Permutation/randomization-based inference for environmental data.

Quantitative inference from environmental contaminant data is almost exclusively from within the classic Neyman/Pearson (N/P) hypothesis-testing model, by which the mean serves as the fundamental quantitative measure, but which is constrained by random sampling and the assumption of normality in the data. Permutation/randomization-based inference originally forwarded by R. A. Fisher derives probability directly from the proportion of the occurrences of interest and is not dependent upon the distribution of data or random sampling. Foundationally, the underlying logic and the interpretation of the significance of the two models vary, but inference using either model can often be successfully applied. However, data examples from airborne environmental fungi (mold), asbestos in settled dust, and 1,2,3,4-tetrachlorobenzene (TeCB) in soil demonstrate potentially misleading inference using traditional N/P hypothesis testing based upon means/variance compared to permutation/randomization inference using differences in frequency of detection (Δf d). Bootstrapping and permutation testing, which are extensions of permutation/randomization, confirm calculated p values via Δf d and should be utilized to verify the appropriateness of a given data analysis by either model.

Bioaerosol data distribution: probability and implications for sampling in evaluating problematic buildings.

Airborne fungal contamination in the indoor environment is a substantial contributor to indoor air quality (IAQ) problems, yet there are no set numerical standards by which to evaluate air sampling data. Intuitively appealing is the operational model that the indoor air should not be significantly different from the outdoor air, but determining what is "significant" as well as where to sample and how many samples to collect to determine significance have not been firmly established. The purpose of this study was to determine the number of samples and their locations necessary to determine significant differences in airborne fungi between the ambient and indoor environments. Sampling results from several hundred air samples for culturable fungi from various sites were used to derive a probability of detection in the outdoor air for problematic or "marker" fungal species. Under the assumption that indoor fungal growth results in an increase in the probability of detection for a given fungal species, mathematical probability dictates the number of samples necessary in the indoor (target zone) and in the outdoor (reference zone) air to demonstrate significance. Ultimately, it is the sparse distribution of the problematic species that drives the number of required samples to demonstrate a significant difference, which varies depending upon the level of significance desired. Therefore, the number of samples in each zone can be adjusted to reach a target difference in detection frequency, or an investigator can assess a sampling scheme to identify the differences in detection frequency that show significance.