Development of the software tool Sample Size for Arbitrary Distributions and exemplarily applying it for calculating minimum numbers of moss samples used as accumulation indicators for atmospheric deposition

Abstract

Background: Do we measure enough to calculate statistically valid characteristic values from random sample measurements, or do we measure too much-without any further increase in knowledge? This question is actually one of the key issues of every empirical measurement design, but is rarely investigated in environmental monitoring. Results: In this study, the methodology used for the design of the German Moss Survey 2015 network to determine statistically valid minimum sample numbers (MSN) for the calculation of the arithmetic mean value in compliance with certain accuracy requirements was further developed for data that are neither normally nor lognormally distributed. The core element of the procedure for estimating MSN without prerequisite to the distribution of data is an iterative Monte Carlo simulation. The methodological principle consists of using reference data (values measured in Moss Surveys preceding that in 2015) for a series of MSN candidate values to determine what accuracy would be achieved with these, and then calculating the MSN with which the specified accuracy requirement is met from a quadratic function between MSN candidates and their accuracy. The program Sample Size for Arbitrary Distributions (SSAD) was developed for the calculation of the MSN in the open programming language R. Conclusions: The SSAD procedure closes a gap in the existing methodology for calculating statistically valid minimum sample numbers.