Consequences of ignoring spatial variation in population trend when conducting a power analysis

Long‐term, large‐scale monitoring programs are becoming increasingly common to document status and trends of wild populations. A successful program for monitoring population trend hinges on the ability to detect the trend of interest. Power analyses are useful for quantifying the sample size needed for trend detection, given expected variation in the population. Four components of variation (within‐year variation at a given site, interannual variation within a site, variation among sites in the interannual variation, and variation among sites in mean abundance or density) are commonly considered in power analyses for population trend, but a fifth is rarely considered: variation among sites in the local trend. Spatial variation in trend is expected to reduce statistical power, but the magnitude of this reduction has not been fully explored. We used computer simulations to evaluate the consequences of ignoring spatial variation in trend under a variety of sampling designs and wide ranges of other components of variation. The effect of spatial variation in trend on power was minor when other input parameters took extreme values that made the trend either very difficult or very easy to detect. However, at moderate values of the other parameters, spatial variation in trend had a strong effect, reducing statistical power by up to 60%. In some cases, ignoring spatial variation in trend resulted in an 80% probability of a type I error (falsely detecting a trend in a stable population). Spatial variation in trend is therefore an important consideration when designing a long‐term monitoring program for many species, especially those affected by local conditions at sites that are repeatedly surveyed. If variation in trend is ignored, as in many previous power analyses, the recommended sampling design will likely be insufficient to detect the trend of interest and lead to potentially false conclusions of a stable population.     

Circadian analysis of large human populations: Inferences from the power grid

Few, if any studies have focused on the daily rhythmic nature of modern industrialized populations. The present study utilized real-time load data from the U.S. Pacific Northwest electrical power grid as a reflection of human operative household activity. This approach involved actigraphic analyses of continuously streaming internet data (provided in 5?min bins) from a human subject pool of approximately 43 million primarily residential users. Rhythm analyses reveal striking seasonal and intra-week differences in human activity patterns, largely devoid of manufacturing and automated load interference. Length of the diurnal activity period (alpha) is longer during the spring than the summer (16.64?h versus 15.98?h, respectively; p?<?0.01). As expected, significantly more activity occurs in the solar dark phase during the winter than during the summer (6.29?h versus 2.03?h, respectively; p?<?0.01). Interestingly, throughout the year a “weekend effect” is evident, where morning activity onset occurs approximately 1?h later than during the work week (5:54 am versus 6:52 am, respectively; p?<?0.01). This indicates a general phase-delaying response to the absence of job-related or other weekday morning arousal cues, substantiating a preference or need to sleep longer on weekends. Finally, a shift in onset time can be seen during the transition to Day Light Saving Time, but not the transition back to Standard Time. The use of grid power load as a means for human actimetry assessment thus offers new insights into the collective diurnal activity patterns of large human populations.     

On the resolving power of principal component analysis in plant community ordination

Summary A comparison between centered and non-centered principal component analysis is made on the basis of the resolving power of the methods. The results indicate the appropriateness of using a centered PCA when the aim is an ordination of plant communities, and the noncentered PCA when the aim is to elicit the taxonomic structure of a collection.Contribution from the Working Group for Data-Processing in Phytosociology, International Society for Vegetation Science.This work was supported by the Italian C.N.R. and the Centro di Calcolo dell'Università di Trieste within the framework of a broader project entitled I metodi statistici e le loro applicazioni mediante l'uso dell'elaboratore.     

Analytical and multibody modeling for the power analysis of standing jumps

Two methods for the power analysis of standing jumps are proposed and compared in this article. The first method is based on a simple analytical formulation which requires as input the coordinates of the center of gravity in three specified instants of the jump. The second method is based on a multibody model that simulates the jumps processing the data obtained by a three-dimensional (3D) motion capture system and the dynamometric measurements obtained by the force platforms. The multibody model is developed with OpenSim, an open-source software which provides tools for the kinematic and dynamic analyses of 3D human body models. The study is focused on two of the typical tests used to evaluate the muscular activity of lower limbs, which are the counter movement jump and the standing long jump. The comparison between the results obtained by the two methods confirms that the proposed analytical formulation is correct and represents a simple tool suitable for a preliminary analysis of total mechanical work and the mean power exerted in standing jumps.     

