Human performance and physiology: A statistical power analysis of ELF electromagnetic field research

Research examining the effects of electromagnetic fields (EMFs) on human performance and physiology has produced inconsistent results; this might be attributable to low statistical power. Statistical power refers to the probability of obtaining a statistically significant result, given the fact that a real effect exists. The results of a survey of published investigations of the effects of EMFs on human performance and physiology show that statistical power levels are very low, ranging from a mean of.08 for small effect sizes to .46 for large effect sizes. Implications of these findings for the interpretation of results are discussed along with suggestions for increasing statistical power. © 1996 Wiley-Liss, Inc.     

Sample Size Calculations for the Mean in a Two Component Nonstandard Mixture Distribution

We are concerned with calculating the sample size required for estimating the mean of the continuous distribution in the context of a two component nonstandard mixture distribution (i.e., a mixture of an identifiable point degenerate function F at a constant with probability P and a continuous distribution G with probability 1 – P). A common ad hoc procedure of escalating the naïve sample size n (calculated under the assumption of no point degenerate function F) by a factor of 1/(1 – P), has about 0.5 probability of achieving the pre‐specified statistical power. Such an ad hoc approach may seriously underestimate the necessary sample size and jeopardize inferences in scientific investigations. We argue that sample size calculations in this context should have a pre‐specified probability of power ≥1 – β set by the researcher at a level greater than 0.5. To that end, we propose an exact method and an approximate method to calculate sample size in this context so that the pre‐specified probability of achieving a desired statistical power is determined by the researcher. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detection of Cyclic Trends in Incidence Data Using the Efficiency Score Method

In studies involving a cyclic regularity, researchers usually have a good working knowledge regarding the peak time in the cycle. Capitalizing on this information, we derive the asymptotically uniformly most powerful unbiased test for detecting a cyclic trend using the likelihood score, and present the asymptotic power function of the test and the approximate formula for sample size. Numerical studies demonstrate great advantages of the proposed test over the standard test in terms of power and sample size. Asymptotic power of the score test is satisfactorily close to actual power. We also generalize this method so that it is applicable for incidence data from unequally spaced intervals or risk populations of unequal size.     

Truncated power laws: a tool for understanding aggregation patterns in animals?

Statistical distributions like the negative binomial distribution are commonly used to describe aggregation patterns in animals. However, recently it has been suggested that truncated power laws (TPLs) may also be used for this kind of analysis. A TPL consists of two power functions separated by a cut-off size ( C *). The cut-off size and the slope of power function one (β₁) for the smallest group sizes have been suggested to have a biological explanatory value.
We applied TPLs to aggregation data of tephritid seed predators on a composite plant, aphids on willows and grey seals on a haulout site. β₁ varied between 0.60 and and −0.72, which is higher than predicted. In addition, resource distribution and animal density influenced β₁ and C *. This indicates that environmental dimensionality suggested to affect β₁ is masked by ecological factors. We conclude that TPLs are useful due to their simplicity and, in comparison with traditional methods, provide additional biologically relevant information. Truncated power laws can therefore prove to be useful in studies of animal behaviour and population dynamics.     

Statistical power in physical anthropology: a technical report

A statistical power analysis of The American Journal of Physical Anthropology (Volume 44, 1976) was conducted. Twenty-five articles, which included 3,304 major significance tests, constituted the final sample. Resultant power estimates of 0.38, 0.62, and 0.81, corresponding to small, medium, and large population effects respectively, were obtained. Although the medium effect size estimate falls short of the recommended 0.80 level, the statistical power of physical anthropological research fares well relative to several of the social scientific fields of inquiry.     

Power calculation for cross-sectional stepped wedge cluster randomized trials with variable cluster sizes

Standard sample size calculation formulas for stepped wedge cluster randomized trials (SW-CRTs) assume that cluster sizes are equal. When cluster sizes vary substantially, ignoring this variation may lead to an under-powered study. We investigate the relative efficiency of a SW-CRT with varying cluster sizes to equal cluster sizes, and derive variance estimators for the intervention effect that account for this variation under a mixed effects model—a commonly used approach for analyzing data from cluster randomized trials. When cluster sizes vary, the power of a SW-CRT depends on the order in which clusters receive the intervention, which is determined through randomization. We first derive a variance formula that corresponds to any particular realization of the randomized sequence and propose efficient algorithms to identify upper and lower bounds of the power. We then obtain an “expected” power based on a first-order approximation to the variance formula, where the expectation is taken with respect to all possible randomization sequences. Finally, we provide a variance formula for more general settings where only the cluster size arithmetic mean and coefficient of variation, instead of exact cluster sizes, are known in the design stage. We evaluate our methods through simulations and illustrate that the average power of a SW-CRT decreases as the variation in cluster sizes increases, and the impact is largest when the number of clusters is small.     

