Example Data Table
| Scenario |
Test |
Input |
Alpha |
Expected use |
| Average score versus 50 |
One sample t test |
Mean 51.4, SD 4.8, n 36, null 50 |
0.05 |
Check whether the mean differs from 50. |
| Two campaign rates |
Two proportion z test |
x1 58, n1 120, x2 43, n2 115 |
0.05 |
Compare conversion rates between groups. |
| Category distribution |
Chi-square goodness of fit |
Observed 24,31,28,17; expected 25 each |
0.05 |
Test whether counts match an expected pattern. |
Formula Used
One mean z test: z = (x̄ - μ0) / (σ / √n)
One mean t test: t = (x̄ - μ0) / (s / √n), df = n - 1
Two mean Welch test: t = ((x̄1 - x̄2) - d0) / √(s1²/n1 + s2²/n2)
One proportion test: z = (p̂ - p0) / √(p0(1 - p0) / n)
Two proportion test: z = ((p̂1 - p̂2) - d0) / √(p̂pool(1 - p̂pool)(1/n1 + 1/n2))
Chi-square test: χ² = Σ((O - E)² / E)
F variance test: F = (s1² / s2²) / null ratio
Correlation test: t = r√((n - 2) / (1 - r²)) when ρ0 = 0
How to Use This Calculator
Choose the test type that matches your data. Enter the null value and alpha level. Add sample means, standard deviations, sample sizes, successes, counts, or table rows as needed. Select the tail direction before submitting. Press the submit button. Review the statistic, p value, decision, interval, and effect size.
For chi-square goodness of fit, enter observed counts and expected counts. If expected counts are missing or mismatched, the calculator uses equal expected counts. For independence tests, enter each table row on a new line. Separate columns with commas.
Why Statistical Significance Matters
Statistical significance helps decide whether sample evidence is strong. A result is significant when its p value is lower than the selected alpha level. This does not prove a claim. It shows that the observed result is unlikely under the null hypothesis.
What This Calculator Does
This calculator supports common significance tests for research summaries and table data. You can run mean tests, proportion tests, chi-square tests, variance tests, and correlation tests. It accepts summary values, counts, lists, and contingency tables. It also reports decisions, tail areas, confidence limits, and practical effect measures.
Choosing the Right Test
Use a z mean test when the standard deviation is known or the sample is large. Use a t test when the standard deviation is estimated from data. Use a proportion z test for pass, fail, yes, no, or conversion data. Use a chi-square test for category counts. Use an F test when comparing two variances. Use a correlation test when checking linear association.
Reading the Result
The test statistic measures distance from the null model. The p value converts that distance into probability. A small p value means the result would be rare if the null model were true. The calculator compares the p value with alpha. If p is less than alpha, the result is statistically significant.
Practical Meaning
Significance is not the same as importance. Very large samples can make small differences significant. Small samples can hide useful effects. Read the effect size with the p value. Cohen's d shows mean difference strength. Proportion difference shows rate change. Cramer's V shows category association. R squared shows shared variation for correlation.
Good Practice
Start with a clear hypothesis. Choose alpha before seeing results. Check sample independence and data quality. Use two-tailed tests when either direction matters. Use one-tailed tests only with a planned direction. Do not test many outcomes without care. Multiple testing can raise false positive risk. Record inputs, formulas, and assumptions. Export results when you need a clean audit trail.
Limits To Remember
No calculator replaces study design. Use results as a decision aid. For regulated, clinical, or legal work, review methods with a qualified statistician before publishing any conclusion and sharing final reports safely.
FAQs
1. What does statistically significant mean?
It means the p value is below the chosen alpha level. The result is unlikely under the null hypothesis. It does not prove practical importance or direct causation.
2. Which alpha level should I use?
Many studies use 0.05. Some use 0.01 for stricter evidence. Choose alpha before analysis, based on risk, domain rules, and research standards.
3. When should I use a two-tailed test?
Use a two-tailed test when results in either direction matter. It is usually the safer default for exploratory or neutral hypotheses.
4. When should I use a one-tailed test?
Use it only when you planned one direction before seeing data. The opposite direction should not count as support for your claim.
5. What is a p value?
A p value is the probability of seeing evidence this extreme, or more extreme, if the null hypothesis were true.
6. Is statistical significance the same as importance?
No. A tiny effect can be significant with a large sample. Always review effect size, context, confidence interval, and study quality.
7. Can I use summary data only?
Yes. Mean, standard deviation, sample size, successes, and category counts are enough for many common significance tests.
8. Why are my results not significant?
The effect may be small, sample size may be low, variation may be high, or the null model may fit the data well.