Z statistic
Calculate left-tailed, right-tailed, or two-tailed p-values from a z statistic.
Free statistics calculator
P-Value Calculator: Find a P-Value From a Test Statistic
Use this p-value calculator to calculate p-values from z, t, chi-square, and F test statistics. Choose the correct test statistic, tail, degrees of freedom, and alpha level, then get a clear decision and interpretation for hypothesis testing homework.
- Z p-values Use normal-distribution p-values for z statistics.
- T p-values Use t distribution p-values with degrees of freedom.
- Chi-square p-values Use right-tail p-values for common chi-square tests.
- F p-values Use F distribution p-values for ANOVA and regression tests.
Calculate a P-Value
Select the statistic from your assignment, formula, calculator, or software output. The tail choice should match the alternative hypothesis or the test type requested by your instructor.
Use two-tailed for alternatives such as not equal.
Most chi-square tests use a right-tailed p-value.
Most ANOVA and regression F tests use a right-tailed p-value.
Results
Z p-value
Method
-
Statistic
-
Tail
-
Degrees of Freedom
-
P-Value
-
Alpha
-
Decision
-
Interpretation
-
The p-value depends on the test statistic, distribution, degrees of freedom, and alternative hypothesis. Match the method to your assignment instructions.
What This Calculator Supports
Use this page when you already have the test statistic from a formula, calculator, or software output and need the p-value and conclusion.
T statistic
Use a t statistic and degrees of freedom to calculate one-tailed or two-tailed p-values.
Chi-square statistic
Calculate p-values for chi-square goodness-of-fit and association tests.
F statistic
Calculate p-values for ANOVA, regression F tests, and variance-ratio style checks.
Which P-Value Method Should I Use?
The p-value method should match the distribution of the test statistic. This is why the same statistic value can lead to different p-values under different tests.
| Statistic | Common use | Typical tail |
|---|---|---|
| Z | Z-tests, normal approximations, and known population SD problems. | Left, right, or two-tailed depending on the alternative. |
| T | T-tests and confidence interval checks when SD is estimated from a sample. | Left, right, or two-tailed depending on the alternative. |
| Chi-square | Goodness-of-fit, independence, association, and variance tests. | Usually right-tailed. |
| F | ANOVA, regression F tests, and variance comparisons. | Usually right-tailed. |
How to Calculate a P-Value Step by Step
A p-value calculation starts with the test statistic and the correct sampling distribution. The calculator does the probability step, but your assignment still needs the setup and conclusion.
- Identify the test type: z, t, chi-square, or F.
- Enter the test statistic from your formula or software output.
- Add degrees of freedom for t, chi-square, and F tests.
- Choose left-tailed, right-tailed, or two-tailed based on the alternative hypothesis.
- Compare the p-value with alpha, usually 0.05 unless your assignment says otherwise.
- Write the decision and conclusion in the context of the question.
P-Value Examples
These examples show how students usually interpret calculator results after entering a test statistic.
| Example | Calculator setup | How to read it |
|---|---|---|
| Z test | z = 1.96, two-tailed, alpha = 0.05 | The p-value is about 0.05, so the result is right at the common significance cutoff. |
| T test | t = 2.10, df = 24, two-tailed, alpha = 0.05 | Use the t distribution because the standard deviation is estimated from sample data. |
| Chi-square test | chi-square = 10.5, df = 4, right-tailed | Most chi-square tests use the right tail because larger values give stronger evidence against the null. |
| ANOVA or regression F test | F = 4.25, numerator df = 3, denominator df = 28, right-tailed | Most F tests use the right tail because larger F statistics indicate stronger evidence. |
Common Mistakes to Avoid
- Using a two-tailed p-value when the alternative hypothesis is one-tailed.
- Using a z distribution when the assignment requires a t distribution with degrees of freedom.
- Reading chi-square or F tests as left-tailed tests when the course expects a right-tail p-value.
- Reporting only the p-value without stating the test statistic, degrees of freedom, alpha, and conclusion.
P-Value Calculator FAQs
What is a p-value?
A p-value is the probability, assuming the null hypothesis is true, of getting a test statistic at least as extreme as the observed result.
Should I use a one-tailed or two-tailed p-value?
Use the tail that matches the alternative hypothesis. Use two-tailed when the alternative says the parameter is different, right-tailed when it says greater, and left-tailed when it says less.
Why do chi-square and F tests usually use the right tail?
Chi-square and F test statistics are usually large when the evidence against the null is stronger, so common goodness-of-fit, association, ANOVA, and regression F tests use right-tail p-values.
Does a small p-value prove the alternative hypothesis?
No. A small p-value means the observed result would be unusual under the null hypothesis. The final conclusion should also consider assumptions, study design, effect size, and context.
Can I calculate a p-value from a test statistic?
Yes. Choose the matching distribution, enter the test statistic, select the correct tail, and add degrees of freedom when required. Z tests use z, t tests use t and df, chi-square tests use chi-square and df, and F tests use numerator and denominator df.
What does p-value less than 0.05 mean?
If alpha is 0.05, a p-value less than 0.05 usually means the result is statistically significant and you reject the null hypothesis. The conclusion should still be written in the context of the problem.
Need Help Explaining the P-Value?
A p-value is only part of a hypothesis test. Your assignment may also need the null and alternative hypotheses, test choice, assumptions, alpha decision, effect size, and a conclusion written in context.
Related Statistics Help
Use Calculators Responsibly
Use this calculator to check p-values, compare software output, and prepare tutoring questions. For graded work, follow your course rules and show the method required.