A statistical measure indicating the probability that a result falls within a specified range.Confidence level is a statistical measure that quantifies how certain we can be that a result falls within a specified range. It is typically expressed as a percentage, such as 95% or 99%, and accompanies a confidence interval — the range of values within which the true value is expected to lie. For example, a 95% confidence level means that if the same experiment were repeated many times, the calculated interval would contain the true value in 95% of those repetitions. It is a cornerstone of hypothesis testing and scientific inference, helping researchers distinguish genuine effects from random fluctuations.
The concept was formalized by Jerzy Neyman in the 1930s, building on earlier work by Ronald Fisher on significance testing. Neyman introduced confidence intervals as a frequentist alternative to Bayesian credible intervals.
The confidence level is derived from the sampling distribution of a statistic. When you estimate a parameter from data, you compute a point estimate and its standard error. The confidence interval is then constructed by adding and subtracting a margin of error, which is the product of a critical value (based on the desired confidence level and the distribution, often the normal or t-distribution) and the standard error. The confidence level itself is not a probability that the true value lies in a specific interval, but rather a long-run frequency: over many samples, the method produces intervals that capture the true value at that rate.
Confidence levels are used across science and medicine to assess the reliability of measurements, such as in clinical trials for drug efficacy, opinion polls, and quality control in manufacturing.
A 95% confidence interval does not mean there is a 95% chance the true value is inside the interval — that is a common misconception; the probability is about the method, not the specific interval.
| R_{UL} | variable | Upper limit on event rate — event rate per second |
| C | variable | Confidence level (probability) — confidence level |
| T | variable | Observation time — time second |
| \ln | operator | Natural logarithm — natural logarithm |
