Factorial design is actually the design consisting of an experiment that examines the level effect on each factor and all the other related factors. So the factorial design analysis is the analysis made on the factorial design with the coordination of analysis of variance and the multiple regressions. The most favorable design for the treatment of statistical data is the factorial design because it creates rapid efficiency in case of the collection of the data. Firstly to examine the formation of factorial design which is comprises of two levels stated as maximum and the minimum. In the analysis of factorial design each possible factor is taken into the view. For example in case of three factor model then it is stated as two to the power three, if with four factor model its combination are comprises of two into the ;power four which is 16 in number. Replication for all the factors is analyzed for number of times. The factorial for each case is identified separately for each and every factors level.[sky]

In case of the analysis of factorial design or factorial experimental design replications are made for each factor using the analysis of variance which includes all sought of repeated evaluations. Other than the factorial design analysis the more appropriate measure is through multiple regressions. The analysis of the factorial design is computed by comparing the different effects of the different types of variable involved in the design. For example if there is a study for three factors then the factorial design will be 23. The analysis of the factorial design is examined through the regression linear equation or statement. The equation is stated as;

y_{i }= b_{ 0}+ b_{ 1}Z_{1i}+ b_{ 2}Z_{2i}+ b_{ 3}Z_{1i}Z_{2i}+e_{i}

In the above stated equation, the yi is the evaluated outcome for the ith unit of value; Bo is the value of the intercept which is the value of beta, B1 is the difference of the two values included in factor 1, similarly the B2 is also the mean value for the related factors of the model that might be factor 2. Beta B3 is the value of interaction of the factor 2 and 3; e is the residual value that is the possibilities of errors in the model. This analysis model involves the dummy variables in the study which are denoted by Z and in the 2×2 factorial models the dummy variables present two main effects and one interaction. The values of the dummy coded variables comprises of 0 and 1 value that is 0 is allotted with control group and 1 is allotted in case of the treatment group. The model most commonly involves the adjustment of the beta values with the variable Z. As the model includes two dummy variables with the involvement of two values, then the equation can be separately written for the maximum number of times as presented in the factorial design. It can also be written as the two equations with Z. In result of these equations, the more appropriate effect is shown.

## References

• Das, M.N., and Giri, N.C., (2003), Design and analysis of experiments. Ed. 2nd:New age international publishers.

• Keisler, H.J. and Robbin, J., (1996), Mathematical Logic and Computability.