Confidence interval

Confidence interval is a statistical term that refers to the range within which the true value of a parameter is expected to fall with a certain probability. It is a measure of the uncertainty or variability associated with a sampling method. A confidence interval is usually expressed in terms of a percentage, for example, a 95% confidence interval means that the true value is expected to fall within the range 95% of the time.

Definition

A confidence interval is a range of values, derived from a statistical analysis, that is likely to contain the value of an unknown parameter. The interval has an associated confidence level that quantifies the level of confidence that the parameter lies within the interval.

Interpretation

The correct interpretation of a confidence interval is probably one of the most misunderstood concepts in statistics. The confidence level is the frequency (i.e., the proportion) of possible confidence intervals that contain the true value of their corresponding parameter. In other words, if confidence intervals are constructed using a given confidence level from an infinite number of independent sample statistics, the proportion of those intervals that contain the true value of the parameter would equate to the confidence level.

Calculation

The calculation of a confidence interval depends on the statistical distribution of the observed data, the size of the sample, and the desired confidence level. For a normal distribution, the confidence interval for the mean is obtained by adding and subtracting the standard error times a constant from the sample mean. The constant is determined by the desired confidence level and is obtained from the quantile of the standard normal distribution.

Applications

Confidence intervals are widely used in medical research, engineering, economics, and many other fields. They provide a useful way to assess the reliability of estimates, comparisons, and other statistical analyses.

See also

• Margin of error
• Standard error
• Statistical significance
• T-distribution
• Z-score

References

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  Normal distribution 50% CI illustration

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  Confidence intervals visual

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  Confidence interval

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  95% confidence interval

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  Neyman Construction Confidence Intervals