Confidence interval: Difference between revisions
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|Display title=confidence interval | |||
{{ | |Definitions={{Definition | ||
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|Meaning=(''Also called'' fiducial interval, confidence band.) A [[range]] of values (''a''<sub>1</sub> < ''a'' < ''a''<sub>2</sub>) determined from a [[sample]] by definite rules so chosen that, in repeated [[random samples]] from the hypothesized [[population]], an arbitrarily fixed proportion (1 - ε) of that range will include the true value α of an estimated [[parameter]]. | |||
|Explanation=The limits (''a''<sub>1</sub> and ''a''<sub>2</sub>) are called confidence limits or fiducial limits, the [[relative frequency]] (1 - ε) with which these limits include α is called the confidence coefficient, and the complementary [[probability]] ε is called the confidence level. As with significance levels, confidence levels are commonly chosen as 0.05 or 0.01, the corresponding confidence coefficients being 0.95 and 0.99. Confidence intervals should never be interpreted as implying that the parameter itself has a range of values; it has only one value, α. On the other hand, the confidence limits (''a''<sub>1</sub>, ''a''<sub>2</sub>), being derived from a sample, are [[random variables]] the values of which on a particular sample either do or do not include the true value α of the parameter. However, in repeated samples, a certain proportion (viz., 1 - ε) of these intervals will include α, provided that the actual population satisfies the initial hypothesis. | |||
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Latest revision as of 11:06, 26 March 2024
(Also called fiducial interval, confidence band.) A range of values (a1 < a < a2) determined from a sample by definite rules so chosen that, in repeated random samples from the hypothesized population, an arbitrarily fixed proportion (1 - ε) of that range will include the true value α of an estimated parameter.
The limits (a1 and a2) are called confidence limits or fiducial limits, the relative frequency (1 - ε) with which these limits include α is called the confidence coefficient, and the complementary probability ε is called the confidence level. As with significance levels, confidence levels are commonly chosen as 0.05 or 0.01, the corresponding confidence coefficients being 0.95 and 0.99. Confidence intervals should never be interpreted as implying that the parameter itself has a range of values; it has only one value, α. On the other hand, the confidence limits (a1, a2), being derived from a sample, are random variables the values of which on a particular sample either do or do not include the true value α of the parameter. However, in repeated samples, a certain proportion (viz., 1 - ε) of these intervals will include α, provided that the actual population satisfies the initial hypothesis.
