Statistical test calculator
Choose a procedure, enter data, and set your inference rules. The calculator selects suitable distributions and reports the decision.
Sample-size and power planning
Estimate sample size from precision, power, and effect assumptions. These planning formulas use standard normal approximations.
Formula guide
Means
Mean tests compare an estimate with a null value. Standard errors measure expected sampling variation. T distributions handle estimated population spread more carefully.
Proportions
Proportion tests compare success rates across populations. Wilson intervals remain bounded near zero and one. Sparse outcomes may require exact methods instead.
Counts
Chi-square tests compare observed and expected frequencies. Expected cells should usually remain sufficiently large. Small cells weaken the usual approximation considerably.
Association
Correlation measures linear association between paired variables. Regression estimates change in outcomes per predictor unit. Significance does not establish causation by itself.
Intervals
A confidence interval gives plausible parameter values. Its confidence level describes long-run method performance. It does not assign probability after calculation.
Power
Power estimates the chance of detecting real effects. Larger samples generally increase power and precision. Planning still depends on realistic effect assumptions.
How to use this calculator
Select the statistical procedure matching your research question. Choose raw data or summary statistics where supported. Enter the null value and alternative direction carefully.
Set the confidence level and significance threshold before calculating. Review assumption notices beside the numerical output. Report estimates, intervals, test statistics, and p-values together.
Use the sample-size planner before collecting new observations. Compare precision and power requirements for your study. Always justify assumptions with subject knowledge and design.
Example data
| Procedure | Example inputs | Research question |
|---|---|---|
| One mean | x̄ = 52.4, s = 8.1, n = 36, μ₀ = 50 | Does the population mean differ from 50? |
| Two means | Group A: 81, 12, 40; Group B: 76, 15, 35 | Do independent group means differ? |
| One proportion | 62 successes, 100 observations, p₀ = 0.50 | Is the population success rate above 50%? |
| Correlation | r = 0.42, n = 48 | Is the linear association statistically significant? |
Frequently asked questions
What does a confidence interval mean?
It gives a range produced by a repeatable method. Wider intervals indicate less precise parameter estimation. Interpretation depends on assumptions and sampling design.
When should I use a z-test?
Use it when normal approximations are appropriate. Mean z-tests also require known population standard deviation. Large samples may support approximate z procedures.
When should I use a t-test?
Use t methods for means with estimated spread. They account for extra uncertainty in standard errors. Smaller samples produce heavier-tailed critical values.
What does the p-value show?
It measures compatibility with the null model. Smaller values indicate more unusual sample evidence. It is not the null hypothesis probability.
Why is failing to reject different from accepting?
Insufficient evidence does not prove the null statement. A study may simply lack adequate power. Report uncertainty instead of claiming exact equality.
Should equal variances be assumed?
Equal variance requires a defensible population assumption. Welch’s test works well without that requirement. It is usually the safer default choice.
What causes unreliable chi-square results?
Small expected counts weaken the reference approximation. Empty rows or columns also create problems. Combine categories only when scientifically defensible.
Does statistical significance imply practical importance?
No, significance depends partly on sample size. Effect sizes describe the magnitude more directly. Use context to judge practical consequences carefully.
Can this replace professional statistical review?
This tool supports common calculations and learning. Complex designs may require specialised modelling choices. Important decisions deserve qualified statistical review.