Quantitative laboratory results: normal or lognormal distribution?

The identification of a suitable distribution model is a prerequisite for the parametric estimation of reference intervals and other statistical laboratory tasks. Classification of normal vs. lognormal distributions from healthy populations is easy, but from mixed populations, containing unknown proportions of abnormal results, it is challenging. We demonstrate that Bowley’s skewness coefficient differentiates between normal and lognormal distributions. This classifier is robust and easy to calculate from the quartiles Q1–Q3 according to the formula (Q1 − 2 · Q2 + Q3)/(Q3 − Q1). We validate our algorithm with a more complex procedure, which optimizes the exponent λ of a power transformation. As a practical application, we show that Bowley’s skewness coefficient is suited selecting the adequate distribution model for the estimation of reference limits according to a recent International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) recommendation, especially if the data is right-skewed.