scope_rl.utils.estimate_confidence_interval_by_t_test#
- scope_rl.utils.estimate_confidence_interval_by_t_test(samples, alpha=0.05, **kwargs)[source]#
Estimate the confidence interval by Student T-test.
Note
Student T-test assumes that \(X \sim p(X)\) follows a normal distribution. Based on this assumption, the \(1 - \alpha\) % confidence interval of \(\mu := \mathbb{E}[X]\) is derived as follows.
\[|\hat{\mu} - \mu| \leq \frac{T_{\mathrm{test}}(1 - \alpha, n-1)}{\sqrt{n} / \hat{\sigma}},\]where \(n\) is the data size, \(T_{\mathrm{test}}(\cdot,\cdot)\) is the T-value, and \(\sigma\) is the standard deviation, respectively.