Choose the reference distribution, significance level and tail direction. Get the exact cutoff, rejection rule and a visual tail map; degrees of freedom appear only when the distribution needs them.
Pick the distribution first. Only the degrees-of-freedom fields that matter for that distribution appear.
| α | Critical value(s) | Region |
|---|
This table keeps distribution, tail and df fixed while changing α so you can compare thresholds without changing the main setup.
Turn the selected critical value into an explicit decision rule and compare common alpha levels.
| Alpha | Critical value(s) | Decision region |
|---|
Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.
Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.
Use the interactive product above first. These notes add interpretation, verification and limits below the results and product controls.
A two-sided test splits alpha across both tails, while one-sided tests place the rejection probability in one direction. Choose the tail from the hypothesis before looking at the observed statistic rather than switching afterward to get a smaller threshold.
Student t, chi-square and F critical values depend on degrees of freedom. Confirm how df is derived for the specific test instead of entering sample size blindly, and remember that F uses separate numerator and denominator df.
For a fixed alpha and test specification, comparing a statistic with the critical boundary should agree with comparing its p-value with alpha. Use that equivalence as a cross-check when both are available.
A central 95% interval usually corresponds to alpha 0.05 split across two tails. One-sided procedures place the same alpha differently, so do not copy a two-sided critical value into a one-sided decision.
Crossing a critical value says the statistic falls in the chosen rejection region under the reference model. It does not tell you whether the estimated effect is large, useful or practically important.
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