How to use Statistical Hypothesis Test Calculator

Select a supported test and its alternative.
Enter valid sample summaries or observed and expected counts.
Review the statistic, p-value and assumption checks.

Example: Statistical Hypothesis Test Calculator

Statistical Hypothesis Test Calculator: p=0.0196541751166; reject at α=0.05.

You add

Test: t Alternative hypothesis: two Significance level α: 0.05 Sample mean / first sample mean: 10 SD / first sample SD: 2 Sample size / first sample size: 25 Null mean: 9 Second sample mean: 9 Second sample SD: 3 Second sample size: 30 Observed and expected counts: 20 25 30 25 25 25 25 25 Distribution parameters estimated from these counts: 0

You get

p=0.0196541751166; reject at α=0.05. Test: t Alternative: two Statistic: 2.5 Degrees of freedom: 24 p-value: 0.0196541751166 Significance level: 0.05 Decision at this α: Reject the null hypothesis Sample mean=10; null mean=9; n=25; SD=2. A p-value is computed under the null hypothesis and stated model; it is not the probability that the null is true. Failure to reject does not establish equality. Mean tests assume independent observations and an appropriate normal model or sample size; Welch assumes independent samples. Chi-square refuses expected cells below 5, uses matched totals and subtracts the entered fitted-parameter count. No paired tests, weights, contingency-table ind Test | t Alternative | two Statistic | 2.5

Options

Test and summaries: Choose the supported test before entering its required summaries. Welch compares independent means without assuming equal variances.
Alternative and alpha: Choose the direction and significance threshold before interpreting the result. Changing the tail after seeing the output changes the question being tested.

Supported inputs and limits

Supported one-sample t/known-deviation z, Welch two-sample t and chi-square goodness-of-fit methods only. Impossible or degenerate summaries are refused. Counts need adequate expected frequencies and correct degrees of freedom. A p-value does not establish causality or the probability that a hypothesis is true.

Where your input is processed

This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.

A small p-value does not describe the size of an effect

The p-value measures compatibility with the null model through the selected test statistic and tail. It does not give the probability that the null is true. Review assumptions, sample design and effect size alongside the result; a threshold decision alone cannot establish cause or practical importance.

Questions about Statistical Hypothesis Test Calculator

Does a large p-value prove the null hypothesis?

No. It means this supported test did not provide sufficient evidence against the stated null at the chosen threshold.

Does Welch require equal variances?

No. It uses the two entered variances and its own degrees-of-freedom estimate.

Can I choose expected counts after inspecting a result?

Expected counts and any fitted parameters need a defensible model; changing them after testing changes the question.

Project manager: Tony Hines · Content updated 4 October 2026 · Report a problem

Statistical Hypothesis Test Calculator

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