Why sample size is important
- Larger samples reduce random noise and make estimates more stable.
- Precision improves: confidence intervals become narrower.
- With larger n, sampling distributions become more "normal" (CLT intuition).
The "n ≥ 30" idea is a rule of thumb, not a law — skewed/heavy-tail data may need more.
Real Dental Scenario
Mouthwash Gingivitis Study
The question: A researcher wants to study whether a new chlorhexidine mouthwash reduces gingivitis scores (Gingival Index, scale 0–3) compared to a placebo. The true population mean reduction is 0.4 points. How does sample size affect the reliability of the estimate?
Estimate jumps wildly between studies. One trial might show 0.1, another 0.8.
Estimate settles down. Most studies find values between 0.25 and 0.55.
Estimate is precise. Consistently near 0.4, with a tight confidence interval.
Animated Sampling Demo
Each dot is a simulated study. The shaded bands show the 95% confidence interval. Notice how it narrows as n grows.
Mini CLT demo (sample means)
Pick a population shape and sample size n. We repeatedly sample and plot the distribution of sample means.
Distribution of sample means
As n increases, the sample-mean distribution becomes tighter and more bell-shaped.
Dental context
For outcomes like DMFT or plaque scores, skewness is common. If you plan parametric tests, consider transformations or nonparametric alternatives, and plan n accordingly.