Confidence Interval

Introduction: CI

A confidence interval (CI) is a statistical range used to estimate the true value of a population parameter, such as a mean or proportion. Instead of giving a single number, it provides a range that is likely to contain the true value, offering a clearer picture of uncertainty.

Background

Confidence intervals became widely used in the 20th century as a way to complement p-values. While p-values indicate whether an effect is significant, confidence intervals show the possible size and direction of that effect. Together, they provide stronger evidence for decision-making in research and practice.

Key Elements / Features

• Range – Shows upper and lower limits (e.g., 45–55).
• Confidence level – Often 95%, meaning we are 95% confident the true value lies within the interval.
• Connection to alpha risk – A 95% CI corresponds to an alpha level of 0.05.
• Width – Narrow intervals suggest precise estimates; wide intervals show more uncertainty.

Applications / Examples

• Medicine – Estimating the effectiveness of a treatment. Example: a drug reduces blood pressure by 8 mmHg (95% CI: 5–11).
• Business – Measuring customer satisfaction scores with uncertainty ranges.
• Manufacturing – Estimating defect rates with precision for quality control.

For instance, if a study finds that a new training programme increases productivity by 10%, with a 95% CI of 4–16%, the range shows the true effect is likely positive but could vary in size.

Relevance / Impact

Confidence intervals make research results easier to interpret by showing not just whether an effect exists, but how large it might be. They encourage researchers and managers to consider both statistical and practical significance.

See also

• p-Value
• Alpha Risk (Type I Error)
• Beta Risk (Type II Error)
• Hypothesis Testing