Scaling law in sizes of protein sequence families: from super-families to orphan genes

It has been observed that the size of protein sequence families is unevenly distributed, with few super families with a large number of members and many "orphan" proteins that do not belong to any family. Here it is shown that the distribution of sizes of protein families in different databases and classifications (Protomap, Prodom, Cog) follows a power-law behavior with similar scaling exponents, which is characteristic of self-organizing systems. Since large databases are used in this study, a more detailed analysis of the data than in previous studies was possible. Hence, it is shown that the size distribution is governed by two exponents, different for the super families and the orphan proteins. A simple model of protein evolution is proposed, in which proteins are dynamically generated and clustered into families. The model yields a scaling behavior very similar to the distribution observed in the actual sequence databases, including the two distinct regimes for the large and small families, and thus suggests that the existence of "super families" of proteins and "orphan" proteins are two manifestations of the same evolutionary process.     

电厂温排水增温对浮游动物粒径谱的影响

利用浮游生物Ⅰ(孔径505 μm)、Ⅱ(160 μm)、Ⅲ(77 μm)型拖网所得的10个站位、4个季节丰度数据,以浮游动物生物体积为单位划分粒级,探讨了国华电厂排水口附近海域浮游动物Sheldon型粒径谱和标准化粒径谱的时空变化特征,以期探明海域增温对浮游动物粒径谱影响.结果表明: 浮游动物个体体积范围为0.00012～127.0 mm³·ind^-1,可划分为21个对数粒级组,对数范围为-13.06～6.99.据Sheldon型粒径谱结果,构成不同月份粒径谱主谱峰的主要种类有桡足幼体、墨氏胸刺水蚤、中华哲水蚤、仔鱼、百陶箭虫、拿卡箭虫和球型侧腕水母,小谱峰大多由个体较小的幼体类、剑水蚤类、针刺拟哲水蚤构成.在不同增温区断面中,桡足幼体、鱼卵和剑水蚤类等基本不受增温影响,而大型浮游动物,如百陶箭虫、拿卡箭虫、球型侧腕水母、中华哲水蚤和瓜水母等明显倾向于迁离排水口.从标准化粒径谱参数变化看,截距从低到高分别发生在11、2、5和8月;斜率变化以2月最小,5月与8月斜率相似且较大,表明2月小型浮游动物在群落中所占比例最高,而中大型浮游动物以5月和8月较高.在不同断面中,斜率以距离排水口0.2 km断面最低,且随着断面距离增加而增加,说明距离排水口越近,浮游动物小型化越明显.象山港标准化粒径谱年平均截距为4.68,斜率为-0.655.     

Power analysis and sample size estimation for RNA-Seq differential expression

It is crucial for researchers to optimize RNA-seq experimental designs for differential expression detection. Currently, the field lacks general methods to estimate power and sample size for RNA-Seq in complex experimental designs, under the assumption of the negative binomial distribution. We simulate RNA-Seq count data based on parameters estimated from six widely different public data sets (including cell line comparison, tissue comparison, and cancer data sets) and calculate the statistical power in paired and unpaired sample experiments. We comprehensively compare five differential expression analysis packages (DESeq, edgeR, DESeq2, sSeq, and EBSeq) and evaluate their performance by power, receiver operator characteristic (ROC) curves, and other metrics including areas under the curve (AUC), Matthews correlation coefficient (MCC), and F-measures. DESeq2 and edgeR tend to give the best performance in general. Increasing sample size or sequencing depth increases power; however, increasing sample size is more potent than sequencing depth to increase power, especially when the sequencing depth reaches 20 million reads. Long intergenic noncoding RNAs (lincRNA) yields lower power relative to the protein coding mRNAs, given their lower expression level in the same RNA-Seq experiment. On the other hand, paired-sample RNA-Seq significantly enhances the statistical power, confirming the importance of considering the multifactor experimental design. Finally, a local optimal power is achievable for a given budget constraint, and the dominant contributing factor is sample size rather than the sequencing depth. In conclusion, we provide a power analysis tool (http://www2.hawaii.edu/~lgarmire/RNASeqPowerCalculator.htm) that captures the dispersion in the data and can serve as a practical reference under the budget constraint of RNA-Seq experiments.     

