<p>Initial laboratory or animal studies are typically small with sample sizes ranging from a few to a few dozen. Yet biomarker values can have markedly non-Gaussian distributions complicating inference for quantile statistics, such as the median. A common challenge encountered by practitioners is the decision of whether to employ a Box–Cox transformation when constructing this confidence interval. A standard approach is to decide based on a normality test, such as the Shapiro–Wilk or Anderson–Darling tests. These tests, however, possess limited power with small sample sizes. To address these limitations, this paper introduces a unified likelihood ratio approach for establishing a confidence interval for the median. In order to mitigate issues stemming from the small sample size, a nonparametric bootstrap likelihood ratio method is employed to derive critical values. Through comprehensive simulations, the proposed method demonstrates remarkable accuracy in achieving coverage, even when the sample size is 5 and the underlying distribution deviates from normality following the application of the Box–Cox transformation. The effectiveness of our method is demonstrated by its application in analyzing data from a randomized clinical trial, aimed at assessing how well sulindac works as a preventive measure against familial adenomatous polyposis (FAP).</p>