Joseph F. Mudge

Setting an optimal α that minimizes errors in null hypothesis significance tests.

Null hypothesis significance testing has been under attack in recent years, partly owing to the arbitrary nature of setting α (the decision-making threshold and probability of Type I error) at a constant value, usually 0.05. If the goal of null hypothesis testing is to present conclusions in which we have the highest possible confidence, then the only logical decision-making threshold is the value that minimizes the probability (or occasionally, cost) of making errors. Setting α to minimize the combination of Type I and Type II error at a critical effect size can easily be accomplished for traditional statistical tests by calculating the α associated with the minimum average of α and β at the critical effect size. This technique also has the flexibility to incorporate prior probabilities of null and alternate hypotheses and/or relative costs of Type I and Type II errors, if known. Using an optimal α results in stronger scientific inferences because it estimates and minimizes both Type I errors and relevant Type II errors for a test. It also results in greater transparency concerning assumptions about relevant effect size(s) and the relative costs of Type I and II errors. By contrast, the use of α = 0.05 results in arbitrary decisions about what effect sizes will likely be considered significant, if real, and results in arbitrary amounts of Type II error for meaningful potential effect sizes. We cannot identify a rationale for continuing to arbitrarily use α = 0.05 for null hypothesis significance tests in any field, when it is possible to determine an optimal α.

C60 Fullerene Soil Sorption, Biodegradation, and Plant Uptake

Assessments of potential exposure to fullerenes and their derivatives in the environment are important, given their increasing production and use. Our study focused on fate processes that determine the movement and bioavailability of fullerenes in soil. We evaluated the sorption, biodegradation, and plant uptake of C60 fullerene using (14)C-labeled C60 solutions in water produced by either solvent exchange with tetrahydrofuran or sonication/extended mixing in water. Organic carbon appeared to have an important influence on C60 soil sorption. The log Koc values for (14)C60 were equivalent for sandy loam and silt loam (3.55 log[mL/g]) but higher for loam (4.00 log[mL/g]), suggesting that other factors, such as pH, clay content and mineralogy, and cation exchange capacity, also influence C60 soil sorption. There was little (14)CO2 production in the silt loam or the sandy loam soil after 754 and 328 days, respectively, suggesting high resistance of C60 to mineralization in soil. Plant uptake was generally low (∼7%), with most of the uptaken (14)C accumulating in the roots (40-47%) and smaller amounts of accumulation in the tuber (22-23%), stem (12-16%), and leaves (18-22%). Our results indicate that C60 released to the environment will not be highly bioavailable but will likely persist in soil for extended periods.

The direct and indirect effects of a glyphosate‐based herbicide and nutrients on Chironomidae (Diptera) emerging from small wetlands

Laboratory and mesocosm experiments have demonstrated that some glyphosate-based herbicides can have negative effects on benthic invertebrate species. Although these herbicides are among the most widely used in agriculture, there have been few multiple-stressor, natural system-based investigations of the impacts of glyphosate-based herbicides in combination with fertilizers on the emergence patterns of chironomids from wetlands. Using a replicated, split-wetland experiment, the authors examined the effects of 2 nominal concentrations (2.88 mg acid equivalents/L and 0.21 mg acid equivalents/L) of the glyphosate herbicide Roundup WeatherMax, alone or in combination with nutrient additions, on the emergence of Chironomidae (Diptera) before and after herbicide-induced damage to macrophytes. There were no direct effects of treatment on the structure of the Chironomidae community or on the overall emergence rates. However, after macrophyte cover declined as a result of herbicide application, there were statistically significant increases in emergence in all but the highest herbicide treatment, which had also received no nutrients. There was a negative relationship between chironomid abundance and macrophyte cover on the treated sides of wetlands. Fertilizer application did not appear to compound the effects of the herbicide treatments. Although direct toxicity of Roundup WeatherMax was not apparent, the authors observed longer-term impacts, suggesting that the indirect effects of this herbicide deserve more consideration when assessing the ecological risk of using herbicides in proximity to wetlands.

