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This study examines the residential self-selection issue from conceptual and methodological aspects, with an empirical application. The study was motivated by the challenge of interpreting the results of an endogenous switching model and the lack of convenient/proper equations for calculating treatment effects when the dependent variable is log-transformed. We classify expected returns from living in a certain kind of area (urban vs. non-urban) into location-related versus transportation-related, and economic versus lifestyle, aspects. From that, we note that the outcome variable of interest to this study among many others—vehicle-miles driven (VMD)—may not correspond to the returns an individual is seeking to optimize when choosing where to live. Previous studies tend to expect negative error correlations between selection and outcome equations, on the presumption that urbanite people would desire to drive less (so, unobserved traits increasing the utility of an urban neighborhood should also tend to decrease VMD). However, given the variety of possible expected returns, we argue that error correlations (and thus the directions of selection corrections) could be either positive or negative. As an empirical application, we apply the endogenous switching model to modeling VMD, where the treatment is living in an urban area (vs. living in a less urban area). In addition, the paper provides conceptual and graphical illustrations to improve the understanding of treatment effects and their mathematical mechanisms. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new distribution developed using the alpha power transformation, called the alpha power exponentiated generalized Pareto distribution. This distribution is particularly useful for analyzing heavy-tailed data and for financial risk management. We provide important mathematical properties of the proposed distribution, including its linear representation, moment-generating function, moments, and order statistics. The model parameters are estimated using the methods of maximum likelihood, least squares, and Cramér–von Mises estimation. We evaluate the performance of these estimation methods through simulation studies. Additionally, we apply the APEGP distribution to real-life financial data and demonstrate its effectiveness in calculating Value at Risk, showcasing its suitability for assessing potential losses in financial contexts. [ABSTRACT FROM AUTHOR]

This work deals with a semilinear system of parabolic partial differential equations (PDEs) on an unbounded domain, related to environmental pollution modeling. Although we study a one-dimensional sub-model of a vertical advection–diffusion, the results can be extended in each direction for any number of spatial dimensions and different boundary conditions. The transformation of the independent variable is applied to convert the nonlinear problem into a finite interval, which can be selected in advance. We investigate the positivity of the solution of the new, degenerated parabolic system with a non-standard nonlinear right-hand side. Then, we design a fitted finite volume difference discretization in space and prove the non-negativity of the solution. The full discretization is obtained by implicit–explicit time stepping, taking into account the sign of the coefficients in the nonlinear term so as to preserve the non-negativity of the numerical solution and to avoid the iteration process. The method is realized on adaptive graded spatial meshes to attain second-order of accuracy in space. Some results from computations are presented. [ABSTRACT FROM AUTHOR]

Tree care license requirements are expected to improve service quality and provider competencies. The study elicits the licensing fee Georgia firms would pay using survey data from 153 tree care firms. An empirical relationship identifies firm characteristics that influence the fee size using the inverse hyperbolic sine transformation function. Results show that respondents who propose higher annual licensing fees are on average younger, more educated, male, and likely to agree that mandatory licensing is necessary to establish professionalism in the tree care industry. Also, those often engaged in tree trimming services and firms with higher annual revenues contemplate paying higher licensing fees. [ABSTRACT FROM AUTHOR]

This study was performed to improve the ability to predict the concentrations of Escherichia coli in oyster meat and estuarine waters by using environmental parameters, and microbiological and heavy metal contamination from shellfish growing area in southern Thailand. Oyster meat (n = 144) and estuarine waters (n = 96) were tested for microbiological and heavy metal contamination from March 2016 to February 2017. Prevalence and mean concentrations of E. coli were 93.1% and 4.6 × 103 most probable number (MPN)/g in oyster meat, and 78.1% and 2.2 × 102 MPN/100 mL in estuarine water. Average 7-day precipitation, ambient air temperature, and the presence of Salmonella were associated with the concentrations of E. coli in oyster meat (p < 0.05). Raw data (MPN/g of oyster meat and MPN/100 mL of estuarine water) and log-transformed data (logMPN/g of oyster meat and logMPN/100 mL of estuarine water) of E. coli concentrations were examined within two contrasting regression models. However, the more valid predictions were conducted using non-log transformed values. These findings indicate that non-log transformed data can be used for building more accurate statistical models in microbiological food safety, and that significant environmental parameters can be used as a part of a rapid warning system to predict levels of E. coli before harvesting oysters.

