Critical Value
Definition
The value from a reference distribution (z or t) that cuts off the desired tail probability. For a 95% two-sided interval using the normal distribution, the critical value is 1.96.
- Source
- Reference distribution, z or t
- Function
- Cuts off desired tail probability
- 95% two-sided normal example
- 1.96
Common questions
Why is 1.96 specifically the critical value for a 95% two-sided confidence interval?+
Under the standard normal distribution, 1.96 standard deviations from the mean leaves 2.5% of probability in each tail, totalling 5%, which matches the 95% coverage the interval is built to achieve.
When would a t-distribution critical value be used instead of a z critical value?+
The t-distribution is used when the population standard deviation is unknown and estimated from a small sample, since it has heavier tails than the normal distribution and its critical value depends on the sample's degrees of freedom.
Related terms
- Bayesian Credible Interval
- An interval computed from the posterior distribution of a parameter, given a prior and the observed data. Unlike a confidence interval, a...
- Confidence Interval (CI)
- A range computed from sample data using a procedure that, over many repetitions, would contain the true population parameter a stated percentage...
- Coverage Probability
- The true long-run proportion of intervals, from repeated sampling, that contain the parameter. If a procedure has 95% nominal coverage and its...
- Margin of Error
- Half the width of a symmetric confidence interval, equal to the critical value multiplied by the standard error. Commonly reported in survey...
- Standard Error (SE)
- The standard deviation of the sampling distribution of an estimator. For the sample mean, SE equals the population standard deviation divided by...