Explicit consideration of critical effect sizes and costs of errors can improve decision-making in plant science.

Ensuring that sound science informs policy decisions has been suggested as one of themost important societal issues faced by plant scientists in the twenty-first century (Grierson et al., 2011). Plant scientists therefore are responsible for ensuring that data are analyzed and presented in a way that facilitates good decisionmaking. Good statistical practices can be an important tool for ensuring objective and transparent and data analysis. Despite frequent criticism over the last few decades (Cohen, 1994; Gigerenzer, 2004; Rinella & James, 2010), null hypothesis significance testing (NHST) remains widely used in plant science. While others have argued that the persistence of NHST is due to ignorance of alternative approaches or resistance to change (Fidler et al., 2004; Gigerenzer et al., 2004), its persistence is likely at least partly due to its usefulness as a decision-making tool (Robinson & Wainer, 2002; Mogie, 2004; Stephens et al., 2007). Are different plant species equivalent in their ability to remediate toxic land? Are different management actions equivalent in their ability to control invasive plant species? Are there differences in antibiotic activity among different plant metabolites? Do more diverse plant communities provide greater levels of a particular ecosystem service than less diverse plant communities? Each of these questions could be appropriately answered using null hypothesis significance tests. Other tests might also be appropriate, but it would not be wrong to use NHST. The utility of NHST as a decision-making tool does not, however, warrant ignoring the problems that are associated with these statistical tests. The problems associated with NHST need to be addressed in order for it to better informpolicy decisions that involve plant science. The major flaws of NHST primarily surround the use of an arbitrary threshold for judging statistical significance. Although the use of a = 0.05 does represent a common criterion for Type I errors that everyonemust adhere to, consistent use of this threshold results in Type II error rates that vary wildly among studies. The value of 0.05 as a significance criterion has no logical foundation, nor does the practice of holdingType I errors consistent while allowingType II errors to vary (Cowles & Davis, 1982). Consistent use of an arbitrary significance threshold also causes statistical significance to frequently differ from biological significance (Mart ınez-Abra ın, 2008) and makes significance heavily influenced by sample size (Johnson, 1999), with high sample sizes tending to make even trivial effects statistically significant (Nakagawa & Cuthill, 2007) and low sample sizes leading to even large effects being considered non-significant (Sedlmeier & Gigerenzer, 1989). Use of a consistent significance threshold regardless of sample size has contributed to frequent misinterpretations of P-values as being ‘highly significant’ or ‘marginally significant’, and/or as measures of how likely the alternate hypothesis is to be true (Hubbard & Bayarri, 2003). If using a consistent arbitrary significance level is problematic, how should significance levels be set? I argue that the significance threshold for a null hypothesis significance test should be set to achieve the goal of the statistical test. One (and perhaps the only) reasonable goal ofNHST is tominimize the chances and/or costs of making wrongful conclusions concerning a set of collected data. If the goal of NHST is tominimize the chances and/or costs of errors, then the decision-making threshold (a) should be set to minimize the combined probabilities and/or combined costs of Type I and Type II errors.Mudge et al. (2012a) describe a general approach for calculating study-specific optimal significance levels that minimize the combined probabilities and/or costs of Type I errors under the null hypothesis and Type II errors under the alternate hypothesis. The optimal a approach for null hypothesis significance tests is paralleled by signal detection theory in electrical engineering (Peterson et al., 1954) and psychology (Green & Swets, 1966) and has recently been applied in environmental monitoring (Mudge et al., 2012b) and physiology (Mudge et al., 2012c). The calculation of an optimal significance level requires estimates of the same parameters that are needed to calculate statistical power for a null hypothesis significance test (sample size and a critical effect size relative to variability) and also requires an estimate of the relative costs of Type I vs Type II error, to minimize the combined costs of Type I and Type II error (the relative prior probabilities of null and alternate hypotheses, if known, can also be incorporated into the calculation of an optimal significance level, however studies with prior probability estimates typically employ Bayesian statistical methods). Although the need to explicitly consider and specify a critical effect size relative to variability and the relative costs of Type I vs Type II error may appear to constitute a barrier to calculating optimal significance levels in plant science, it should not be viewed as such. Critical effect sizes, costs of errors and prior probabilities of null and alternate hypotheses are important to consider for any research question, and failure to incorporate them into the statistical decision-making threshold leads to implicit and unexamined assumptions about them when using a = 0.05. A critical effect size is the smallest size of effect that would be considered biologically meaningful if it were to exist. What is the minimum meaningful magnitude of antibiotic activity for a plant metabolite? How much variability among different management actions is enough to warrant a change in management policy for controlling invasive plant species? What is a biologically meaningful strength of relationship between plant species diversity and

