© 2015 Lomonosov Moscow State University. Quantitative psychological research is focused on detecting the occurrence of certain population phenomena by analyzing data from a sample, and statistics is a particularly helpful mathematical tool that is used by researchers to evaluate hypotheses and make decisions to accept or reject such hypotheses. In this paper, the various statistical tools in psychological research are reviewed. The limitations of null hypothesis significance testing (NHST) and the advantages of using effect size and its respective confidence intervals are explained, as the latter two measurements can provide important information about the results of a study. These measurements also can facilitate data interpretation and easily detect trivial effects, enabling researchers to make decisions in a more clinically relevant fashion. Moreover, it is recommended to establish an appropriate sample size by calculating the optimum statistical power at the moment that the research is designed. Psychological journal editors are encouraged to follow APA recommendations strictly and ask authors of original research studies to report the effect size, its confidence intervals, statistical power and, when required, any measure of clinical significance. Additionally, we must account for the teaching of statistics at the graduate level. At that level, students do not receive sufficient information concerning the importance of using different types of effect sizes and their confidence intervals according to the different types of research designs; instead, most of the information is focused on the various tools of NHST.