Objective  To explore the performance of hypothesis testing methods for two independent quantitative data hypothesis tests with extremely small samples.

Methods  Monte Carlo method was used to generate data with different mean difference, dis-tribution and sample size. T-test, Wilcoxon rank sum test and Bootstrap method were used to test the hypothesis, and the statistical efficiency was estimated in different scenarios.

Results  When the sample size was extremely small, the statistical efficiency of Wilcoxon rank sum test was very low. The Bootstrap confidence interval method was prone to make type II errors when the data were skew distributed. When the mean difference was large, the method still had high statistical efficiency. Whether the data followed normal distribution or not, when the sample size was extremely small, t-test performed better than Wilcoxon rank sum test.

Conclusion  According to the results of this simulation study, when the data follow the normal distribution, it is suggested to use t-test to analyze the extremely small samples. When the data does not follow the normal distribution, it is suggested to use the Bootstrap confidence interval method to analyze the extremely small samples.

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