Statistical reporting deficiencies in environmental toxicology.

Null hypothesis significance testing is one of the most widely used forms of statistical testing in environmental toxicology. In this short communication, the authors show that the reporting of statistical information when using null hypothesis significance testing is frequently inadequate in environmental toxicology research. The authors demonstrate this by analyzing the statistical information reported for papers employing t tests or analyses of variance in the Environmental Toxicology section of Environmental Toxicology and Chemistry in 2010, which comprised 68% of papers published by this journal in that year. Of these papers, 60% fail to report exact p values, 85% fail to provide degrees of freedom, and 90% fail to report critical effect sizes. Statistical power was reported in only <2% of the published papers. The insufficient provision of statistical information makes interpretation of study results by reviewers and readers difficult. Consistently reporting exact p values with degrees of freedom, considering and explicitly stating biologically relevant critical effect sizes, and reporting statistical power associated with nonsignificant results would be easy to implement and would promote scientific progress in environmental toxicology through increased statistical transparency.

Temporal monitoring of perfluorooctane sulfonate accumulation in aquatic biota downstream of historical aqueous film forming foam use areas

Perfluoroalkyl substances (PFAS) have recently received increased research attention, particularly concerning aquatic organisms and in regions of exposure to aqueous film forming foams (AFFFs). Air Force bases historically applied AFFFs in the interest of fire training exercises and have since expressed concern for PFAS contamination in biota from water bodies surrounding former fire training areas. Six PFAS were monitored, including perfluorooctane sulfonate (PFOS), in aquatic species from 8 bayou locations at Barksdale Air Force Base in Bossier City, Louisiana (USA) over the course of 1 yr. The focus was to evaluate temporal and spatial variability in PFAS concentrations from historic use of AFFF. The PFOS concentrations in fish peaked in early summer, and also increased significantly downstream of former fire training areas. Benthic organisms had lower PFOS concentrations than pelagic species, contrary to previous literature observations. Bioconcentration factors varied with time but were reduced compared with previously reported literature values. The highest concentration of PFOS in whole fish was 9349 ng/g dry weight, with 15% of samples exceeding what is believed to be the maximum whole fish concentration reported to date of 1500 ng/g wet weight. Further studies are ongoing, to measure PFAS in larger fish and tissue-specific partitioning data to compare with the current whole fish values. The high concentrations presently observed could have effects on higher trophic level organisms in this system or pose a potential risk to humans consuming contaminated fish. Environ Toxicol Chem 2017;36:2022-2029.

Optimizing α for better statistical decisions: A case study involving the pace‐of‐life syndrome hypothesis

Setting optimal significance levels that minimize Type I and Type II errors allows for more transparent and well‐considered statistical decision making compared to the traditional α = 0.05 significance level. We use the optimal α approach to re‐assess conclusions reached by three recently published tests of the pace‐of‐life syndrome hypothesis, which attempts to unify occurrences of different physiological, behavioral, and life history characteristics under one theory, over different scales of biological organization. While some of the conclusions reached using optimal α were consistent to those previously reported using the traditional α = 0.05 threshold, opposing conclusions were also frequently reached. The optimal α approach reduced probabilities of Type I and Type II errors, and ensured statistical significance was associated with biological relevance. Biologists should seriously consider their choice of α when conducting null hypothesis significance tests, as there are serious disadvantages with consistent reliance on the traditional but arbitrary α = 0.05 significance level.