Critical Value Calculation Results
| Critical Value | ||
| Critical Region (Right-Sided) | ||
| Critical Values (Two-tailed) | ||
| Critical Regions (Two-tailed) |
Created by CalculatorOK Team · Last updated: Jan 7, 2025
Critical Value Calculator
What a critical value tells you
Every hypothesis test draws a line in the sand, and the critical value draws it for you. It is the cutoff your test statistic must cross before the data count as too unusual to blame on chance. Statisticians, students, and A/B testers all rely on it to decide when a result is significant rather than random noise.
The cutoff shifts with the distribution your statistic follows. A z statistic uses the standard normal curve, while t, chi-square, and F statistics each use their own tables whose shape is set by the degrees of freedom you supply.
How the cutoff is computed
The calculator finds the point where the tail area of your chosen distribution equals the significance level. For a two-tailed z test at alpha 0.05, each tail holds 0.025 and the cutoff sits at 1.96 on either side. For a t distribution with 24 degrees of freedom at the same level, the two-tailed cutoff rises to about 2.064 because heavier tails demand stronger evidence.
Test type matters too. A one-tailed test at 0.05 needs only 1.645 for z, while the two-tailed version of the same test needs 1.96.
Using the calculator step by step
Start by typing your Significance level, usually 0.05. Next, under The statistic is, pick T-distributed, Z-distributed, Chi-square distributed, or F-distributed. Then enter the Degrees of freedom, or the Numerator degrees of freedom and Denominator degrees of freedom when an F test is selected.
Choose the Type of test, one-tailed or two-tailed, and press Calculate Critical Value. The tool returns the cutoff for your exact setup. Compare it with your test statistic: if the statistic lands further into the tail, you reject the null hypothesis and may report the finding as significant.
Frequently Asked Questions
What is the z critical value for alpha 0.05?
For a two-tailed test at the 0.05 significance level, the z critical value is 1.96, meaning 2.5 percent of the standard normal curve sits in each tail. A one-tailed 0.05 test uses 1.645 instead.
How do degrees of freedom change the cutoff?
They pick the member of the t, chi-square, or F family, and heavier tails push cutoffs up. With 10 degrees of freedom, a two-tailed t test at 0.05 uses about 2.23, comfortably above 1.96.
One-tailed versus two-tailed: which cutoff applies?
A one-tailed test places the whole alpha in one tail, so z at 0.05 gives 1.645, while a two-tailed test splits it and gives 1.96. Match the cutoff to the hypothesis you actually wrote before collecting data.
Which distribution should my test statistic use?
Use the z distribution for known population variance or large samples, t for small samples with estimated variance, chi-square for variance or goodness-of-fit questions, and F for comparing two variances or ANOVA designs.
When do I reject the null hypothesis?
Reject when your statistic falls beyond the critical value in the tail your test type specifies. A z of 2.2 against a two-tailed 1.96 cutoff is significant evidence against the null.