Factorial designs in th presence of covariates

In this study, factorial designs that have covariate are considered. Classical theory for these designs is obtained based on normality assumption. On the other hand if the error terms do not have normal distribution, it is shown that the efficiency of the least squares (EKK) estimators of the model parameters and the power and robustness of test statistics decrease via Monte-Carlo simulation study. These results require to obtain more efficient estimators and powerful and robustness test statistics alternative to EKK when the normality assumption is not valid in factorial designs that have covariate.For these reasons it is assumed that the error terms in factorial designs that have covariate have independently and identically long tailed symmetric (LTS) distribution. Since the maximum likelihood estimators are not obtained analytically, modified maximum likelihood method is used in that case and estimators of the parameters are expressed with explicit formulas based on this method. The modified maximum likelihood (UEÇO) estimators are shown to be more efficient than EKK estimators in Monte-Carlo simulation study. Furthermore, test statistics are developed based on UEÇO estimators. These test statistics have asymptotically F distribution is proved and it shown that they have F distribution also for small sample sizes by means of Monte-Carlo simulation. Additionally, the test statistics developed based on UEÇO estimators are shown to be more powerful and robust than classical test statistics in Monte-Carlo simulation study. The developed method is applied on a real life example.