p value calculator

What is a p-value?

A p-value is the probability of observing a test statistic at least as extreme as your sample result, assuming the null hypothesis is true. It helps you assess whether your data are unusual under a “no effect” or “no difference” assumption.

Smaller p-values indicate stronger evidence against the null hypothesis. For example, a p-value of 0.01 means that if the null were true, you'd expect results this extreme only about 1% of the time.

How to use this p value calculator

• Choose distribution: Use Z when population standard deviation is known (or large-sample approximation); use t when standard deviation is estimated from sample data.
• Enter your test statistic: This is your computed z-score or t-score from your hypothesis test.
• Select tail type: Two-tailed for “not equal,” right-tailed for “greater than,” left-tailed for “less than.”
• Set α level: Common values are 0.05 or 0.01. The calculator will tell you whether your p-value is below α.

Z-test vs t-test: which one should you choose?

Z distribution

Use the standard normal (Z) distribution when your test statistic follows normal assumptions with known population variability, or when a large sample allows normal approximation.

Student's t distribution

Use the t distribution when population standard deviation is unknown and estimated from sample data. The shape depends on degrees of freedom; with small samples, tails are heavier, often producing larger p-values than Z.

One-tailed vs two-tailed p-values

• Two-tailed: tests for any difference in either direction (e.g., mean is not equal to benchmark).
• Right-tailed: tests whether parameter is greater than benchmark.
• Left-tailed: tests whether parameter is less than benchmark.

Important: decide your tail direction before looking at results. Choosing tails afterward can bias conclusions.

Interpreting your output

The calculator returns your p-value and compares it to α. A common decision rule:

• If p ≤ α, reject the null hypothesis (statistically significant).
• If p > α, fail to reject the null hypothesis (not statistically significant).

Statistical significance does not automatically imply practical importance. Pair p-values with effect sizes and confidence intervals whenever possible.

Example

Suppose you run a t-test and get t = 2.10 with df = 18, two-tailed. Enter those values and the calculator gives a p-value around 0.05. At α = 0.05, the result is borderline. In a report, you would also include sample size, effect size, and confidence interval.

Common mistakes to avoid

• Interpreting p-value as the probability that the null hypothesis is true.
• Switching between one-tailed and two-tailed tests after seeing data.
• Ignoring assumptions (independence, approximate normality, random sampling).
• Relying on p-values alone without effect size and context.

Quick FAQ

Is p = 0.049 meaningfully different from p = 0.051?

No. They are very close; treat results continuously and emphasize effect magnitude and uncertainty, not only a threshold.

Can I use this for chi-square or F tests?

This tool is designed for z and t statistics. For chi-square and F tests, use a dedicated calculator for those distributions.

Can the p-value ever be exactly zero?

Theoretical p-values are greater than zero. Extremely small values may display as 0 due to rounding or machine precision limits.