Calculator
Formula Used
The p value is the probability area under the selected reference distribution.
- Left tailed test: p = P(X ≤ test statistic)
- Right tailed test: p = P(X ≥ test statistic)
- Two tailed z or t test: p = 2 × min(left area, right area)
- t distribution: uses the given degrees of freedom.
- Chi square distribution: CDF uses df / 2 and statistic / 2.
- F distribution: CDF uses df1, df2, and F statistic.
How to Use This Calculator
- Select the test distribution.
- Choose left tailed, right tailed, or two tailed.
- Enter the test statistic from your hypothesis test.
- Enter degrees of freedom when needed.
- Enter the alpha level for the decision rule.
- Press the submit button to view the p value.
- Use CSV or PDF to save the result.
Example Data Table
| Distribution | Statistic | df1 | df2 | Tail | Alpha | Expected Use |
|---|---|---|---|---|---|---|
| z | 1.96 | Not needed | Not needed | Two tailed | 0.05 | Large sample mean test |
| t | 2.228 | 10 | Not needed | Right tailed | 0.05 | Small sample mean test |
| Chi square | 18.31 | 10 | Not needed | Right tailed | 0.05 | Variance or goodness fit |
| F | 3.49 | 4 | 20 | Right tailed | 0.05 | ANOVA or variance ratio |
About P Values From Test Statistics
Purpose of the Calculator
A p value from a test statistic calculator helps turn a computed statistic into a probability. That probability shows how unusual the observed result is when the null hypothesis is assumed true. This page supports z, t, chi square, and F distributions. It also supports left tailed, right tailed, and two tailed tests.
Why the Tail Choice Matters
Statistical tests often end with one number, such as z, t, X squared, or F. That number alone is not always easy to interpret. The p value gives the probability area in the chosen tail. A small p value means the result is less consistent with the null model. It does not prove the alternative hypothesis. It only measures evidence against the null assumption.
Tail selection matters. A left tailed test measures probability below the statistic. A right tailed test measures probability above it. A two tailed z or t test doubles the smaller tail area. For chi square and F tests, two sided results use a central tail method. Many courses prefer one sided values for these skewed distributions.
Degrees of Freedom
Degrees of freedom also matter. The t distribution needs one degree of freedom value. Chi square also needs one. The F distribution needs numerator and denominator degrees of freedom. Larger degrees of freedom usually make the curve behave more predictably.
Decision With Alpha
Use the alpha level to decide statistical significance. Common choices are 0.10, 0.05, and 0.01. If the p value is less than or equal to alpha, reject the null hypothesis. If it is larger, do not reject it. This wording is important. A large p value does not prove the null hypothesis.
Export and Review
The calculator also creates useful export records. The CSV file is helpful for spreadsheets. The PDF report is useful for assignments and documentation. Always keep the original statistic, distribution, tail, and degrees of freedom with the p value. These inputs explain how the probability was produced.
This calculator is designed for learning and quick checking. It should not replace study design, assumption checks, or expert review. Check independence, sample size, normality, and variance assumptions before making strong decisions. Good interpretation needs both math and context.
Report rounding should stay consistent, especially when results are near alpha or used across repeated class examples.
FAQs
What is a p value?
A p value is a probability. It shows how likely a result as extreme as your statistic is, assuming the null hypothesis is true.
Which distributions are supported?
The calculator supports z, t, chi square, and F distributions. These cover many common tests in introductory and advanced statistics work.
When should I use a two tailed test?
Use a two tailed test when the alternative hypothesis allows change in either direction. It checks both unusually low and unusually high results.
Do I need degrees of freedom?
You need degrees of freedom for t, chi square, and F tests. A z test does not require degrees of freedom.
What does alpha mean?
Alpha is the chosen significance level. Common values are 0.05, 0.01, and 0.10. It sets the rejection rule.
Can a p value prove the null hypothesis?
No. A large p value only means the result is not strong enough to reject the null hypothesis under the selected model.
Why are chi square and F tests different?
They are skewed and nonnegative distributions. Many practical chi square and F tests use right tailed p values rather than symmetric two tailed logic.
Can I export the calculation?
Yes. After calculating, use the CSV button for spreadsheet records or the PDF button for a simple printable report.