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.     

Hazards of power supplies

Electrophoretic power supplies which are not isolated from the power lines are an unnecessary lethal hazard. Their use should be discouraged.     

用心率变异功率谱研究出生后心率变慢的机理

目的 :探讨神经机制及心源性因素在出生后心率变慢中的作用。方法 :运用心率变异性的频域和时域分析方法 ,主要为功率谱分析方法 ,以不同年龄组的人和家兔为实验对象 ,对出生后心脏的自主神经调控进行初步探讨 ;并通过观察不同年龄组离体灌流兔心 (无神经体液因素影响 )自律性的变化 ,探讨心脏本身因素是否参与出生后心率变慢的调控。结果 :人和家兔迷走交感对心率的调控作用比在各年龄组之间有显著差异 ,且随年龄增长逐渐升高 ;家兔离体心脏的自主心率在各年龄组之间有显著差异 ,且随年龄增长逐渐降低。结论 :出生后心率减慢与神经机制有关 ,也有心脏本身因素的参与     

Statistical power of replicated helicopter surveys in southern African conservation areas

Understanding the ecology of large ungulates in southern Africa requires accurate and precise measures of population size. Recovery or exploitation of ungulates in reserves is currently instigated when population size changes exceed 15% per annum, but monitoring is usually undertaken with single counts from helicopters, for which precision and the power to detect change are untested. In essence, power being the strength of a monitoring result in showing change over time. Retrospective power analysis is a useful technique to investigate the variability of single‐count aerial surveys. Using replicated helicopter‐based counts of southern African ungulates and post hoc analysis, we investigated the power of currently used single‐count surveys across five common ungulate species and 11 wildlife reserves. We expected high variability in count data and set α = 0.1 and 0.2 (α being the type I error rate), and asked two questions: ‘How much does power vary in replicated aerial counts of southern African wildlife across reserves and species?’ and ‘Can current single‐count aerial surveys detect population changes in response to management actions or are the statistical errors intractable?’ Single counts were mostly unreliable; only one of 42 had sufficient power to detect meaningful changes in population size or their trends at α = 0.1, and only three had sufficient power at α = 0.2. Power varied widely according to species (e.g. warthog, median power at α = 0.1; 0.12–0.37: blue wildebeest, median power at α = 0.1; 0.23–0.74), and, within species, between replicates and reserves. Our retrospective calculations demonstrated insensitivity and ineffectiveness in most currently applied single counts from helicopters. Consequently, it is impossible to interpret the effects of ungulate conservation actions on many southern African reserves. Retrospective power analyses enables determination of which previous aerial surveys were useful for population assessment and adaptive management, and which should be discarded. We recommend that prospective power analyses are undertaken to determine future helicopter survey sample size and replication requirements, especially in small reserves.     

Lack of statistical power as a major limitation in understanding MHC‐mediated immunocompetence in wild vertebrate populations

Disentangling the sources of variation in developing an effective immune response against pathogens is of major interest to immunoecology and evolutionary biology. To date, the link between immunocompetence and genetic variation at the major histocompatibility complex (MHC) has received little attention in wild animals, despite the key role of MHC genes in activating the adaptive immune system. Although several studies point to a link between MHC and immunocompetence, negative findings have also been reported. Such disparate findings suggest that limited statistical power might be affecting studies on this topic, owing to insufficient sample sizes and/or a generally small effect of MHC on the immunocompetence of wild vertebrates. To clarify this issue, we investigated the link between MHC variation and seven immunocompetence proxies in a large sample of barn owls and estimated the effect sizes and statistical power of this and published studies on this topic. We found that MHC poorly explained variation in immunocompetence of barn owls, with small‐to‐moderate associations between MHC and immunocompetence in owls (effect size: .1 ≥ r ≤ .3) similar to other vertebrates studied to date. Such small‐to‐moderate effects were largely associated with insufficient power, which was only sufficient (>0.8) to detect moderate‐to‐large effect sizes (r ≥ .3). Thus, studies linking MHC variation with immunocompetence in wild populations are underpowered to detect MHC effects, which are likely to be of generally small magnitude. Larger sample sizes (>200) will be required to achieve sufficient power in future studies aiming to robustly test for a link between MHC variation and immunocompetence.     

