Critical Value Calculator
Find common two-tailed z critical values from a confidence level.
What Is a Critical Value?
A critical value marks a boundary in a reference distribution. For common two-tailed normal confidence intervals, widely used z critical values are 1.645 for 90%, 1.960 for 95%, and 2.576 for 99%.
What a Critical Value Represents
A critical value marks the boundary of a rejection region for a statistical test. Its size depends on the selected significance level and whether the test is one-tailed or two-tailed.
Critical Value Example
For a common two-tailed z-test at the 5% significance level, the critical values are approximately -1.96 and +1.96.
Using Critical Values
Compare the observed test statistic with the critical boundary. Crossing that boundary indicates that the result falls in the rejection region for the chosen significance level.
Frequently Asked Questions
Does a smaller alpha create a larger critical value?
Usually yes, because stronger evidence is required.
Are one-tailed and two-tailed values different?
Yes.
Is a critical value the same as a p-value?
No. They are two different ways to make the same testing decision.
Methodology, Assumptions and Interpretation
A critical z value is a standard-normal quantile determined by confidence level and whether the test is one- or two-tailed. For a two-sided 95% interval the familiar value is about 1.96; changing tail allocation changes the cutoff.