Written by Dackohn; last reviewed November 2026.
The confidence level and the significance level add up to 100%: confidence = 1 − α. A 95% confidence interval goes with a test at α = .05. For a two-sided test, the result is significant exactly when the interval excludes the null value, such as zero.
What each one means
The significance level (α) is the false-positive rate you accept: how often you would declare an effect when none exists. The confidence level is how often an interval built this way would contain the true value across repeated samples. Both describe the long-run behaviour of a procedure, not the probability that one particular result is right.
| Confidence level | Significance level | z critical value |
|---|---|---|
| 90% | .10 | 1.645 |
| 95% | .05 | 1.960 |
| 99% | .01 | 2.576 |
Worked example: the same result, two ways
A study finds a mean difference of 4.2 with standard error 1.8 and 30 degrees of freedom, so t = 4.2 / 1.8 = 2.33.
- As a test: the two-sided p-value is .027, below .05, so the result is significant.
- As an interval: the 95% CI is 4.2 ± 2.042 × 1.8, which is 0.52 to 7.88. It excludes 0, which tells you the same thing.
- At a stricter level: the 99% CI is −0.75 to 9.15, which includes 0. This agrees with p = .027 being above .01.
Why the interval tells you more
The p-value only says whether the result crosses a line. The interval adds the size and the precision of the effect. “0.52 to 7.88” shows the effect could be almost nothing or fairly large, which “p = .027” hides. Most reporting guidelines ask for both.
When the match breaks down
- One-sided tests match a one-sided interval. A one-sided test at .05 matches a two-sided 90% interval at one end.
- Some methods use different formulas for the test and the interval, such as a z-test for a proportion alongside a Wilson interval, so results near the boundary can disagree slightly.
- Two separate intervals overlapping does not mean the difference is non-significant. Overlapping 95% intervals can still come with p < .05, so test the difference itself.
Common mistakes
- “There is a 95% probability the true value is in this interval.” The 95% describes the method. Watch it in the confidence interval simulator.
- Mixing up α and p. α is chosen in advance. The p-value comes from the data.
- Raising the confidence level without thinking about width. Higher confidence means a wider interval for the same data.
Try it yourself
Confidence Interval Calculator →Build an interval from your data or summary statistics. P-Value Calculator →Get the exact p-value from a test statistic.Frequently asked questions
Is the confidence level the same as the significance level?
No, but they are linked: confidence level = 1 minus alpha. A 95% confidence interval corresponds to a significance level of .05.
If a 95% CI excludes zero, is p below .05?
Yes for the standard two-sided case, where the test and the interval use the same method.
Do overlapping confidence intervals mean no significant difference?
Not necessarily. Two 95% intervals can overlap while the difference is still significant, so test the difference directly.
Related reading: Confidence intervals explained · How to interpret a p-value · What statistical significance means
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.