P-Value Table

How to read a p-value from a table

• Compute your test statistic first, then find its degrees of freedom. A printed table lists critical values for a few significance levels, so it can only bracket the p-value. For t = 2.31 with df = 24, the two-tailed critical values are 2.064 at 0.05 and 2.492 at 0.02. Your t sits between them, so the p-value lies between 0.02 and 0.05.
• The calculator above removes the bracket and gives the exact value, 0.0298 for that example. Use the quick tables on this page when you only need a rough answer: |z| = 1.96 gives a two-tailed p of 0.0500 and |z| = 2.58 gives 0.0099. For the critical values themselves, see the full z table, t table, chi-square table and F distribution table linked below.

One-tailed versus two-tailed p-values

A two-tailed p-value counts extreme results in both directions, so for a symmetric distribution such as z or t it is twice the smaller tail. For t = 2.31 with df = 24 the right tail is 0.0149 and the two-tailed value is 0.0298. Use a one-tailed p-value only when you named a single direction before collecting data, and say so in the report. In the usual chi-square and F tests (goodness of fit, independence, ANOVA), only a large statistic counts against the null hypothesis, so the right tail is the p-value and this page shows no two-tailed value. Two-sided tests of a variance are a separate case that this calculator does not cover. To compare a p-value with your significance level α, reject the null hypothesis when p is smaller than α, for example p = 0.0298 is below α = 0.05 but not below α = 0.01.

Very small p-values

Software often prints a tiny p-value as 0.000, which is not a probability of zero. Write it as p < .001 in a paper, as the APA guide says. A table that prints four decimals may show < 0.0001 instead, which is a display choice, not an APA rule. The calculator shows both the plain form and scientific notation. For example z = 5 has a two-tailed p-value of 5.733 × 10⁻7. Values this small are accurate here, but they depend on the model assumptions being true far into the tail, so treat them as "very small" and not as a literal chance.

How to report a p-value in APA 7

• The APA Style Numbers and Statistics Guide says to report exact p-values to two or three decimals, to write p < .001 when p is smaller than that, and to leave out the zero before the decimal point because p cannot exceed 1. It also asks for italic letters for statistical symbols, upright Greek letters, and a space on both sides of =, < and >.
• Independent-samples t test: t(24) = 2.31, p = .030
• One-way ANOVA: F(3, 20) = 4.12, p = .020
• Chi-square test: χ²(5, N = 120) = 13.20, p = .022. Chi-square results usually also give the sample size, and N = 120 here is an example value.
• Pearson correlation: r(10) = .65, p = .022. The test of r assumes the two variables are roughly bivariate normal.
• Putting the degrees of freedom in brackets after the symbol is the usual layout in published results, and the calculator uses it. Your journal or department may ask for something different, so check its guidelines.

Significance stars are a convention

Many tables mark p < .05 with one star, p < .01 with two and p < .001 with three. This is a convention that varies by journal and field, not a standard. Some fields add a dagger for p < .10, and many journals prefer exact p-values to stars. If you use stars, define them in a note under the table, and remember that a star only says which threshold p crossed, not how large the effect is.