In brief: the significance level (α) is a threshold chosen for a hypothesis test; the confidence level (1−α) describes the long-run coverage of an interval method; and a confidence interval is the range calculated from sample data. A 95% confidence interval corresponds to a 5% significance level only for a matching two-sided test using the same method and assumptions.
How the three terms differ
| Concept | What it does | What you get | Common misinterpretation |
|---|---|---|---|
| Significance level (α) | Sets a hypothesis test’s threshold for a Type I error: rejecting a null hypothesis that is actually true. | A rule for deciding whether to reject a specified null hypothesis. | It is not the probability that the null hypothesis is false. [NIST] |
| Confidence level (1−α) | States the long-run coverage rate of an interval-producing method over repeated samples. | A coverage property, such as 95%. | It does not mean a particular calculated interval has a 95% probability of containing the fixed parameter. [NIST] |
| Confidence interval | Uses sample data to estimate a population parameter. | A lower and upper bound, conveying a range and precision. | Including a value does not prove it is true; excluding a value does not establish practical importance. [NIST] |
NIST lists 0.10, 0.05, and 0.01 as common significance-level choices. The α=0.05 choice pairs with a 95% confidence level because 1−α=0.95. [NIST] [NIST]
How a 95% interval relates to a 5% test
For a matching two-sided hypothesis test and confidence interval, the interval contains the null-hypothesis values that would not be rejected at significance level α. Thus, if the null value is outside a 95% interval, the corresponding test rejects it at α=0.05; if it is inside, the test does not reject it. [NIST]
Example: testing a hypothesized mean
Suppose a test asks whether a population mean equals 100. If the matching 95% interval for that mean is [102, 108], 100 is outside the interval, so the corresponding two-sided test rejects the null value at the 5% level. If the interval is [98, 106], 100 is inside, so the test does not reject it. The interval reports plausible values under the method; the test makes a decision about the specified null value.
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This correspondence depends on using the same statistical model, sidedness, and assumptions for both procedures. A one-sided test should not be compared as though it were the matching two-sided test.
What a confidence interval says about precision
The interval’s width indicates how precisely the method estimates the parameter: larger samples generally produce narrower intervals, while greater sample variability generally produces wider ones. For a normal-mean interval when the population standard deviation σ is known, NIST gives the form sample mean ± z(1−α/2) × σ/√N, where N is sample size and z(1−α/2) is the relevant standard-normal critical value. [NIST]
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Statistical significance is not a measure of effect size or practical importance. Read the interval’s endpoints and width to judge the estimated magnitude and its precision, rather than treating a test’s reject/do-not-reject result as a complete description of the effect.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How to interpret the p-value and a non-significant result
A p-value is calculated under the null hypothesis: it is the probability of observing a result at least as extreme as the one obtained, assuming the null is true. Compare it with the significance level chosen in advance; a p-value at or below α meets that test’s rejection threshold. [NIST]
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If a result is not statistically significant, the data did not cross the chosen threshold. That does not establish that the null hypothesis is true or that there is no effect. NIST cautions that accepting a hypothesis does not mean it is true; it means there is not evidence to believe otherwise. [NIST]
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