 2 levels. Factorial experiment 2 2 It is also often written in the form of a 2x2 factorial experiment. The last symbol is often used for factorial experiments where the level of each factor is different, for example 2 levels for factor A and 3 levels for factor B, the experiment is called a 2x3 factorial experiment. A 2x2x3 factorial experiment means a factorial experiment consisting of 3 factors with levels for each factor of 2, 2, and 3. described previously, and the next stage is the selection of the environmental design, which involves the form of experimental designs such as:
Sub-discussion:
The full discussion can be read in the document below.
In the previous discussion we have discussed the effect of single treatment on certain responses. The single treatment is called a factor, and the level or level of the factor is called a level. Factors are symbolized by capital letters while the degree of factors is symbolized by lowercase. If we simultaneously observe the effect of several factors in the same study, then the experiment is called a factorial experiment.
A factorial experiment is an experiment whose treatment consists of all possible combinations of several factors. Experiments using f factors with level for each factor are symbolized by factorial experiments f t . For example, the factorial experiment 2 2 means that we use 2 factors, and the level of each factor consists of 2 levels. Factorial experiments 2 2 are also often written in the form of 2x2 factorial experiments. The latter is often used for factorial experiments where the levels of each factor are different, for example 2 levels for factor A and 3 levels for factor B, then the experiment is called a factorial experiment 2x3. A 2x2x3 factorial experiment means a factorial experiment consisting of 3 factors with a level for each of its factors 2, 2, and 3 respectively. Thus, in the factorial experiment, there are two stages that need to be carried out, firstly, namely the treatment design, as previously described, and then the stage of selecting the environmental design, which concerns experimental design forms such as CRD, RCBD, LATIN, Split-plot, Split-Block.
The purpose of the factorial experiment is to look at the interactions between the factors we are trying. Sometimes the two factors synergize with each other to the (positive) response, but sometimes also the existence of one factor hinders the performance of other (negative) factors. The existence of these two mechanisms tends to increase the effect of interactions between the two factors. Interaction measures the failure of the effect of one factor to remain the same at every level of another factor or simply, the interaction between factors is whether the effect of a particular factor depends on the degree of another factor? For example, if the simple effect of N is the same at each level of fertilizer application P, the two factors are mutually independent and it is said that there is no interaction, while if the application of N has a different effect on each level of P, it is said that there is an interaction between Factor N and Factor P.
For example, if we want to observe the effect of nitrogen (N) administration consisting of 2 levels (n0, and n1) and phosphorus administration (P) consisting of 2 levels (p0, p1) on certain responses, with the following results:
Table 19. Simple effect, main effect, and Interaction effect
Factor
Nitrogen (N)
Average P
Simple effect n