Which approach is used to compute a 95% upper confidence limit (UCL) for lognormal exposure data with a small sample size?

• A. Use raw data and apply a z-based upper limit on the arithmetic mean.
• B. Log-transform data, compute mean and SD, use t_(n-1,0.95) * s / sqrt(n).
• C. Use the maximum observed value as UCL.
• D. Use the geometric mean alone to determine UCL.

Answer: (B)

Lognormal exposure data are skewed, so you don’t rely on the raw scale for confidence limits. Transforming the data with a natural log makes the distribution of the transformed values approximately normal, which lets you use normal-theory concepts. Because the sample is small, you don’t know the population standard deviation, so you use the t distribution instead of the z distribution to account for that extra uncertainty.

The correct approach is: take logs, compute the mean and standard deviation of the log-transformed data, and then form a one-sided 95% upper limit for the log-mean using the t critical value with n−1 degrees of freedom: upper_log = mean_log + t_(n−1, 0.95) × (sd_log / sqrt(n)). This gives an upper bound on the mean of the log scale. If you want a limit on the original exposure scale, you exponentiate to translate that upper log-mean limit back, yielding an upper confidence limit for the geometric mean of the exposure. This method properly incorporates skewness, small-sample uncertainty, and the lognormal nature of the data.

The other approaches don’t fit: using raw data with a z-based limit assumes normality and known sigma; relying on the maximum observation ignores sampling variability; using only the geometric mean without a confidence limit doesn’t provide a bound on the population value.