In this talk, the limitations of normal model for Analysis of Covariance for positive right-skewed variables are considered. Specifically, an Inverse Gaussian variable is considered whose variance depends on its mean thus violating the usual assumptions of Normal linear model. Instead of appealing to transformations which makes interpretations of the results awkward, we propose a method of direct statistical analysis from both Maximum Likelihood and Bayesian perspectives. The formulas for adjusting treatment effects are given and their properties are discussed. To provide explicit formulas, conjugate priors are considered. The posterior distributions are derived and procedures of adjustment for covariates are presented.