We consider the estimation of the intra-cluster correlation for the one-way random effects model in the case of balanced and unbalanced cluster sizes. It is well-known that the standard variance component methods, such as the ANOVA method, can produce zero and negative estimates of the intra-cluster correlation, which is inherently a strictly positive parameter. In this paper, we present an adjusted maximum likelihood estimator for the intra-cluster correlation coefficient and compare the proposed estimator with the commonly used ANOVA estimator using a Monte Carlo simulation for normal and beta-binomial distributed variables.