What is the absolute minimum sample size for a nonparametric 95% RI?

What is the absolute minimum sample size for a nonparametric 95% RI?

• A. 29
• B. 39
• C. 49
• D. 59

Answer: (B)

Nonparametric reference intervals rely on the data’s order and don’t assume a normal distribution. To define a two‑sided 95% RI, you need to identify the lower and upper bounds corresponding to the 2.5th and 97.5th percentiles and have enough data so these bounds can be estimated with 95% confidence. When you work through the exact binomial confidence limits for percentile estimates, the smallest sample size that guarantees those two bounds with 95% confidence is 39 observations. With fewer samples, the bounds can’t be claimed with that level of confidence. In practice, larger samples are preferred for stability, but 39 is the theoretical minimum for a nonparametric 95% RI.

Nonparametric reference intervals rely on the data’s order and don’t assume a normal distribution. To define a two‑sided 95% RI, you need to identify the lower and upper bounds corresponding to the 2.5th and 97.5th percentiles and have enough data so these bounds can be estimated with 95% confidence. When you work through the exact binomial confidence limits for percentile estimates, the smallest sample size that guarantees those two bounds with 95% confidence is 39 observations. With fewer samples, the bounds can’t be claimed with that level of confidence. In practice, larger samples are preferred for stability, but 39 is the theoretical minimum for a nonparametric 95% RI.