Critical Value Calculator
Calculate critical value using your data.
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What this tool does
Calculate critical value using your data. Compare your test statistic with the critical value: statistics beyond it (larger in absolute value for two-sided z/t, larger for right-tail χ²/F) reject the null hypothesis at the chosen α.
How to use the Critical Value Calculator
- Enter or select distribution.
- Enter or select significance level (α).
- Enter or select degrees of freedom (t / χ² df, or f numerator df).
- Enter or select f denominator df (f only).
- Read the calculated result; change any measurement to compare alternatives.
Formula
critical values invert the distribution tails used in statistics.ts: z by Acklam's inverse normal, t and χ² and F by bisection on the beta/gamma tail functions
- dist
- Distribution
- alpha
- Significance level (α)
- df1
- Degrees of freedom (t / χ² df, or F numerator df)
- df2
- F denominator df (F only)
Compare your test statistic with the critical value: statistics beyond it (larger in absolute value for two-sided z/t, larger for right-tail χ²/F) reject the null hypothesis at the chosen α.
Worked example
For critical value calculator, the following measurements illustrate the exact method: Distribution: z; Significance level (α): 0.05; Degrees of freedom (t / χ² df, or F numerator df): 10; F denominator df (F only): 20.
Inputs
- DistributionStandard normal (z) — two-sided
- Significance level (α)5%
- Degrees of freedom (t / χ² df, or F numerator df)10
- F denominator df (F only)20
Result
- Critical value1.96
- Significance level (α)0.05
Results explained
- Critical value
- Critical value from the formula above. Compare your test statistic with the critical value: statistics beyond it (larger in absolute value for two-sided z/t, larger for right-tail χ²/F) reject the null hypothesis at the chosen α.
- Significance level (α)
- Significance level (α) from the formula above. Compare your test statistic with the critical value: statistics beyond it (larger in absolute value for two-sided z/t, larger for right-tail χ²/F) reject the null hypothesis at the chosen α.
Frequently asked questions
critical values invert the distribution tails used in statistics.ts: z by Acklam's inverse normal, t and χ² and F by bisection on the beta/gamma tail functions
Compare your test statistic with the critical value: statistics beyond it (larger in absolute value for two-sided z/t, larger for right-tail χ²/F) reject the null hypothesis at the chosen α.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.