Can a p-value be negative?

No. P-values are probabilities computed under the null hypothesis and therefore fall between 0 and 1.

What does a low p-value mean?

A small p-value indicates that the sample statistic would be very unlikely if the null hypothesis were true, giving evidence in favor of the alternative.

How do I find p-value from z-score?

Use the standard normal cumulative distribution Φ to evaluate one or both tails: left-tailed p = Φ(z), right-tailed p = 1 − Φ(z), two-tailed p = 2 · Φ(−|z|).

Interactive Visual Practice Ready

Interactive P-value Calculator & Playground

Compute one-sided or two-sided p-values for z, t, chi-square, and F statistics, visualize shaded tails, and challenge yourself with random hypothesis-testing scenarios. Learn, calculate, and play on a single screen.

Built with references from Casella & Berger, Montgomery & Runger, and NIST's Engineering Statistics Handbook.

Why this playground?

1.Unified calculator for the four most common hypothesis-test distributions.
2.Auto-generated examples that reinforce the definition of “extreme under H₀”.
3.Dynamic chart shading to see the exact tail probability area.

P-value Calculator

Enter your test statistic, choose the matching distribution and tail type, and instantly read the p-value and decision at any significance level.

Distribution

Test Statistic

Tail

Significance level α

Degrees of freedom ν (for t) / numerator df (for F)

Denominator df (for F)

Tip

For χ² and F tests the calculator supports left- and two-tailed options, but remember most textbook tests using these statistics are right-tailed.

Practice: Generate a scenario & predict the decision

Each round generates a fresh test statistic, tail, and α. Decide whether you would reject H₀ before revealing the p-value.

Score

0/0

Scenario

Click “New scenario” to begin.

Outcome

Your decision will appear here.

What is a p-value?

A p-value is the probability that a test statistic would be at least as extreme as the observed value assuming the null hypothesis is true. Small p-values indicate that the observed statistic is unlikely under H₀, offering evidence for the alternative hypothesis.

Left-tailed tests measure Pr(S ≤ x | H₀).
Right-tailed tests measure Pr(S ≥ x | H₀).
Two-tailed tests double the probability in the more extreme tail.

How to interpret

Specify α < 0.05, 0.01, or any level before looking at results.
Calculate the p-value under H₀.
If p ≤ α, reject H₀; if p > α, fail to reject H₀.
Remember: a high p-value does not prove H₀ is true.

Source: Casella & Berger (2002); Montgomery & Runger (2014).

Distribution reference

Quick reminders for when to use each curve in the calculator.

Standard Normal (Z)

Large-sample mean tests or whenever σ is known. Symmetric about zero.

Student's t

Unknown σ with moderate sample size. Heavier tails managed by ν degrees of freedom.

Chi-square

Variance tests, goodness-of-fit, independence tests. Right-skewed.

Snedecor's F

ANOVA, regression significance, comparing two variances.

FAQ

Can the p-value be greater than 1 or negative?

No. P-values are probabilities, so they fall between 0 and 1. If you get a negative or >1 value it indicates an issue with the test statistic or calculation.

Does p < 0.05 always mean "significant"?

0.05 is a convention, not a law of nature. Always set α based on context, report the exact p-value, and combine statistics with domain expertise.

What about multiple comparisons?

When testing many hypotheses simultaneously, adjust α or apply corrections (Bonferroni, Holm, FDR). Link to our Bonferroni calculator coming soon.

Related Calculators

Confidence Interval Builder Two-sample t-Test Chi-square Goodness-of-Fit One-way ANOVA