Hypothesis Test P Value Calculator

Calculator

Test family

Alternative tail

Input mode

Known test statistic

Alpha level

Decimal places

DF / numerator DF

Denominator DF

Sample size

Sample mean

Null mean

Sample standard deviation

Population standard deviation

Sample variance one

Variance two or null variance

Formula Used

For a z test, the p value comes from the standard normal curve. For a t test, it comes from the t distribution with selected degrees of freedom. For a chi square test, it uses the chi square distribution. For an F test, it uses the F distribution with numerator and denominator degrees of freedom.

Left tailed p value = P(X ≤ statistic). Right tailed p value = P(X ≥ statistic). Two tailed p value = 2 × the smaller one-tail area, capped at 1.

How to Use This Calculator

Select the test family that matches your study design.
Choose left, right, or two tailed testing.
Enter a known statistic, or use a summary mode.
Add degrees of freedom when the selected test needs them.
Set alpha, choose decimal places, and submit.
Review the p value, decision, and formula note.
Use CSV or PDF buttons to save the output.

Example Data Table

Case	Test	Statistic	DF 1	DF 2	Tail	Alpha
Mean score check	Z test	1.96	Not used	Not used	Two tailed	0.05
Small sample mean	T test	2.15	18	Not used	Right tailed	0.05
Variance claim	Chi square test	24.8	15	Not used	Right tailed	0.01
Variance ratio	F test	3.20	8	12	Two tailed	0.05

Understanding Hypothesis Test P Values

A hypothesis test asks whether sample evidence is unusual under a stated claim. The p value measures that unusualness. It is the probability of observing a test statistic at least as extreme as the one calculated, assuming the null hypothesis is true. A small p value does not prove the alternative hypothesis. It shows that the sample would be rare if the null model were correct.

This calculator supports common p value work for z, t, chi square, and F tests. You can enter a finished statistic. You can also build a statistic from mean or variance summaries. That makes the tool useful for quick checks, homework review, audit notes, and quality reports. Tail selection is important. A left tailed test looks for unusually small values. A right tailed test looks for unusually large values. A two tailed test looks for distance in either direction.

Alpha and Decisions

The alpha level is your cutoff for action. Many studies use 0.05, but that is not automatic. Choose alpha before seeing the result. Compare the p value with alpha. When p is less than or equal to alpha, reject the null hypothesis. When p is larger, fail to reject it. This wording matters. A large p value does not prove the null. It only says the sample did not provide enough evidence against it.

Choosing the Right Test

Good inputs produce useful results. Use z tests when the standard error follows a normal model. Use t tests when a sample standard deviation and degrees of freedom are involved. Use chi square tests for variance or goodness of fit settings. Use F tests for variance ratios or model comparisons. Always match the test family to the study design.

Reporting the Result

Report the statistic, degrees of freedom, tail, p value, alpha, and decision together. Add context in plain language. Mention the measured variable and the practical meaning of the result. Statistical significance is not the same as importance. A tiny effect can be significant with a huge sample. A meaningful effect can be missed with a small sample. Use the p value as one part of a complete analysis. For stronger reporting, include confidence intervals, assumptions, sample limits, and data source notes. These details help readers judge reliability and reuse results carefully.

FAQs

What is a p value?

A p value is the probability of getting a result at least this extreme when the null hypothesis is assumed true. Smaller values show stronger evidence against the null model.

Does a p value prove my hypothesis?

No. It measures compatibility with the null hypothesis. It does not prove the alternative hypothesis, and it does not measure practical importance.

When should I use a two tailed test?

Use a two tailed test when results in either direction would matter. It checks whether the statistic is unusually high or unusually low.

What does alpha mean?

Alpha is the decision cutoff chosen before testing. If p value is less than or equal to alpha, the calculator rejects the null hypothesis.

Which test family should I choose?

Choose z for normal standard error, t for sample standard deviation, chi square for variance counts, and F for variance ratios or model comparisons.

Can I enter a negative statistic?

Negative values are valid for z and t tests. Chi square and F statistics cannot be negative because their distributions start at zero.

Why are degrees of freedom needed?

Degrees of freedom define the shape of t, chi square, and F distributions. Different values can produce different p values for the same statistic.

Why is my p value rounded to zero?

Very small values may appear as scientific notation. Increase decimal places if needed, or use the download options for a saved result.