Dunkleosteus terrelli, an arthrodire placoderm, is one of the most widely recognized fossil vertebrates due to its large size and status as one of the earliest vertebrate apex predators. However, the exact size of this taxon is unclear due to its head and thoracic armor being the only elements of its body regularly preserved in the fossil record. Lengths of 5–10 m are commonly cited, but these estimates are not based on rigorous statistical analysis. Here, I estimate the body size of D. terrelli using a new metric, orbit-opercular length, and a large dataset of arthrodires and extant fishes (3169 observations, 972 species). Orbit-opercular length strongly correlates with total length in fishes (r2 = 0.947, PEcf = 17.55%), and accurately predicts body size in arthrodires known from complete remains. Applying this method to Dunkleosteus terrelli results in much smaller sizes than previous studies: 3.4 m for typical adults (CMNH 5768) with the largest known individuals (CMNH 5936) reaching ~4.1 m. Arthrodires have a short, deep, and cylindrical body plan, distinctly different from either actinopterygians or elasmobranchs. Large arthrodires (Dunkleosteus, Titanichthys) were much smaller than previously thought and vertebrates likely did not reach sizes of 5 m or greater until the Carboniferous. [ABSTRACT FROM AUTHOR]

When studying large multiparametric databases with very heterogeneous parameters (microbiological, chemical, and physicochemical), covering a wide and heterogeneous area, the probability of observing extreme values (Z-score > 2.5) is high. The information carried by these few samples monopolizes a large part of the information conveyed by the entire database. The study of the spatial structure of the data and the identification of the mechanisms responsible for the water quality are then strongly degraded. Data transformation can be proposed to overcome these problems. This study deals with a database of 8110 groundwater analyses (Occitanie region, France), on which the bacteriological load was measured in Escherichia coli and Enterococci, in addition to electrical conductivity, major ions, Mn, Fe, As and pH. Three modes of data conditioning were tested and compared to the treatment with raw data. The results show that log transformation is the best option, revealing a relationship between E. coli content and all the other parameters. By reducing the impact of extreme values without eliminating them, it allowed a concentration of information on the first factorial axes of the PCA, and consequently a better definition of the associated processes. The spatial structure of the principal components and their cartographic representation is improved. The conditioning of the data with the square root function led to an intermediate improvement between the logarithmic transformation and the absence of conditioning. The application of these results should allow a targeted, more efficient, and therefore, less expensive monitoring of water quality by Regional Health Agencies. [ABSTRACT FROM AUTHOR]

Background: While dealing with skewed outcome, researchers often use log-transformation to convert the data into normal and apply commonly used statistical tests like t-test, linear regression, etc. However, the log-transformed data will not be normal at all times. In such situations, Box-Cox transformation (BCT) can be used to transform skewed data into normal. However, the problem arises when researcher wanted to predict the outcome in original scale. Therefore the aim of this paper is to demonstrated the use of BCT for a skewed outcome and predict the outcome in original scale, using regression method. Materials and method: The Cost of Pyelonephritis in Type-2 Diabetes (COPID) study data was used to demonstrate the BCT and back transformation method. This study conducted among patients admitted in the general medical wards in a tertiary care hospital from south India. The BCT was applied for total cost to convert it into normal. The multiple linear regression method was used and the predicted values were back transformed into original scale. Results: The estimated lambda was −0.36. After BCT, total cost was approximately normal (p-value = 0.621). The residual plots suggested that the error follows normal and the variance is constant. The median (IQR) of the observed total cost was 57694(42405, 98621) whereas predicted total cost was 58317(44270, 95375). Conclusion: When the data is skewed, the log-transformation is not appropriate in all scenarios. However, BCT will ensure normal distribution after transformation and also we can back transform the outcome in original scale given the covariates.

The shape of the relationship between a continuous exposure variable and a binary disease variable is often central to epidemiologic investigations. This article investigates a number of issues surrounding inference and the shape of the relationship. Presuming that the relationship can be expressed in terms of regression coefficients and a shape parameter, we investigate how well the shape can be inferred in settings which might typify epidemiologic investigations and risk assessment. We also consider a suitable definition of the median effect of exposure, and investigate how precisely this can be inferred. This is done both in the case of using a model acknowledging uncertainty about the shape parameter and in the case of ignoring this uncertainty and using a two‐step method, where in step one we transform the predictor and in step two we fit a simple logistic model with transformed predictor. All these investigations require a family of exposure‐disease relationships indexed by a shape parameter. For this purpose, we employ a family based on the Box–Cox transformation. [ABSTRACT FROM AUTHOR]

There are numerous types of continuous and positively skewed data. We develop a hierarchical Bayesian generalized gamma regression model for continuous and positively skewed data. For skewed data, the log-transformation is one of the widely used transformation to meet the normality assumption. However, log-transformation could be problematic, so we use a generalized gamma distribution instead. Because the posterior distribution corresponding to this model is complex, we have used a second order Taylor's series to obtain approximate multivariate normal distributions, which provide proposal densities for Metropolis samplers. We have applied our models to consumption data from a national household survey and chose the best-fitted model among the generalized gamma distribution and two special cases, the gamma and the exponential distributions. It is then linked to census data to provide small area estimates for poverty indicators. A simulation study shows that our methodology is reasonable. [ABSTRACT FROM AUTHOR]

