Confidence limits

Confidence limits are a statistical concept related to confidence intervals. They represent the upper and lower boundaries of a confidence interval, providing a range of values that likely contain the true parameter of interest.

Definition

In statistics, confidence limits are the two values that define the range of a confidence interval. They are calculated from the data and the level of confidence. The upper confidence limit (UCL) is the highest value in the range, and the lower confidence limit (LCL) is the lowest value. The interval between these two values is where the true population parameter is likely to fall a certain percentage of the time (the confidence level).

Calculation

The calculation of confidence limits depends on the standard deviation of the sample, the sample size, and the chosen level of confidence. The formula for a confidence interval is:

x̄ ± Z (σ/√n)

where x̄ is the sample mean, Z is the Z-score corresponding to the desired level of confidence, σ is the standard deviation, and n is the sample size. The LCL and UCL are found by subtracting and adding the margin of error (the second part of the formula) from the sample mean, respectively.

Interpretation

Confidence limits are used to indicate the reliability of an estimate. The wider the confidence interval (i.e., the greater the distance between the LCL and UCL), the less precise the estimate. Conversely, a narrow confidence interval indicates a more precise estimate. However, it's important to note that confidence limits do not provide a probability that the true parameter falls within the interval; they merely suggest that if we were to repeat the experiment many times, the true parameter would fall within the interval in a certain percentage of the experiments (the confidence level).

See also

• Confidence interval
• Standard deviation
• Z-score
• Sample size

References

Confidence limits Resources
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