A Influência do tamanho da amostra na credibilidade de testes estatísticos não-paramétricos: uma abordagem com simulações de Monte Carlo

Abstract

Statistics is fundamental in various scientific research. It plays a vital role by enabling the understanding of potential patterns and relationships present in the data, allowing researchers to draw meaningful conclusions and base their findings on solid evidence. The correct application of statistics ensures that the collected information is transformed into reliable and useful knowledge. However, its success largely depends on a key factor: sample size. Thus, the aim of this research project is to investigate how sample size impacts the decision of two of the main non-parametric statistical tests: the likelihood ratio and Pearson's tests. To achieve this objective, the project applied the Monte Carlo method, which allowed for the evaluation of the rejection rates of both tests in different scenarios. The variation in sample size revealed that, as the sample size increases, rejection rates become more consistent, approaching the ideal value of 5%. This suggests that larger sample sizes result in more reliable tests. The research also compared the likelihood ratio and Pearson's tests, concluding that both are equivalent, as they have similar rejection rates. Therefore, either test can be chosen for future analyses, as both are equally effective. In summary, this project highlighted the importance of sample size in non-parametric tests. As sample size increases, the results obtained from these two tests can be considered more reliable, making them more robust for analysis. These conclusions have significant implications for research and informed decision-making in various fields.