# P-Value Calculator

> Z-test, t-test, chi-square, regression and confidence intervals

Free p-value calculator. Run z-test, t-test (one/two-sample/paired), chi-square, linear regression and confidence interval. Exact p-values, step-by-step.

URL: https://tools.scoreroute.com/tools/p-value-calculator/

Markdown: https://tools.scoreroute.com/tools/p-value-calculator/.md

## Exact p-values, computed in your browser. No signup, no ads, no data sent anywhere.

Enter your sample statistics and pick a test. The calculator runs a z-test, t-test (one-sample, two-sample or paired), chi-square goodness of fit, linear regression, or confidence interval - then reports the test statistic, degrees of freedom, exact p-value and a plain-language conclusion. Ideal for statistics homework, quality control, A/B testing and research analysis.


### Settings


### Results


### How to use this p-value calculator

Choose Z-Test (population SD known), T-Test (SD estimated from the sample), Chi-Square (compare observed counts to expected), Regression (fit a line), or Confidence Interval (range around a sample mean).

Fill in the summary statistics for the selected test - means, standard deviations and sample sizes. Lists like observed counts or X/Y pairs are entered comma-separated. Use the sample chips to try realistic data instantly.

Alpha is your significance level - 0.05 (default), 0.01 or 0.10. Two-tailed tests are the standard default; choose one-tailed only when your research question has a definite direction.

Results show the test statistic, degrees of freedom, exact p-value and a plain-language conclusion: reject or fail to reject the null hypothesis at your chosen alpha, with the full step-by-step calculation below.


### Frequently Asked Questions


#### What is a p-value?

A p-value is the probability of getting a test statistic as extreme as the one you observed, assuming the null hypothesis is true. A small p-value (typically below 0.05) means your result is unlikely under the null hypothesis, so you reject it.


#### How do I choose between a z-test and a t-test?

Use a z-test when the population standard deviation is known (or the sample is very large, roughly n above 30). Use a t-test when the standard deviation is estimated from the sample, which is the usual case for one-sample, two-sample and paired comparisons.


#### What does two-tailed vs one-tailed mean?

A two-tailed test checks whether the parameter differs from the null value in either direction. A one-tailed test checks a specific direction - less than or greater than. Two-tailed p-values are twice as large as the corresponding one-tailed value.


#### What is the difference between pooled and Welch t-test?

A pooled (equal variance) t-test assumes both samples come from populations with the same variance and uses n1 + n2 - 2 degrees of freedom. The Welch test does not assume equal variances and uses a lower, adjusted degree of freedom. Welch is the safer default.


#### How is the chi-square test used?

A chi-square goodness of fit test compares observed counts against expected counts across categories. The test statistic sums (observed - expected) squared divided by expected. A large value with a small p-value means the observed distribution differs significantly from expected.


#### What is a confidence interval?

A confidence interval is a range around a sample statistic that is likely to contain the true population parameter. A 95% confidence interval means that if you repeated the sampling many times, about 95% of the intervals would contain the true value.


#### Is the p-value calculator really free and private?

Yes. No signup, no account, no watermark, no data collection. All calculations run entirely in your browser using exact numeric integration of the standard normal, Student's t and chi-square distributions - your data never leaves your device.


#### Can AI chatbots calculate p-values reliably?

No. Chat models frequently produce plausible but wrong p-values - they misapply degrees of freedom, forget pooled vs Welch variance, and invert tails. This tool computes every p-value with deterministic numeric algorithms, so results are exact and reproducible.


### Related Tools

## References

- [NIST — Handbook of Mathematical Functions](https://dlmf.nist.gov/)
- [Wikipedia — Mathematics](https://en.wikipedia.org/wiki/Mathematics)