Two influence diagnostic methods for the common mean model are proposed. First, an investigation of the influence of observations according to minor perturbations of the common mean model is made by adapting the local influence method which is based on the likelihood displacement. It is well known that the maximum likelihood estimates are in general sensitive to influential observations. Case-deletions can be a candidate for detecting influential observations. However, the maximum likelihood estimators are iteratively computed and therefore case-deletions involve an enormous amount of computations. An approximation by Newton`s method to the maximum likelihood estimator obtained after a single observation was deleted can reduce much of computational burden, which will be treated in this work. A numerical example is given for illustration and it shows that the proposed diagnostic methods can be useful tools.