Calculator
Example Data Table
| Scenario | Test | Key Inputs | Question |
|---|---|---|---|
| Average score check | One sample mean t test | n = 30, mean = 102, s = 15, null mean = 100 | Is the average different from the claim? |
| Campaign conversion | One proportion z test | x = 36, n = 60, null proportion = 0.50 | Is the success rate above the target? |
| Two training groups | Welch t test | n1 = 60, mean1 = 82, s1 = 12; n2 = 55, mean2 = 78, s2 = 11 | Do group averages differ? |
Formula Used
The calculator chooses the formula from the selected test type.
| Test | Main statistic |
|---|---|
| One sample mean z test | z = (x̄ - μ0) / (σ / √n) |
| One sample mean t test | t = (x̄ - μ0) / (s / √n) |
| Two sample mean test | statistic = ((x̄1 - x̄2) - d0) / √(s1²/n1 + s2²/n2) |
| Paired t test | t = (d̄ - d0) / (sd / √n) |
| One proportion z test | z = (p̂ - p0) / √(p0(1 - p0) / n) |
| Variance chi-square test | χ² = (n - 1)s² / σ0² |
The p value comes from the chosen distribution and tail. The null hypothesis is rejected when p value is less than or equal to alpha.
How to Use This Calculator
- Select the test that matches your study design.
- Choose a two tailed, left tailed, or right tailed alternative.
- Enter alpha before viewing the final decision.
- Fill only the fields required for your chosen test.
- Press Calculate to show results above the form.
- Use CSV or PDF buttons to save the current report.
For one mean tests, use sample size, sample mean, hypothesized mean, and the correct deviation field. For proportion tests, use success counts and trial counts. For paired tests, use the mean and standard deviation of differences.
Understanding Null Hypothesis Testing
A null hypothesis test helps compare evidence against a starting claim. The starting claim usually says there is no effect, no difference, or no meaningful change. This calculator turns sample statistics into a test statistic, a p value, and a plain decision. It supports common study designs, so one page can handle many classroom, business, and research checks.
Why the Calculator Helps
Manual testing often has many steps. You choose a test, set significance, compute standard error, find a statistic, then compare the p value. Small mistakes can change the decision. This tool keeps the process organized. It also shows the critical value, confidence interval, effect estimate, and interpretation. These extra details help users understand strength, not only pass or fail.
Choosing the Right Test
Use a one sample mean test when one sample is compared with a claimed average. Use a two sample mean test when two independent groups are compared. Use a paired test when the same subjects are measured twice. Use a one proportion test when success counts are compared with a claimed rate. Use the variance test when sample spread is tested against a claimed variance. The calculator uses the selected tail to match the research question.
Reading the Results
A small p value means the sample evidence is unlikely under the null claim. When p is less than alpha, reject the null hypothesis. When p is not less than alpha, do not reject it. This does not prove the null is true. It only means the evidence is not strong enough at the chosen level. The confidence interval gives a useful range for the unknown value.
Good Practice
Enter realistic sample sizes and valid standard deviations. Use alpha before viewing results. Avoid changing the test after seeing a preferred answer. Report the test type, statistic, degrees of freedom, p value, alpha, and conclusion. Export the CSV or PDF when you need a compact record for reports, labs, or review notes.
Limits to Remember
The calculator assumes clean summary data and suitable sampling. Very small samples, skewed data, missing values, or dependent groups may need expert review. Treat each result as statistical guidance, not final proof, before making important formal decisions alone.
FAQs
What is a null hypothesis?
It is the starting claim being tested. It often states no difference, no effect, or no change. The calculator compares your sample evidence against that claim.
When should I reject the null hypothesis?
Reject it when the p value is less than or equal to alpha. This means the sample evidence is statistically significant for the selected test and tail.
Does not rejecting the null prove it is true?
No. It only means the sample did not provide enough evidence against the null claim at the selected significance level.
Which tail should I choose?
Use two tailed for any difference. Use right tailed for greater than questions. Use left tailed for less than questions.
What alpha value should I use?
Many studies use 0.05. Some strict tests use 0.01. Choose alpha before calculating, based on the risk you can accept.
What is a p value?
It is the probability of seeing evidence this extreme, assuming the null claim is true. Smaller values give stronger evidence against the null.
Can I use summary data only?
Yes. This tool is built for summary statistics, such as means, standard deviations, sample sizes, successes, and trial counts.
Why are CSV and PDF downloads useful?
They save the selected test, statistic, p value, decision, and interpretation. Use them for class work, audit notes, reports, or records.