P-Value Calculator

Turn a test statistic into a p-value. Choose z, t, chi-square or F, enter the statistic (and degrees of freedom), pick left, right or two-tailed, and see the shaded tail area and whether the result is significant at your α.

p-value
0.0357
At α = 0.05
Significant

p = 0.0357 is less than α = 0.05, so reject the null hypothesis: a result this extreme would be rare if H₀ were true.

2.1−2.1

The yellow area is the p-value: the probability of a test statistic at least this extreme if the null hypothesis were true.

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

One tail or two? Watch the cut-off move

A significance level α is a budget of “surprise” area. A two-tailed test splits it between both ends, so each tail gets α/2 and the cut-off moves further out. Slide the test statistic and see when it lands in the rejection region.

z = 1.80

Critical value: ±1.960 → not extreme enough: fail to reject H₀

Notice z = 1.80 is significant right-tailed at α = 0.05 (cut-off 1.645) but not two-tailed (cut-off 1.960). Choose the tail from your hypothesis before looking at the data.

What a p-value means

The p-value is the probability of getting a test statistic at least as extreme as yours if the null hypothesis were true. A small p-value means your data would be surprising under H₀, which counts as evidence against it. It is not the probability that H₀ is true, and it says nothing about how large or important the effect is. The American Statistical Association’s 2016 statement on p-values makes exactly these points.

Choosing the tail

Use a two-tailed test when the alternative is “different from” (≠). Use a one-tailed test only when the alternative is directional (> or <) and was decided before seeing the data. Chi-square and F tests are almost always right-tailed, because large statistics indicate a poor fit or big differences.

Frequently asked questions

Is p = 0.05 significant?

By the usual convention, a result is significant when p < α. At exactly 0.05 with α = 0.05 it is borderline; report the exact p-value rather than just “significant”.

How do I get the degrees of freedom?

One-sample or paired t: n − 1. Two-sample pooled t: n₁ + n₂ − 2 (Welch’s test uses a formula; the t-test calculator computes it). Chi-square goodness of fit: categories − 1; independence: (rows − 1)(columns − 1).

Why is my two-tailed p-value double the one-tailed?

Because a two-tailed test counts extreme results in both directions, and the t and z curves are symmetric.