Statistical Comparison of Band Spectral Power: An Aid in Stochastical Analysis of Brain Electrical Activity Part 1: Approximation of the distribution of broad band power by a χ2-distribution

In this study the distribution of estimated broad band spectral power is evaluated. Under weak assumptions it is possible to appropriate this distribution by a χ2-distribution and to construct tolerance intervals with great statistical accuracy. The theoretical results implicate a new methodical basis for statistical comparison of spectral parameters in EEG analysis.     

Socio-biological basis of “power” in man

The difference between individual aggressive behaviour and group violence is discussed. While individual aggressive behaviour has a biological background and has evolutionary significance for the survival of the individual and the species, group violence, like human character, is due to cultural imprinting and is against the survival of both individuals and populations (war).     

The role of statistical power analysis in quantitative proteomics

Designing an experiment for quantitative proteomic analysis is not a trivial task. One of the key factors influencing the success of such studies is the number of biological replicates included in the analysis. This, along with the measured variation will determine the statistical power of the analysis. Presented is a simple yet powerful analysis to determine the appropriate sample size required for reliable and reproducible results, based on the total variation (technical and biological). This approach can also be applied retrospectively for the interpretation of results as it takes into account both significance (p value) and quantitative difference (fold change) of the results.     

煤电生产系统的能值分析及新指标体系的构建

煤电生产是我国废弃物粉尘和酸性气体的排放最主要来源.以某2×600MW超临界燃煤发电机组为案例,按传统能值指标体系分别对简单发电系统、发电加除尘系统和发电加除尘脱硫系统进行能值分析.结果表明,投入废物循环利用系统后可持续性指标反而下降.因此,传统的能值指标已不适合废弃物产生较大的煤电生产系统的可持续性评价.针对这一特点,提出了能反映煤电生产系统的相应指标体系,即有效能值产出率(EEYR)、能值环境影响率(EEIR)、有效能值可持续指数(EESI),计算得出简单发电系统、发电加除尘系统和发电加除尘脱硫系统的EESI分别为2.249、2.628、2.642.随着废物处理程度的提高,系统的可持续性更好,显示出环保系统投入的积极意义.     

Unholey shoes: Experimental considerations when estimating ankle joint complex power during walking and running

For studies that aim to assess biological ankle function, calculating ankle joint complex (AJC) power between the calcaneus and shank is recommended over conventional inverse dynamics estimates between a rigid-body foot and shank. However, when designing a new experiment, it remains unclear whether holes should be cut in footwear to permit motion tracking via skin-mounted markers, or whether marker placement locations should be tightly controlled across conditions. Here we provide data to assist researchers in answering these questions. We performed a gait analysis study of walking (0.8, 1.2, 1.6 m·s⁻¹) and running (2.6, 2.8, 3.0 m·s⁻¹) while subjects (N = 10) wore custom-modified footwear, which allowed markers to be placed either on the shoe, or on the skin via cut-out windows in the shoes. First, we compared foot markers affixed to the skin vs. on the same locations on the shoe. Using statistical non-parametric mapping techniques, we discovered that skin vs. shoe markers had no statistically significant effect on net AJC power estimates throughout stance phase, for all walking and running speeds. Second, we compared calcaneal markers in the nominal shoe configuration vs. markers in a nearby location (∼27 mm below) on the shoe. We observed significant differences when marker placement on the shoe was varied, which may be relevant to repeated-measures study designs. The results suggest that when computing AJC power for walking and running, you may want to put down the scissors (i.e., forego cutting holes in your footwear), and instead pick up a Sharpie® (pen) or use a template, to maintain consistent marker placement across trials and conditions.     

