Essay On Factorial Experiments
Factorial Experiments In a factorial experiment the arrangement of treatment consists of all possible combinations of all levels of all factors under investigation. In this experiment we attempt to analyse two or more sets of treatments simultaneously where all combinations of factor levels are tested. Each observation provides information about all the factors in the experiment making the factorial experiment most efficient. It also provides a logical method of investigating the relationships among the effects of different factors in terms of what we call the interactions. The factorial experiment not only allows us to analyse interactions between factor levels, but is also particularly useful when little is known about factors and all combinations …show more content…
The Y-axis represents the response and the X-axis represents levels of factor A. The connected symbols represent the levels of factor B. The slope of the lines indicates whether there is presence of interaction between two factors or not. If the lines are roughly parallel, this means that there is no interaction. Any difference in slope between the lines indicates a possible interaction, the greater the difference in slope, the stronger the interaction. Figure Graphic representation of interaction between two factors A and B In this chapter, a 2 X 2 factorial experiment is described. As the rationale for three or more factors remains the same, one can carry out analysis of data in a factorial experiment of any order. Two factor factorial experiment Let us describe a factorial experiment with two factors A and B having their levels as a and b, respectively such that the number of experimental units for each A X B combination is r. Thus, there will be a total of rab experimental units divided into ab combinations of A and B. The set of treatments consists of ab possible combinations of factor levels. The model for a factorial experiment with two factors A and B is: where: Yijk = kth observation in ith level of factor A and jth level of factor B μ = the overall
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