ClarityHow to use this tool
- Enter reference distribution, test statistic, degrees of freedom (t only), alternative hypothesis, significance level.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Reference distribution | Choose Student t / Standard normal (z). | Student t |
| Test statistic | Numeric value. | 2 |
| Degrees of freedom (t only) | Numeric value. Minimum: 1. Maximum: 100000. | 20 |
| Alternative hypothesis | Choose Two-sided: different / One-sided: greater / One-sided: less. | Two-sided: different |
| Significance level | Numeric value. Minimum: 0.0001. Maximum: 0.2. | 0.05 |
Result for these sample inputs
0.0592655354 probability
- Test statistic
- 2
- Degrees of freedom
- 20
- Decision at chosen alpha
- Do not reject the null hypothesis
The p-value is not the probability that the null hypothesis is true. Choose the hypothesis and significance level before inspecting the result; statistical significance does not measure practical importance.
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
Use the selected reference distribution to find the probability in the tail specified by the alternative. Two-sided probability doubles the tail beyond the absolute statistic.
Using reference distribution = t, test statistic = 2, degrees of freedom (t only) = 20, alternative hypothesis = two, significance level = 0.05, the result is 0.0592655354 probability. Change these example inputs to match your task; use the method above to check each step.
What to keep in mind
The entered statistic must already be standardized under the null model. This tool does not validate the study design. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.
Reference: NIST: statistical methods handbook
Common questions
Should I choose a one-sided or two-sided test?
Use two-sided when departures in either direction matter. Use a one-sided alternative only if its direction was chosen before seeing the data. Switching tails after inspecting a result changes the test.
Where do I get the test statistic?
A z or t statistic comes from a specified statistical test, not from a raw observation. Use the linked one-sample, paired or independent-sample test when you have observations rather than a standardized statistic.
Methodology maintained by ClarityKit. How these tools are built and checked.