The 90% confidence interval calculator takes sample mean (x̅), sample size (n), standard deviation (s) and or z-score (z) and returns or right tailed p value, margin of error (e) and confidence level. It is built for quick answers, for checking somebody else’s arithmetic, and for the moments when a formula book is not within reach.
What Is the 90% Confidence Interval Calculator?
The 90% confidence interval calculator turns a set of measurements into or right tailed p value, margin of error (e) and confidence level, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the 90% Confidence Interval Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with sample mean (x̅) set to 10, sample size (n) set to 5, standard deviation (s) set to 2, the calculator returns confidence level of 1, and standard error of 0.89443, and margin of error (e) of 89.442719. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out or right tailed p value?
Enter sample mean (x̅), sample size (n), standard deviation (s) and or z-score (z). The calculator then works through the relationship and reports or right tailed p value, margin of error (e) and confidence level.
What does the 90% confidence interval actually calculate?
It takes sample mean (x̅), sample size (n), standard deviation (s) and or z-score (z) and converts them into or right tailed p value, margin of error (e) and confidence level using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter sample mean (x̅)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.