A confidence interval (CI) is an estimated range of probable values, calculated from sample data, within which we expect to find the true but unknown population parameter.
It represents our uncertainty regarding the exact true population value and provides a range that gives a specific level of confidence.
The interval is composed of two boundaries: a lower confidence limit and an upper confidence limit.
The mathematical calculation of a CI relies heavily on the Standard Error (SE).
For a standard 95% CI of a mean, the formula utilised is the Sample Mean ± (1.96 × SE).
Key Characteristics
Interpretation: The scientifically precise interpretation of a 95% CI states that if an experiment is repeated an infinite number of times under the same conditions, 95% of all constructed confidence intervals will contain the true population mean.
Effect of Sample Size: The width of the CI is directly influenced by the sample size; taking a larger sample size reduces the standard error, which mathematically results in a narrower and more precise confidence interval.
Effect of Confidence Level: Adjusting the desired confidence level alters the interval’s width; for example, a 90% CI will be narrower than a 95% CI because it allows for a larger margin of error (10% versus 5%).
Clinical Application and Interpretation
Confidence intervals are highly useful in medical research to simultaneously gauge the size of the clinical effect and its statistical significance.
The relationship between the 95% CI and statistical significance (at a p-value of 0.05) depends on whether the interval contains the null value.
Statistical Measure
Null Value
Interpretation if Null Value is within the 95% CI
Mean Difference (e.g., comparing two groups)
0
The difference between the groups is not statistically significant.
Absolute Risk Reduction (ARR)
0
The risk reduction is not statistically significant.
Ratios (e.g., Odds Ratio, Relative Risk)
1
The association or risk difference is not statistically significant.
