Choose a scenario and enter summary statistics. The wizard returns test statistics, critical values, confidence intervals, p-values, and a clear step log. Share the URL to reproduce the same setup.
Results
Provide inputs and run the analysis to see the summary, interval, and decision.
Key metrics
Conclusion
How it is computed
P-value visual
Teacher notes
- Student’s t quantiles are derived via the regularised incomplete beta, matching textbook lookup tables even for small samples.
- Welch degrees of freedom, Wilson score, and Newcombe’s difference keep coverage accurate for unequal variances or proportions near the boundary.
- The shareable URL stores the scenario, summary statistics, tail choice, and confidence level so group members can replicate the report instantly.
How to use this calculator effectively
This guide helps you use Confidence Interval & Hypothesis Test Wizard in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.
How it works
The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.
When to use
Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.
Common mistakes to avoid
- Changing multiple parameters at once, which hides the true cause of output movement.
- Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
- Comparing with another tool without aligning defaults, constants, and rounding rules.
- Using rounded display values as exact downstream inputs without re-checking precision.
Interpretation and worked example
Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.
See also
FAQ
What does the p-value shading show?
The shaded area matches the p-value under the null distribution. Two-tailed tests shade both sides, while one-tailed tests shade only one side.
How are the Wilson and Newcombe intervals computed?
Wilson intervals use the adjusted proportion with a z critical value. Newcombe combines two Wilson intervals to form bounds for the difference.
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
Why does this page differ from another tool?
Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.
How reliable are the displayed values?
Values are computed in the browser and rounded for display. They are good for planning and educational checks, but for regulated or high-stakes decisions you should validate assumptions with official guidance or professional review.