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P-Value Calculator Calculate p-values from Z or t test statistics with one-tailed and two-tailed options.

P-Value Calculator illustration
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P-Value Calculator

Calculate p-values from Z or t test statistics with one-tailed and two-tailed options.

1

Select Test Type

Choose Z-test or t-test and set the tail type.

2

Enter Test Statistic

Input your Z or t statistic (and degrees of freedom for t-test).

3

View P-Value

See the p-value, significance decision, and whether to reject H₀.

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What Is P-Value Calculator?

The P-Value Calculator determines the probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true. It supports both Z-tests (for large samples or known population variance) and t-tests (for small samples with unknown variance), with options for two-tailed, left-tailed, and right-tailed tests. The calculator compares the p-value against your chosen significance level (α) to determine whether to reject the null hypothesis. Understanding p-values is fundamental to hypothesis testing in statistics.

Why Use P-Value Calculator?

  • Supports both Z-test and t-test calculations
  • One-tailed and two-tailed test options
  • Multiple significance levels (0.01, 0.05, 0.10)
  • Clear decision output: reject or fail to reject H₀

Common Use Cases

Academic Research

Determine if experimental results are statistically significant.

A/B Testing

Evaluate whether differences between variants are significant.

Quality Control

Test whether a process meets specification parameters.

Statistics Coursework

Solve hypothesis testing problems for classes.

Technical Guide

For Z-tests, the p-value is calculated from the standard normal CDF. Two-tailed: p = 2 × (1 - Φ(|Z|)). Left-tailed: p = Φ(Z). Right-tailed: p = 1 - Φ(Z). For t-tests, the t-distribution CDF is used with the specified degrees of freedom. For large df (≥30), the t-distribution approaches the normal distribution. The CDF is computed using the Wilson-Hilferty approximation for the chi-square distribution, which provides good accuracy. Statistical significance is determined by comparing p to α: if p < α, reject H₀.

Tips & Best Practices

  • 1
    p < 0.05 does not mean the null hypothesis is false — it means the data is unlikely under H₀
  • 2
    A smaller p-value indicates stronger evidence against the null hypothesis
  • 3
    Two-tailed tests are more conservative than one-tailed tests
  • 4
    Always specify your alpha level BEFORE conducting the test to avoid bias
  • 5
    Statistical significance does not imply practical significance

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Frequently Asked Questions

Q What is a p-value?
A p-value is the probability of observing results at least as extreme as the data, assuming the null hypothesis is true. A small p-value suggests the data is inconsistent with H₀.
Q What p-value is considered significant?
Conventionally, p < 0.05 is significant. However, the threshold depends on context: medical research may use 0.01, while exploratory studies might use 0.10.
Q When should I use one-tailed vs two-tailed?
Use one-tailed when you predict a specific direction (e.g., treatment increases scores). Use two-tailed when testing for any difference in either direction.
Q What is the difference between Z-test and t-test?
Z-test is used when the population standard deviation is known or sample size is large (>30). T-test is used for small samples with unknown population standard deviation.
Q Can a p-value be exactly 0?
Theoretically no, but practically very small p-values may be displayed as 0 due to computational limits. The calculator shows scientific notation for very small values.

About This Tool

P-Value Calculator is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.