Calculator
Example Data Table
| Case | Test | Statistic | df1 | df2 | Tail | Alpha | Expected Meaning |
|---|---|---|---|---|---|---|---|
| Mean test | Z | 1.96 | N/A | N/A | Two tailed | 0.05 | Near common five percent cutoff |
| Small sample mean | T | 2.228 | 10 | N/A | Two tailed | 0.05 | Uses sample degrees of freedom |
| Variance check | Chi Square | 18.307 | 10 | N/A | Right tailed | 0.05 | Checks high variance evidence |
| Variance ratio | F | 3.14 | 3 | 20 | Right tailed | 0.05 | Compares model or variance ratios |
Formula Used
Left tailed test: p = CDF(x)
Right tailed test: p = 1 - CDF(x)
Two tailed test: p = 2 × min(CDF(x), 1 - CDF(x))
Z test: CDF comes from the standard normal distribution.
T test: CDF comes from Student's t distribution.
Chi square test: CDF comes from the chi square distribution.
F test: CDF comes from the F distribution.
Decision rule: reject H0 when p ≤ alpha.
How to Use This Calculator
- Select the test distribution that matches your statistic.
- Choose left, right, or two tailed testing.
- Enter the observed test statistic.
- Enter alpha, such as 0.05 or 0.01.
- Enter degrees of freedom when required.
- Add hypothesis notes for your report.
- Press the calculate button.
- Download the result as CSV or PDF.
Article
About This P Value Calculator
A p value helps you judge evidence against a null hypothesis. It shows how unusual your test statistic is, assuming the null claim is true. This calculator supports common hypothesis tests. You can use a z test, t test, chi square test, or F test. Each option uses the selected tail rule. It then compares the p value with your alpha level.
Why P Values Matter
The tool is useful for class work, reports, audits, and quick research checks. It does not replace study design. It also does not decide whether a study is useful. It only measures statistical evidence under a chosen model. Good conclusions still need clean data, valid assumptions, and practical judgment.
Choosing Tails and Distributions
Tail choice matters. A right tailed test checks whether a statistic is unusually high. A left tailed test checks whether it is unusually low. A two tailed test checks both directions. Use the two tailed option when the alternative says “different.” Use one tail only when the direction was planned before analysis.
Distribution choice also matters. Use a z test for standard normal statistics. Use a t test when the statistic follows Student's t distribution. Enter degrees of freedom for t results. Use a chi square test for variance tests and goodness of fit work. Use an F test for variance ratios and many model comparisons. Enter numerator and denominator degrees of freedom for F tests.
Reading the Decision
The decision rule is simple. If the p value is less than or equal to alpha, reject the null hypothesis. If it is greater than alpha, do not reject it. This wording is important. A large p value does not prove the null hypothesis. It only says the sample did not give enough evidence against it.
Reporting the Result
Always report the test type, statistic, degrees of freedom, tail, alpha, and p value. Add context in plain language. For example, say whether the observed effect is meaningful in the real problem. The download buttons help save the calculation. Use the CSV file for spreadsheets. Use the PDF file for a printable summary. Keep the output with your notes, dataset, and assumptions. Check assumptions before trusting the result. Outliers, dependence, rounding, and small samples can distort evidence. When needed, ask a statistician to review the analysis carefully.
FAQs
What is a p value?
A p value measures how unusual your result is when the null hypothesis is assumed true. Smaller values give stronger evidence against the null hypothesis.
When should I use a two tailed test?
Use a two tailed test when your alternative hypothesis checks for any difference. It considers unusually low and unusually high results.
When should I use a right tailed test?
Use a right tailed test when your planned alternative expects the statistic to be unusually high. The p value equals one minus the CDF.
When should I use a left tailed test?
Use a left tailed test when your planned alternative expects the statistic to be unusually low. The p value equals the CDF.
What alpha level should I enter?
Common alpha levels are 0.05, 0.01, and 0.10. Choose alpha before testing. Do not change it after seeing results.
Does a small p value prove the alternative hypothesis?
No. A small p value gives evidence against the null hypothesis. It does not prove the alternative or confirm practical importance.
Why do some tests need degrees of freedom?
Degrees of freedom define the distribution shape. T, chi square, and F tests need them to calculate accurate probabilities.
Can I export the result?
Yes. After calculation, use the CSV button for spreadsheet work. Use the PDF button for a printable report summary.