Graph
Example Data Table
| P Value | Effect | SE | Confidence | Estimated CI |
|---|---|---|---|---|
| 0.050 | 2.50 | 0.45 | 95% | 1.62 to 3.38 |
| 0.010 | 4.20 | 0.70 | 95% | 2.83 to 5.57 |
| 0.100 | 1.80 | 0.60 | 90% | 0.81 to 2.79 |
Formula Used
Alpha: α = 1 − confidence level
Critical value: z = inverse normal probability of 1 − α / 2
Margin of error: ME = critical value × standard error
Confidence interval: effect size ± margin of error
Estimated test statistic from p value: z = inverse normal probability of 1 − p / 2 for two tailed tests.
How To Use This Calculator
Enter the reported p value from your test. Add the effect size, such as mean difference, coefficient, risk difference, or estimate. Enter the standard error. Choose the confidence level. Select one tailed or two tailed testing. Press calculate. The result appears above the form. Use CSV or PDF buttons to save your output.
About P Values And Confidence Intervals
Why This Conversion Helps
A p value shows how unusual a result may be under a null hypothesis. It does not show the practical size of the result. A confidence interval gives a range of likely values for the effect. This makes the result easier to interpret.
Effect Size Matters
The effect size is the center of the interval. It may be a difference, ratio, coefficient, or other estimate. A small p value can still have a small effect. A large effect may also have wide uncertainty.
Standard Error Controls Width
The standard error measures sampling uncertainty. A smaller standard error creates a narrower interval. A larger standard error creates a wider interval. This is why sample size and variation are important.
Confidence Level Choice
A 95% interval is common. A 90% interval is narrower. A 99% interval is wider. Higher confidence gives more caution. Lower confidence gives a tighter range, but less certainty.
Careful Interpretation
This calculator uses a normal approximation. It is best for large samples or estimates that follow an approximately normal distribution. For small samples, exact methods or t based methods may be better. Always match the method to your study design.
Use In Reports
Reports should include the effect estimate, confidence interval, p value, sample size, and method. This gives readers more context. It also avoids over reliance on a single significance result.
FAQs
1. Can a p value directly create a confidence interval?
Not alone. You also need an effect size and standard error. The p value helps estimate test strength, but the interval needs scale information.
2. What is the best confidence level?
Use 95% for most reports. Use 90% for exploratory work. Use 99% when you need stronger caution and wider uncertainty limits.
3. Why is my interval very wide?
A wide interval usually means high standard error, small sample size, large variation, or a high confidence level.
4. Does a confidence interval replace a p value?
No. It complements it. The interval shows range and precision. The p value shows evidence against a null hypothesis.
5. What does it mean if zero is inside the interval?
For difference based estimates, zero inside the interval often means the result is not statistically significant at that confidence level.
6. Can I use this for regression coefficients?
Yes, if you have the coefficient estimate and standard error. The normal approximation should also be reasonable.
7. Is this calculator exact for all tests?
No. It uses a normal approximation. Some tests need t, chi square, binomial, or specialized interval methods.
8. What should I report with the result?
Report effect size, confidence interval, p value, standard error, sample size, test type, and confidence level.