Confidence intervals and practical significance

Learning objectives

• Interpret confidence intervals correctly.
• Separate statistical from practical significance.
• Compare estimated effect against a minimum important difference.

Confidence intervals in plain terms

A 95% confidence interval is produced by a method that captures the true parameter 95% of the time in the long run. It does not say the fixed parameter has a 95% probability of being inside a single computed interval.

Width depends on variability, sample size and confidence level. Narrow intervals sharpen decisions.

Effect and importance

• Define the minimum important difference for the CTQ before the test.
• Report the estimate, interval and comparison with that threshold.
• State the operational consequence in plain language.

Garment-factory example

A cycle-time reduction of 0.3 minutes (95% CI 0.1–0.5) is statistically clear but irrelevant when takt requires 1.5 minutes.

Method

1. Define effect and important difference in advance.
2. Compute estimate and CI in a free spreadsheet.
3. Compare with zero and with the minimum important difference.
4. Communicate operational meaning, not just p.

Common mistakes

• Claiming a 95% probability for a fixed parameter inside a specific CI.
• Focusing only on the p-value.