Power laws without complexity

Power laws have been invoked in describing the sizes of a wide variety of objects in evolution and ecology. The apparent ubiquity of power laws is commonly attributed to a form of complex behaviour called self‐organizing criticality. It is shown that power law behaviour inevitably arises from the statistics of large values from heavy‐tailed distributions and that such distributions can be generated by processes that do not involve self‐organized criticality. It follows that power law behaviour cannot be taken as prima facie evidence of self‐organizing criticality.     

Density-dependent mortality,growth and size inequality in roadside populations of the annual herbGalium aparine L.

Biomass, plant size, plant density and the inequality of sizes were assessed for autumn-emerging roadside populations dominated byGalium aparine during early stages of growth in two independent studies. A third data set dealt with the survival of labelled seedlings belonging to different cohorts of emergence. One data set showed that the slope of the log-log size/density relationship for all plant species present in the samples was closer to −1.5 and that forG. aparine was closer to −1.0 in five separate populations. Biomass increase and density decrease was not found to take place in any of these simultaneously. The size inequality ofG. aparine tended to increase or to remain constant during periods of high mortality, and in the early harvests it was negatively related to population density. The second data set revealed simultaneous decreases of both biomass and density ofG. aparine and of all plant species during a period of a month soon after emergence, and a higher size inequality ofG. aparine in those patches where plant density (and that ofG. aparine) was lower. The labelling of seedlings indicated density-dependent mortality and a higher probability of survival for seedlings emerging very early. The size/density relationship of roadside populations dominated byG. aparine may follow a trajectory over time similar to that predicted by the 3/2 power law of self-thinning, but this species seems to have a weak size hierarchy development and limited individual growth at high population densities. The importance of plant architecture in relation to this response is discussed.     

National Forest Inventories in North America for monitoring forest tree species diversity

Abstract

A successful forest tree diversity-monitoring programme delivers reliable estimates of rates of occurrence, the spatial extent and the abundance of all forest-dwelling tree species. Sample-based estimators of these characteristics are provided for North American national forest inventories and discussed in the context of monitoring for forest tree diversity. The expected performance of the Canadian, the United States, and Mexican national forest inventory is quantified for three regions in each country. As expected, estimates for many less common and rare species are imprecise and sometimes these species are missed completely. We suggest augmenting existing national forest inventories by purposive sampling for these species.     

Maternal investment in reproduction and its consequences in leatherback turtles

Maternal investment in reproduction by oviparous non-avian reptiles is usually limited to pre-ovipositional allocations to the number and size of eggs and clutches, thus making these species good subjects for testing hypotheses of reproductive optimality models. Because leatherback turtles (Dermochelys coriacea) stand out among oviparous amniotes by having the highest clutch frequency and producing the largest mass of eggs per reproductive season, we quantified maternal investment of 146 female leatherbacks over four nesting seasons (2001–2004) and found high inter- and intra-female variation in several reproductive characteristics. Estimated clutch frequency [coefficient of variation (CV) = 31%] and clutch size (CV = 26%) varied more among females than did egg mass (CV = 9%) and hatchling mass (CV = 7%). Moreover, clutch size had an approximately threefold higher effect on clutch mass than did egg mass. These results generally support predictions of reproductive optimality models in which species that lay several, large clutches per reproductive season should exhibit low variation in egg size and instead maximize egg number (clutch frequency and/or size). The number of hatchlings emerging per nest was positively correlated with clutch size, but fraction of eggs in a clutch yielding hatchlings (emergence success) was not correlated with clutch size and varied highly among females. In addition, seasonal fecundity and seasonal hatchling production increased with the frequency and the size of clutches (in order of effect size). Our results demonstrate that female leatherbacks exhibit high phenotypic variation in reproductive traits, possibly in response to environmental variability and/or resulting from genotypic variability within the population. Furthermore, high seasonal and lifetime fecundity of leatherbacks probably reflect compensation for high and unpredictable mortality during early life history stages in this species.     

