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Specifically, I was about to use the two-sided $1-\alpha$ confidence interval of an estimate $\hat{\theta}$ to check whether this estimate lies within a predefined equivalence interval $(\theta_L,\theta_U … For which test statistics is the two-sided confidence interval not identical to the intersection of the one-sided confidence intervals (i.e. the TOST-CI)? …

Question: is it appropriate to use a two-sided confidence interval? … However, if you report a 95% two-sided confidence interval for $\Delta$, this will contain 0, because the two-sided p-value of the data is 0.08. …

For that, I wanted to compute a 95% confidence interval on these values. Question: The question is: in this case does it make more sense to compute the one-sided confidence interval or the two-sided? … Also, I realized that if I compute the two-sided confidence interval, the lower boundary is always 0, which means that that 2.5% fraction on the left is all 0s. Does this affect the decision? …

Say that I compute a two-sided confidence interval. … For example say I compute a confidence interval for a binomial proportion with significance level $\alpha$ as lower, upper = conf_interval(count=95, trials=100, significance=$\alpha$) If I only use the …

Suppose I have a hypothesis test for $H_0: est_{LCL} \le 0.4$ vs $H_1: est_{LCL} > 0.4$ where $est_{LCL}$ denotes the lower confidence limit for a two-sided $100(1-a)\%$ confidence interval for $est$ … For a two-sided $100(1-a)\%$ confidence interval, the $est_{LCL}$ can be calculated as $ est_{LCL} = est- z_{1-a/2}\sqrt{var(est)}$. …

I was wondering given a one-sided (one-tailed) hypothesis with an alpha-level of .05, can we be talking about 95% confidence intervals? … For example, can we construct separately "one-sided" and "two-sided" confidence intervals for a one-sided Z or t test? …

The task is to construct a symmetric, two-sided confidence interval for the parameter $\lambda$ with confidence level $1-\alpha$ with the help of $T_1$. How do I proceed here ? … Furthermore the symmetric confidence interval is always given by $I=[T_1^{-1}(F^{-1}(\frac{\alpha}{2})),T_1^{-1}(F^{-1}(1-\frac{\alpha}{2}))]$, where F is a knows distribution. …

I've seen examples to reject a null hypothesis, but don't understand how to use a one-sided confidence interval to show significance. … If you have two samples, x and y, how you would you use a one sided confidence interval to show $H_1:\mu_x > \mu_y$ is significant with 95%? …

Furthermore, if I take the one-sided confidence interval with $\alpha =0.05$ it has the same upper bound as the two-sided interval. … Edit: Found this answer Matching Confidence limits with One-Sided Hypothesis tests which explains it the other way around - why the two-sided interval should have been constructed with $\alpha=0.9$. …

Building on this question: Confidence interval and sample size multinomial probabilities In a binomial confidence interval, a 90% two-sided CI corresponds to a 95% one-sided CI. … or strictly less than the upper bound of that two-sided CI? …

However, for computing the 95% confidence interval, it seems to use a two-sided test. Is this mixing of tests legitimate, and, if so, why? … Wouldn't a one-sided confidence interval be more appropriate? …

The lower bound on a $1-\alpha$ two-sided confidence interval for the proportion of successes will of course be zero. … Note: In R, binom::binom.confint returns an upper bound such that $ (1 - UB)^n = \alpha/2 $ when a $1 - \alpha$ confidence level is specified. …

If you used a two-sided interval in situations where you observed non-zero counts and one-sided intervals when you observed all zero counts, your confidence intervals would no longer have their nominal … My question here is how would a Bayesian argue one way or the other for one- vs two-sided credible intervals for the same situation with all zero counts. …

$\beta_1 \lt k$, the confidence interval for $\beta_1$ is unbounded on one side: $[a,+\infty)$ rather than $[a,b]$ (or bounded by the limit of the sample space on one side, like $[a,1]$ with a binary outcome … What does that region look like if you have a one-sided confidence interval for the nulls $\beta_1 \ge k$ and $\beta_2 \le m$? How does that change if only one of the two hypotheses is one-sided? …

Assessing non-inferiority I would only look at the lower CI, thus, my two-sided 90% CI would correspond to a one-sided 95% (and alpha=5%). My question is: 1) is this correctly understood? … My initial though is something like: "A two-sided 90% CI, alpha=0.10, corresponding to a one-sided 95%CI, alpha=0.05). Thanks for your time. …