Critical Value Calculator
Choose a distribution (standard normal or Student's t), specify alpha and tail type, and obtain critical values.
Critical value(s)
-1.9600 , +1.9600
Two-tailed test rejects H₀ when statistic < -1.9600 or > 1.9600
How to Use This Calculator
- Select the appropriate distribution for your test statistic.
- Specify one-tailed or two-tailed test setup.
- Enter the desired significance level α (e.g., 0.05).
- For t-distribution critical values, provide degrees of freedom.
Formula
Zcrit = Φ−1(1 − α) for one tail, Φ−1(1 − α/2) for two tails
tcrit = F−1t,ν(1 − α) where ν = degrees of freedom
Φ−1 is the inverse standard normal CDF. F−1t,ν is the inverse Student's t CDF with ν degrees of freedom.
Full Description
Critical values define rejection regions in hypothesis testing. For a given α and tail selection, they represent thresholds beyond which the null hypothesis is rejected. This calculator supports z (normal) and t distributions commonly used in parametric tests.
Frequently Asked Questions
When should I use t instead of z?
Use t when population standard deviation is unknown and sample size is small (typically n < 30), assuming roughly normal data.
Can I compute left-tailed critical values?
For left-tailed tests, negate the reported one-tailed critical value.
What if α is greater than 0.5?
Significance levels should lie between 0 and 1, typically ≤ 0.10. The calculator enforces this range.
Is the approximation accurate for very small df?
Yes, the series expansion provides good accuracy for df ≥ 1. Extremely small df may require exact tables for critical decisions.