Test Statistic to P Value Calculator

Calculator

Example Data Table

Formula Used

The calculator first finds the cumulative probability, also called CDF. Then it converts that CDF into the selected tail probability.

• Z: Left p = Φ(z). Right p = 1 - Φ(z). Two sided p = 2 × min(Φ(z), 1 - Φ(z)).
• T: The t CDF is evaluated with the regularized incomplete beta function.
• Chi-square: CDF = P(k / 2, x / 2), using the regularized lower gamma function.
• F: CDF = I[(d1F) / (d1F + d2)](d1 / 2, d2 / 2).

For two tailed chi-square and F calculations, this page reports an equal tail style value. Always match the reported method to your course, paper, or software standard.

How to Use This Calculator

1. Select the distribution that matches your test statistic.
2. Enter the statistic from your hypothesis test.
3. Add degrees of freedom when the distribution needs them.
4. Choose left, right, or two tailed testing.
5. Enter your alpha level, such as 0.05.
6. Press the calculate button.
7. Read the p value, decision, and interpretation.
8. Use CSV or PDF export when you need a record.

Article

Understanding P Values

A p value translates a test statistic into probability language. It estimates how unusual the statistic is when the null hypothesis is assumed true. This calculator supports common mathematical tests. It accepts z, t, chi-square, and F statistics. It also supports left, right, and two sided alternatives.

Choosing the Distribution

Good p value work starts with the right distribution. A z statistic is used when the standard normal model applies. A t statistic uses degrees of freedom. It is common in mean testing and regression. A chi-square statistic is nonnegative. It is used for variance tests, goodness of fit, and independence checks. An F statistic compares scaled variances. It needs numerator and denominator degrees of freedom.

Choosing the Tail

The tail choice changes the final answer. A right tailed test measures probability beyond the statistic. A left tailed test measures probability below the statistic. A two tailed test doubles the smaller tail for symmetric tests. For chi-square and F tests, this page reports an equal tail style value. Always match the tail to your alternative hypothesis.

Reading the Decision

The alpha value gives a decision rule. Common alpha levels are 0.10, 0.05, and 0.01. If the p value is less than alpha, the result is statistically significant. That does not prove practical importance. It only suggests the observed statistic is rare under the null model.

Reporting the Result

This tool is designed for reports and study checks. It shows the cumulative probability, selected tail probability, alpha comparison, and clear decision text. It also gives export buttons for records. The CSV file is useful for spreadsheets. The PDF file is useful for sharing a compact result summary.

Best Practice

Use precise inputs when possible. Round only after the calculation. Check degrees of freedom before submitting. A small input error can change a borderline decision. If your course or software uses a different two sided rule for nonsymmetric distributions, state that rule in your report. Clear assumptions make p values easier to audit. They also help readers understand your statistical conclusion.

Final Note

The calculator is not a substitute for study design. It should support sound reasoning. Review sampling, independence, and model conditions first. Then use the computed value as one part of your final interpretation. Careful context keeps numerical decisions honest and useful always.

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