P value calculator from a t, z, F, chi-square or r statistic.

What is a p value?

A p value is the probability of getting a test result at least as extreme as yours if the null hypothesis were true. Small p values, usually below .05, suggest the result is unlikely to be due to chance alone. A p value does not tell you how large or important the effect is.

How the p value is calculated

• z: two-tailed p = 2 × P(Z > |z|) from the standard normal distribution
• t: two-tailed p = 2 × P(T > |t|) from the t distribution with df degrees of freedom
• F: right-tailed p = P(F > F observed) with (df₁, df₂)
• χ²: right-tailed p = P(χ² > χ² observed) with df
• r: converted to t = r√(n − 2) ÷ √(1 − r²) with df = n − 2

Worked example: p value from a t statistic

A t-test gives t = 2.50 with 20 degrees of freedom.

1. Find the upper-tail area: P(T > 2.50) with df = 20 is 0.0106.
2. Double it for a two-tailed test: p = 0.0212.
3. Compare with α = .05: 0.021 is smaller, so the result is significant.
4. Write it as t(20) = 2.50, p = .021.

One-tailed or two-tailed?

Use a two-tailed p value unless you stated a direction before you saw the data. A one-tailed test only counts evidence in one direction, so it halves the p value when the result goes the predicted way and gives a large p when it goes the other way.

How to report a p value (APA style)

Report exact p values to two or three decimals without a leading zero (p = .021), and write p < .001 for anything smaller. Always give the test statistic and degrees of freedom next to it, plus an effect size.

References

• American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
• Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129–133.