While running any experiment, we often have to consider the statistical power to ensure an effective study. Statistical power or power ensures that we can observe an effect with high probability if such a true effect exists. However, several studies lack the appropriate planning for determining the optimal sample size to ensure adequate power. Thus, careful planning ensures that the power remains high even under high measurement errors while keeping the type 1 error constrained. We study the impact of differential privacy on experiments and theoretically analyze the change in sample size required due to the Gaussian mechanisms. Further, we provide an empirical method to improve the accuracy of private statistics with simple bootstrapping.

翻译：在进行任何实验时，我们通常需要考虑统计功效以确保研究的有效性。统计功效确保在真实效应存在时能以高概率观测到该效应。然而，许多研究缺乏适当规划以确定能够保证充足功效的最优样本量。因此，精心规划能确保即使在测量误差较高的情况下功效仍保持高水平，同时将第一类错误控制在约束范围内。本研究探讨了差分隐私对实验的影响，并从理论上分析了因高斯机制导致的样本量变化。此外，我们提出了一种经验方法，通过简单的自助法提高私有统计量的准确性。