Unscheduled DNA synthesis: Some statistical thoughts

Statistical interpretation of results of experiments involving unscheduled DNA synthesis is examined from a design standpoint. Most appropriate methods currently in use are evaluated and some modifications and extensions are suggested. Concerns about replication and/or interaction errors are evaluated and methods for their appropriate handling are discussed. It is suggested that methods incorporating both dose-response and heterogeneity statistics should be considered in treating results from unscheduled DNA synthesis experiments. Proper designs for such experiments are emphasized.Abbreviations ANOVA analysis of variance - MSE mean square error - UDS unscheduled DNA synthesis     

Statistical power for detecting epistasis QTL effects under the F-2 design

Epistasis refers to gene interaction effect involving two or more genes. Statistical methods for mapping quantitative trait loci (QTL) with epistasis effects have become available recently. However, little is known about the statistical power and sample size requirements for mapping epistatic QTL using genetic markers. In this study, we developed analytical formulae to calculate the statistical power and sample requirement for detecting each epistasis effect under the F-2 design based on crossing inbred lines. Assuming two unlinked interactive QTL and the same absolute value for all epistasis effects, the heritability of additive × additive (a × a) effect is twice as large as that of additive × dominance (a × d) or dominance × additive (d × a) effect, and is four times as large as that of dominance × dominance (d × d) effect. Consequently, among the four types of epistasis effects involving two loci, ''a × a'' effect is the easiest to detect whereas ''d × d'' effect is the most difficult to detect. The statistical power for detecting ''a × a'' effect is similar to that for detecting dominance effect of a single QTL. The sample size requirements for detecting ''a × d'', ''d × a'' and ''d × d'' are highly sensitive to increased distance between the markers and the interacting QTLs. Therefore, using dense marker coverage is critical to detecting those effects.     

A sample size adjustment procedure for clinical trials based on conditional power

When designing clinical trials, researchers often encounter the uncertainty in the treatment effect or variability assumptions. Hence the sample size calculation at the planning stage of a clinical trial may also be questionable. Adjustment of the sample size during the mid-course of a clinical trial has become a popular strategy lately. In this paper we propose a procedure for calculating additional sample size needed based on conditional power, and adjusting the final-stage critical value to protect the overall type-I error rate. Compared to other previous procedures, the proposed procedure uses the definition of the conditional type-I error directly without appealing to an extra special function for it. It has better flexibility in setting up interim decision rules and the final-stage test is a likelihood ratio test.     

Sampling strategy optimization to increase statistical power in landscape genomics: A simulation‐based approach

An increasing number of studies are using landscape genomics to investigate local adaptation in wild and domestic populations. Implementation of this approach requires the sampling phase to consider the complexity of environmental settings and the burden of logistical constraints. These important aspects are often underestimated in the literature dedicated to sampling strategies. In this study, we computed simulated genomic data sets to run against actual environmental data in order to trial landscape genomics experiments under distinct sampling strategies. These strategies differed by design approach (to enhance environmental and/or geographical representativeness at study sites), number of sampling locations and sample sizes. We then evaluated how these elements affected statistical performances (power and false discoveries) under two antithetical demographic scenarios. Our results highlight the importance of selecting an appropriate sample size, which should be modified based on the demographic characteristics of the studied population. For species with limited dispersal, sample sizes above 200 units are generally sufficient to detect most adaptive signals, while in random mating populations this threshold should be increased to 400 units. Furthermore, we describe a design approach that maximizes both environmental and geographical representativeness of sampling sites and show how it systematically outperforms random or regular sampling schemes. Finally, we show that although having more sampling locations (between 40 and 50 sites) increase statistical power and reduce false discovery rate, similar results can be achieved with a moderate number of sites (20 sites). Overall, this study provides valuable guidelines for optimizing sampling strategies for landscape genomics experiments.     

Taylor's law and body size in exploited marine ecosystems

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density‐mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance‐mass allometry). Marine size spectra are known to exhibit density‐mass allometry, but variance‐mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size‐at‐entry fishing, in which only fish above a certain size may legally be caught.     

Assembly of local communities: consequences of an optimal body size for the organization of competitively structured communities

Much empirical evidence suggests that there is an optimal body size for mammals and that this optimum is in the vicinity of l00g. This presumably reflects an underlying fitness function that is greatest at this mass. Here, I combine such a fitness function with an equilibrium model of competitive character displacement to assess the potential influence of a globally optimal body size in structuring local ecological communities. The model accurately predicts the range of body sizes and the average difference in size for species in communities of varying species richness. The model also predicts a uniform spacing of body sizes, rather than the gaps and clumps in the sizes of coexisting species observed in real communities. Alternative explanations for this phenomenon are discussed. The allometric relationships that result in a body size optimum subsume a large number of characteristics associated with the physiological, behavioral, demographic, and evolutionary dynamics of the species. Further integration of the underlying dynamics (e.g. individual energetics) of these relationships into all hierarchical levels of ecology will have to incorporate multiple interactive sites, spatial heterogeneity, and phylogenetic structure, but it has the potential to provide important discoveries into the means by which natural selection operates.