Relationship between aerobic fitness and metabolic power metrics in elite male soccer players

The aim was to assess the relationship between aerobic fitness and metabolic power metrics in elite male soccer players, and the possible differences that playing positions might impose during match play over new metabolic power metrics. Sixty-two elite professional male soccer players (13 central backs, 13 side backs, 22 midfielders, and 14 forwards) took part in the study. Players were monitored during eleven months of full training (including pre-season and in-season) and over all official matches (Serie A matches, Italy Cup matches). Aerobic fitness tests were conducted one week after the start of the preseason, and 8, 24 and 36 weeks after the beginning of the Championship. Players’ aerobic fitness and metabolic power metrics were considered as the mean of all seasonal testing and of pooling data of 38 championship matches and 3 or 6 Italy Cup matches for all the calculations respectively. The velocity at 4 mmol·L^-1 (VL₄) was significantly related to metabolic power metrics match variables with correlation ranging from trivial to very large (r = 0.32 to r = 0.89). Receiver-operating-characteristic (ROC) analysis showed that speed at VL₄ was sensitive in detecting high metabolic power distance (HMPD) changes in all but central back players as revealed by area under the curve (central back .78, 95%CI .47 to .95; full back .93, 95%CI .64 to 0.99; midfielder .88, 95%CI .67 to 0.98; forward .90, 95%CI .62 to 0.99). This study’s findings provide further evidence for the ecological validity of aerobic fitness in elite male soccer players. Players having a HMPD cut-off equal to or higher than > 1450 m for central backs, > 1990 m for full backs, > 2170 m for midfielders and > 1670 m for forwards may be considered as possessing superior aerobic fitness status. In light of this study’s findings, the VL₄ test may be considered a valid test to evaluate meaningful information for direct generic aerobic training in soccer players.     

Spatial heterogeneity in a grassland community: Use of power law

A new regression analysis was proposed to evaluate the degree of spatial heterogeneity for individual species comprising a plant grassland community. The weighted average of the heterogeneity value of all the species comprising the community provides a measure of community-level heterogeneity. A field survey was carried out, as an example, in order to analyze the spatial heterogeneity of a pasture with grazing cows, using 100 quadrats 50 cm × 50 cm, each of which was divided into four smaller quadrats 25 cm × 25 cm, on a 50 m long line-transect. The frequency of occurrence for all the species in each small quadrat was recorded. The regression associated with the ratio of the theoretical and observed variances of occurence counts was used to analyse the frequency distribution of species in a pasture community. A good fit to the regression for the whole community was obtained. These results indicate that (i) each species in the example was distributed more heterogeneously than a random pattern; and (ii) the regression could well describe the spatial heterogeneity of the grassland plant community. In most of the observed species, spatial heterogeneity is often characterized by species-specific propagation traits and the architecture of plant bodies. Thus, the spatial patterns of a grassland community can be evaluated in detail by this power-law approach. This measure is suitable for field surveys and comparative studies of grassland communities, and for other plant communities that are generally short in height.     

Gender differences in anaerobic power tests

The purpose of this study was to determine if the differences in anaerobic power between males and females could be accounted for by differences in body composition, strength, and neuromuscular function. A total of 82 untrained men and 99 women took part in the study. Body composition, somatotype, isometric strength, neuromuscular function were measured, and four anaerobic power tests performed. The men were significantly different from the women on all strength, power, and neuromuscular measurements except reaction time and on all anthropometric and somatotype dimensions except ectomorphy. Strength and anthropometric dimensions were similarly related to anaerobic power values within each sex. Relative fat (%fat) exerted different degrees of influence on sprint and jump performances in each sex. Removing the influence of anthropometric, strength, and neuromuscular differences by analysis of covariance reduced, but did not remove, the significant differences between the sexes. Therefore, factors other than lean body mass, leg strength, and neuromuscular function may be operating in short-term, explosive power performances to account for the differences between the sexes. The task-specific nature of anaerobic power tests and the relatively large influence of anthropometric factors on power production were confirmed.     

Coaxial lines for multiphase power distribution

A coaxial cable can be used to reduce the magnetic and electric fields that extend into environments in the vicinity of transmission lines and distribution lines and in-house or building wiring for power distribution systems. The use of the coaxial geometry may prove useful in cases where there are environmental concerns with respect to health effects and in cases where there is a need to run high-speed data communications in close proximity to power distribution systems. © 1996 Wiley-Liss, Inc.