Formula Used
One mean z test: z = (x̄ - μ0) / (σ / √n)
One mean t test: t = (x̄ - μ0) / (s / √n)
Two mean test: statistic = [(x̄1 - x̄2) - d0] / SE
Paired t test: t = (d̄ - d0) / (sd / √n)
One proportion z test: z = (p̂ - p0) / √[p0(1 - p0) / n]
Two proportion z test: z = [(p̂1 - p̂2) - d0] / √[p̂(1 - p̂)(1/n1 + 1/n2)]
Correlation test: t = r√[(n - 2) / (1 - r²)]
The p value is calculated from the selected test distribution and tail direction.
How to Use This Calculator
- Select the test type that matches your study design.
- Choose the alternative hypothesis direction.
- Enter alpha, such as 0.05 or 0.01.
- Enter summary values, raw data, or both.
- Use raw sample boxes for automatic mean, deviation, paired, or correlation input.
- Press Calculate to view the result above the form.
- Use CSV or PDF buttons to save the computed result.
Example Data Table
| Test |
Input Values |
Alpha |
Expected Output |
| One sample t test |
x̄ = 52, μ0 = 50, s = 6, n = 36 |
0.05 |
t statistic, p value, decision, confidence interval |
| Two proportion z test |
x1 = 72, n1 = 120, x2 = 58, n2 = 115 |
0.05 |
z statistic, p value, proportion difference |
| Correlation test |
r = 0.42, n = 48 |
0.01 |
t statistic, p value, significance decision |
Statistical Significance Test Overview
A statistical significance test helps compare observed data with a stated claim. It checks whether the observed difference is likely to be random variation. This calculator supports common tests for means, proportions, paired changes, and correlation. Each method returns a test statistic, p value, confidence interval, and decision.
Why Significance Matters
Significance testing is useful in research, quality control, marketing, education, medicine, and surveys. It gives a structured way to judge evidence. A small p value means the data would be unusual if the null hypothesis were true. That does not prove a result is practically important. It only shows that the result is statistically unlikely under the tested assumption.
Choosing the Right Test
Use a one sample mean test when one average is compared with a target value. Choose a two sample mean test when two independent group averages are compared. Use the paired t test when the same subjects are measured twice. Use a one proportion test for a single rate. Use a two proportion test when two rates are compared. Use the correlation test when you need to check whether a linear relationship differs from zero.
Interpreting the Output
The alpha value is the selected risk level. Common choices are 0.05, 0.01, and 0.10. If the p value is less than or equal to alpha, the calculator rejects the null hypothesis. If the p value is greater than alpha, it does not reject the null hypothesis. This wording is important. A non significant result does not prove the null claim. It only means the sample did not give enough evidence against it.
Good Practice Notes
Check assumptions before trusting any result. Mean tests need suitable sample design. The z test needs a known population standard deviation or a large sample. The t test uses sample variation. Proportion tests need valid counts and enough expected successes and failures. Correlation testing needs paired numeric data and a roughly linear pattern. Always report the sample size, test type, alpha level, statistic, p value, and interval. Use the export buttons to save results for later review. Keep notes about data sources, units, and study design. Clear records make repeated analysis easier and more reliable.
FAQs
What is statistical significance?
Statistical significance means the result is unlikely under the null hypothesis at the chosen alpha level. It does not automatically mean the result is large, useful, or important in practice.
What p value is significant?
A p value is significant when it is less than or equal to alpha. Many studies use 0.05, but 0.01 and 0.10 are also common.
Which test should I choose for one average?
Use a one sample z test when the population standard deviation is known. Use a one sample t test when you only have the sample standard deviation.
When should I use a paired t test?
Use a paired t test when two measurements come from the same subjects, matched pairs, or before and after observations.
Can I paste raw data?
Yes. Paste numbers separated by commas, spaces, semicolons, or line breaks. The calculator can use raw data for mean tests, paired tests, and correlation.
What does fail to reject mean?
It means the sample did not provide enough evidence against the null hypothesis. It does not prove the null hypothesis is true.
Why is alpha important?
Alpha sets the rejection cutoff. A smaller alpha requires stronger evidence before calling a result statistically significant.
Does this calculator replace statistical judgment?
No. Check sample design, assumptions, data quality, and practical importance before making conclusions from any significance test.