title: Complications with using ratios for environmental data: comparing enantiomeric ratios (ERs) and enantiomer fractions (EFs).
abstract: Complications arise when ratios are used to present environmental data because ratios are an unbounded, multiplicative scale that can lead to asymmetrical (skewed) data distributions. Enantiomeric ratios (ERs), historically used in discussions of chiral signatures, often are published as mean ER+/-single-value standard deviation. Application of statistical summaries, such as the widely used sample mean and standard deviation, to skewed ratio data is misleading and often inappropriate. Comparison of statistically summarized ER and enantiomer fraction (EF) data (which are based on a bounded, additive scale) for a range of hypothetical values reveals substantial discrepancies when conversion between ER and EF formats is used. These discrepancies are largest when the ratio data are greater than one and have large variability, because the data are more skewed. In many cases, the use of fractions instead of ratios can help to minimize misrepresentation of environmental data, including chiral data. The use of nonparametric statistical summaries, e.g., median and percentiles, provides a more robust indicator of the typical value and spread for both ER and EF data.
authors.affiliation: U.S. Geological Survey, National Water Quality Laboratory, Denver, CO 80225, USA.
authors.forename: Elin M
authors.initials: EM
authors.lastname: Ulrich
authors.forename: Dennis R
authors.initials: DR
authors.lastname: Helsel
authors.forename: William T
authors.initials: WT
authors.lastname: Foreman
mesh_terms: D003627:Data Interpretation, Statistical; D004784:Environmental Monitoring / Q000379:methods*; D012107:Research Design / Q000706:statistics & numerical data*; D018709:Statistics, Nonparametric