Confidence Intervals

Precision of estimates (e.g., prevalence of periodontal disease)

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What does a 95% CI mean?

A confidence interval is a range of plausible values for a population parameter. If you repeated the same study many times, about 95% of such intervals would contain the true value.

Wider CI = less precision; narrower CI = more precision (often from larger sample size).

Real Dental Scenario

Childhood Caries Prevalence Survey

The study: A dental public health survey screened 200 children in a rural community. Of these, 45 children had untreated dental caries. What is the estimated prevalence and how precise is it?

Step-by-Step CI Calculation

1

Compute the sample proportion (p-hat)

p̂ = events / n
p̂ = 45 / 200
p̂ = 0.225 (22.5%)
2

Compute the Standard Error (SE)

SE = sqrt( p̂ * (1 - p̂) / n )
SE = sqrt( 0.225 * 0.775 / 200 )
SE = sqrt( 0.000872 )
SE = 0.0295
3

Compute the 95% Confidence Interval

CI = p̂ ± z * SE
CI = 0.225 ± 1.96 * 0.0295
CI = 0.225 ± 0.0578
CI = ( 0.167 , 0.283 )

Visual: Confidence Interval on a Number Line

0%10%20%30%40%50%
16.7%
22.5% (p̂)
28.3%

Interpretation

We are 95% confident that the true prevalence of untreated dental caries in this population is between 16.7% and 28.3%.

This means: if we repeated this survey many times with fresh random samples of 200 children, about 95 out of 100 such intervals would capture the true population prevalence.

Interactive: CI for a proportion

Use events and total sample size. This uses a simple normal approximation for teaching.

Prevalence: -
95% CI: -
0%point0%

Tip: if n is small or p is near 0/1, use Wilson or exact methods in real analyses.

CI width vs sample size

Fix prevalence and see how CI shrinks as n increases.

30%

Dental use cases