In this article we explore the testing of non-inferiority and equivalence hypotheses arising from multiple centers when the assumption of normality is violated. In a multicenter study, the trials are typically conducted at different centers which vary in terms of location, environment, demographics among others, leading to substantial amount of heterogeneity in the patient population. This unexplained variation in a multi-center clinical study is usually modeled using a random effects model, where the centers are assumed to be a random sample from the population of centers. Most research in this direction uses a parametric normal distribution which can be restrictive and may lead to biased result if the actual distribution is nonnormal. In this article, we overcome this parametric assumption by considering a broader class of random effects distribution for the centers. In particular, we develop a novel nested Dirichlet process (nDP) model to explore the sensitivity of the fixed treatment effects under various hypotheses, in the presence of nonnormality. Additional advantage of our proposed method is that it facilitates a hierarchical clustering structure. At one hand it clusters the centers according to their effects, and hence outlying centers can be identified. Simultaneously, subjects from the clustered centers are again clustered together enabling a borrowing of information across similar centers. Further, we present the methodology to test between the models with nDP versus a normal random center effects models. We discuss the results of our proposed methodology in a real example of a multi-center clinical trial on Scleroderma lung study. The results of the analysis along with the extensive simulation study show the advantage of our method when the center effects distribution is not normal.