Statistical assessment of data sets for indoor air and house dust from the environmental survey GerES V using non-linear regression analysis, non-parametric methods and Monte-Carlo simulations

Abstract

Environmental surveys are essential tools to investigate the impact of pollutants on the living and non-living environment. Their data often form a basis to derive recommendations for preventive measures protecting health and ecosystems and identify the need for political action. Therefore, representative environmental data sets need to be free of systematic artifacts; their statistical structure should be explored and understood as good as possible. The German Environmental Survey (GerES) is a nationwide study conducted at unregular intervals. The data collected within the GerES V (2014–2017) campaign is important for recording and assessing pollutants in households with children and adolescents. Due to its sampling characteristics, GerES claims to be representative of the population in Germany and, with its standardized measurements and sampling protocols, as well as the selection of sampling points, provides a prime example of a study on the statistical nature of pollutants concentrations. In this work data sets from 19 pollutants in indoor air and house dust were selected from the GerES V pool. The parameters obtained from descriptive statistics were compared with the modeled data of a lognormal probability function and a lognormal cumulative density function. Confidence intervals were calculated using a bootstrap method. Monte-Carlo simulations were used to quantify uncertainties in estimators of theoretical distribution assumptions and to investigate the influence of classifying data into equidistant intervals (bins) on nonlinear regression analysis with respect to data count and bin width. The results of our study provide better insight into the general statistical nature of environmental observations, enabling a more reliable assessment of the parameters derived from the data. © 2026 The Authors.