When should I use a one-tailed vs two-tailed test?

Use two-tailed when testing for any difference (higher or lower). Use one-tailed when you have a specific directional hypothesis before collecting data. Example: "Drug improves outcomes" (one-tailed) vs "Drug has some effect" (two-tailed). One-tailed tests have more power but only in one direction.

What is the difference between z-test and t-test?

Use z-test when population standard deviation is known or sample is large (n>30). Use t-test when population SD is unknown and sample is small. The t-distribution has heavier tails, accounting for uncertainty in the estimated SD. As sample size grows, t approaches z.

Does a small p-value prove my hypothesis is true?

No. A small p-value only indicates statistical significance - that the result is unlikely under the null hypothesis. It doesnt prove your alternative hypothesis, establish causation, or indicate practical importance. Effect size and context matter too.

Why is p < 0.05 the standard threshold?

The 0.05 threshold is a convention, not a mathematical law. R.A. Fisher suggested it in 1925 as a convenient benchmark. Many fields now use stricter thresholds (0.01 or 0.001). The right threshold depends on consequences of errors and field norms.

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P-Value Calculator

Test statistical significance from z or t scores

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Last verified: February 2026Accuracy tested

Calculated in your browser — we never store your dataVerified formulas with automated testing

Test Type

Tail Type

Z-Statistic

Significance Level (α)

Try:

P-Value (Two-tailed)

0.0500

Significant at α = 0.05 *

Standard Normal Distribution

Shaded area = p-value (5.00%)

Left-tailed

0.9750

Two-tailed

0.0500

Right-tailed

0.0250

Interpretation

The p-value (0.0500) is less than α (0.05).
Reject the null hypothesis. There is statistically significant evidence to support the alternative hypothesis.

Common Significance Levels

Understanding P-Values

What P-Value Means

The probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true.

P-Value ≠ Probability H₀ is True

A common misconception. P-value is about the data, not the hypothesis itself.

Sources & Methodology

Formula: P-value from test statistic using normal/t distribution

Statistical significance testing

Source: Statistical hypothesis testing

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How to Use the P-Value Calculator

The p-value calculator determines statistical significance from z-scores, t-scores, chi-square, or F-statistics. Visualize the rejection region on a distribution curve and get plain-English interpretation of your results.

What is a P-Value?

The p-value is the probability of obtaining results at least as extreme as your observed results, assuming the null hypothesis is true. In simpler terms: "What's the chance of seeing this result if nothing special is happening?"

Interpreting P-Values

p ≤ 0.01: Very strong evidence against null hypothesis
p ≤ 0.05: Strong evidence against null hypothesis (standard threshold)
p ≤ 0.10: Weak evidence against null hypothesis
p > 0.10: Insufficient evidence to reject null hypothesis

One-Tailed vs Two-Tailed Tests

Two-tailed: Tests if results are different (in either direction)
One-tailed (left): Tests if results are less than expected
One-tailed (right): Tests if results are greater than expected

Types of Test Statistics

Z-score: For large samples (n > 30) with known population standard deviation
T-score: For small samples or unknown population standard deviation
Chi-square: For categorical data and goodness-of-fit tests
F-statistic: For comparing variances (ANOVA)

Common Misconceptions

P-value is NOT the probability that the null hypothesis is true
A small p-value doesn't prove practical significance
Statistical significance doesn't mean important or meaningful

Related Calculators

For confidence intervals, use our confidence interval calculator. For standard deviation, try our standard deviation calculator.

Frequently Asked Questions

A p-value of 0.05 means theres a 5% chance of seeing results this extreme if the null hypothesis is true (i.e., if theres no real effect). Its NOT the probability that the null hypothesis is true. At p < 0.05, we typically reject the null hypothesis.