confidence interval

A confidence interval is a range of values calculated from sample data that is likely to contain the true value of an unknown population parameter. It provides an estimate of the precision and uncertainty associated with a statistical estimate. The interval is constructed at a specified confidence level, such as 95% or 99%.

Context and Usage

Confidence intervals are widely used in statistical analysis, scientific research, medical studies, and data science to quantify uncertainty in parameter estimates. Researchers and analysts use them when working with sample data to make inferences about larger populations. They appear in academic papers, clinical trial results, market research reports, and quality control processes to provide more informative estimates than single-point values.

Common Challenges

Users often misinterpret confidence intervals as the probability that the parameter lies within the interval, rather than understanding they relate to the procedure's long-term performance. Small sample sizes can produce very wide intervals that offer little practical information. The assumption of normality may be violated, leading to inaccurate intervals. Multiple comparisons can inflate the apparent significance without proper adjustment.

Related Topics: statistical inference, hypothesis testing, margin of error, p-value, sample size estimation, bootstrap method, standard error