This work analyses and discusses several statistical and econometric methodologies for estimation of the Average Treatment Effect (ATE) and its application to causality analysis through a case study with data from an educational policy. In a perfectly controlled and randomized experiment, there is homogeneity of individuals in the treated and non-treated groups. Therefore, the ATE can be estimated simply by the difference between the sample means of the two groups. However, such experiments do not happen very often and it is convenient to have statistical methodologies to relax the hypothesis of perfect randomness. If we assume that, despite the non-randomness of treatment, it is possible to explain its selection through a set of observed variables, we can consistently estimate the ATE through a linear regression of the result variable on the treatment variable and on the other observed explanatory variables. Under the same hypothesis, we can estimate the ATE from the estimation of the propensity score, which is a matching method based on the estimation of the individual probability of treatment selection. Finally, if there is no randomness and we cannot explain treatment selection, we can obtain a consistent estimation for the ATE through the method of Instrumental Variables. The only condition is that one of the observed variables is both correlated with treatment selection and uncorrelated with the linear regression error term. The methodologies were applied to data from an educational policy implemented in the United States in the 1980 s. Its goal was to quantify the effect of class size reduction in student learning. The results show a statistically significant positive effect. However, such effect is very small, which leads to a debate on the relevance and practical viability of such policy.