In this study, parameters of the one-way analysis of variance (ANOVA) model based on the type II censored samples are estimated when the distribution of the error terms is Jones and Faddy's skew t. In the estimation procedure, maximum likelihood (ML) methodology is used. Solutions of the likelihood equations are obtained using an iterative method because of the nonlinear terms existing in the likelihood equations. A modified version of the ML methodology is also used. It gives the explicit estimators of the model parameters and has no computational difficulties. A new test statistic is proposed for testing the equality of the treatment effects. An extensive Monte Carlo simulation study is carried out to compare the powers of the test statistics based on the ML and the modified ML estimators of the parameters. Real data are analyzed at the end of the study to illustrate the implementation of the proposed methodologies.