Critical Value Calculator
Calculate critical values for various statistical distributions.
Enter Your Parameters
Table of Contents
What is a Critical Value?
A critical value is a point on the distribution of a test statistic that marks the boundary of the rejection region for a hypothesis test. It helps determine whether to reject or fail to reject the null hypothesis.
- Critical values depend on the significance level (α)
- They vary by distribution type
- They help make decisions in hypothesis testing
- They are used to determine confidence intervals
Statistical Distributions
This calculator supports four common statistical distributions:
t-distribution
Used for small sample sizes or when population standard deviation is unknown.
z-distribution
Used for large sample sizes with known population standard deviation.
Chi-square
Used for testing variance and goodness of fit.
F-distribution
Used for comparing variances and ANOVA.
How to Use Critical Values
-
1Choose the distribution type
Select the appropriate distribution based on your statistical test.
-
2Set the confidence level
Enter your desired confidence level (e.g., 95 for 95%).
-
3Enter degrees of freedom
Provide the appropriate degrees of freedom for your test.
-
4Calculate and interpret
Use the critical value to make decisions in your hypothesis test.
Examples
Example 1 t-test
For a two-tailed t-test with 95% confidence and 10 degrees of freedom:
Critical Value ≈ ±2.228
This means we reject the null hypothesis if |t| > 2.228
Example 2 Chi-square test
For a chi-square test with 95% confidence and 5 degrees of freedom:
Critical Value ≈ 11.070
We reject the null hypothesis if χ² > 11.070
Example 3 F-test
For an F-test with 95% confidence, 5 and 10 degrees of freedom:
Critical Value ≈ 3.326
We reject the null hypothesis if F > 3.326