It is well known that the least squares method is optimal only if the error distributions are normally distributed. However, in practice, non-normal distributions are more prevalent. If the error terms have a non-normal distribution, then the efficiency, of least squares estimates and tests is very low. In this paper, we consider the 2 (k) factorial. design when the distribution of error terms are Weibull W(p, sigma). From the methodology of modified likelihood, we develop robust and efficient estimators for the parameters in 2 (k) factorial design. F statistics based on modified maximum likelihood estimators (MMLE) for testing the main effects and interaction are defined. They are shown to have high powers and better robustness properties as compared to the normal theory solutions. A real data set is analysed.