Confidence Interval (CI) — Easy Explanation

1. What is a Confidence Interval?

A confidence interval (CI) gives a range of values that is likely to contain the true effect in the population.

You measure a sample → get a mean or risk → but you want to estimate what the true population value is.

The CI gives you the best estimate + uncertainty.

2. Why do we need a CI?

When you take a sample (e.g., 100 patients), the mean or risk you calculate is not exact — it varies with sampling.

The CI tells you:

• how precise your estimate is
• whether the result is statistically significant
• whether the sample size was large enough

3. The meaning of a 95% CI

A 95% CI means:

➡️ “If you repeated this study 100 times, the true population value would fall within this interval in 95 of those studies.”

It does NOT mean “95% of people fall in this range.”

4. How to interpret it (the part examiners LOVE)

Example 1 — Mean Difference

Study A:

Mean BP drop = 20 mmHg

95% CI = 15 to 25

Interpretation:

• The true BP reduction is likely between 15 and 25 mmHg
• CI does NOT include zero, so it is statistically significant

Example 2 — Mean Difference

Study B:

Mean BP drop = 20 mmHg

95% CI = –5 to +45

Interpretation:

• CI includes zero → drug might have no effect
• Not statistically significant

5. CI and Statistical Significance

For mean differences

✔️ Significant → CI does not cross 0

❌ Not significant → CI includes 0

For risk ratio / odds ratio / hazard ratio

✔️ Significant → CI does not cross 1

❌ Not significant → CI includes 1

6. What affects the width of a CI?

A narrow CI = precise estimate

A wide CI = imprecise estimate

CI gets narrower with:

• larger sample size
• less variability in the data

CI gets wider with:

• small sample
• high variability

Example from the book:

• Study A (100 patients) → CI: 15–25 (narrower)
• Study B (50 patients) → CI: –5 to +45 (wider)

7. Forest Plots (blobbograms)

Meta-analyses often show CIs visually:

• Each line = CI
• Each box = effect estimate
• The vertical line = “no effect”

The combined result is a diamond.

If the diamond does NOT touch the “no effect” line → significant.

8. CI vs Standard Deviation (SD)

SD = variability within the sample

CI = accuracy of the sample mean as an estimate of the population

They are not the same.

9. Summary for Exams

• CI gives a range likely to contain the true population value.
• 95% CI = 95% confidence the true value lies within the interval.
• If CI crosses 0 → mean difference is not significant.
• If CI crosses 1 → risk ratio/odds ratio/hazard ratio not significant.
• Narrow CI = precise (large sample).
• Wide CI = imprecise (small sample).