Title: Confidence Interval Calculator - calculates a one-sample or two-sample (difference of means) CI
Headings: Confidence Interval Calculator
Confidence Interval Calculator
Confidence interval
Standard deviation
Sample mean
Confidence level
Quick navigation:
Using the confidence interval calculator
What is a confidence interval and "confidence level"
Confidence interval formula
CIbounds = X ± SE
Common critical values Z
How to interpret a confidence interval
Logically, we can infer one of three things:
Common misinterpretations of confidence intervals
Probability statements about specific intervals
A 95% confidence predicts where 95% of estimates from future studies will fall
An interval containing the null is less precise than one excluding it
One-sided vs. two-sided intervals
Confidence intervals for relative difference
References
Cite this calculator & page

Content: E.g. for a 95% one-sided interval use the critical value for a 90% two-sided interval above: 1.6449. How to interpret a confidence interval
Confidence intervals are useful in visualizing the full range of effect sizes compatible with the data. Basically, any value outside of the interval is rejected: a null with that value would be rejected by a NHST with a significance threshold equal to the interval confidence level (the p-value statistic will be in the rejection region). Conversely, any value inside the interval cannot be rejected, thus when the null hypothesis of interest is covered by the interval it cannot be rejected. The latter, of course, assumes that there is a way to calculate exact interval bounds - many types of confidence intervals achieve their nominal coverage only approximately, that is their coverage is not guaranteed, but approximate. This is especially true in complicated scenarios, not covered in this confidence interval calculator. The above essentially means that the values outside the interval are the ones we can make inferences about. For the values within the interval we can only say that they cannot be rejected given the data at hand.