The non-parametric kernel density estimation is used in practice to estimate population abundance using the line transect sampling method. Kernel estimator of f(0) usually produces an underestimated value. Assuming the kernel method, this article applies shifted logarithmic transformation to line transect data that violating shoulder condition. Mathematically, the proposed log-transform estimator was shown to be more efficient than the classical kernel estimator. The simulation results present the good properties of the proposed estimator compared to the performance of the classical kernel estimators. [ABSTRACT FROM AUTHOR]

Abstract Background In healthcare research, outcomes with skewed probability distributions are common. Sample size calculations for such outcomes are typically based on estimates on a transformed scale (e.g. log) which may sometimes be difficult to obtain. In contrast, estimates of median and variance on the untransformed scale are generally easier to pre-specify. The aim of this paper is to describe how to calculate a sample size for a two group comparison of interest based on median and untransformed variance estimates for log-normal outcome data. Methods A log-normal distribution for outcome data is assumed and a sample size calculation approach for a two-sample t-test that compares log-transformed outcome data is demonstrated where the change of interest is specified as difference in median values on the untransformed scale. A simulation study is used to compare the method with a non-parametric alternative (Mann-Whitney U test) in a variety of scenarios and the method is applied to a real example in neurosurgery. Results The method attained a nominal power value in simulation studies and was favourable in comparison to a Mann-Whitney U test and a two-sample t-test of untransformed outcomes. In addition, the method can be adjusted and used in some situations where the outcome distribution is not strictly log-normal. Conclusions We recommend the use of this sample size calculation approach for outcome data that are expected to be positively skewed and where a two group comparison on a log-transformed scale is planned. An advantage of this method over usual calculations based on estimates on the log-transformed scale is that it allows clinical efficacy to be specified as a difference in medians and requires a variance estimate on the untransformed scale. Such estimates are often easier to obtain and more interpretable than those for log-transformed outcomes.

Abstract Background Meta-analysis is very useful to summarize the effect of a treatment or a risk factor for a given disease. Often studies report results based on log-transformed variables in order to achieve the principal assumptions of a linear regression model. If this is the case for some, but not all studies, the effects need to be homogenized. Methods We derived a set of formulae to transform absolute changes into relative ones, and vice versa, to allow including all results in a meta-analysis. We applied our procedure to all possible combinations of log-transformed independent or dependent variables. We also evaluated it in a simulation based on two variables either normally or asymmetrically distributed. Results In all the scenarios, and based on different change criteria, the effect size estimated by the derived set of formulae was equivalent to the real effect size. To avoid biased estimates of the effect, this procedure should be used with caution in the case of independent variables with asymmetric distributions that significantly differ from the normal distribution. We illustrate an application of this procedure by an application to a meta-analysis on the potential effects on neurodevelopment in children exposed to arsenic and manganese. Conclusions The procedure proposed has been shown to be valid and capable of expressing the effect size of a linear regression model based on different change criteria in the variables. Homogenizing the results from different studies beforehand allows them to be combined in a meta-analysis, independently of whether the transformations had been performed on the dependent and/or independent variables.

Regression analysis with compositional response, observations carrying relative information, is an appropriate tool for statistical modelling in many scientific areas (e.g. medicine, geochemistry, geology, economics). Even though this technique has been recently intensively studied, there are still some practical aspects that deserve to be further analysed. Here we discuss the issue related to the coordinate representation of compositional data. It is shown that linear relation between particular orthonormal coordinates and centred log-ratio coordinates can be utilized to simplify the computation concerning regression parameters estimation and hypothesis testing. To enhance interpretation of regression parameters, the orthogonal coordinates and their relation with orthonormal and centred log-ratio coordinates are presented. Further we discuss the quality of prediction in different coordinate system. It is shown that the mean squared error (MSE) for orthonormal coordinates is less or equal to the MSE for log-transformed data. Finally, an illustrative real-world example from geology is presented.

Background: In healthcare research, outcomes with skewed probability distributions are common. Sample size calculations for such outcomes are typically based on estimates on a transformed scale (e.g. log) which may sometimes be difficult to obtain. In contrast, estimates of median and variance on the untransformed scale are generally easier to pre-specify. The aim of this paper is to describe how to calculate a sample size for a two group comparison of interest based on median and untransformed variance estimates for log-normal outcome data.Methods: A log-normal distribution for outcome data is assumed and a sample size calculation approach for a two-sample t-test that compares log-transformed outcome data is demonstrated where the change of interest is specified as difference in median values on the untransformed scale. A simulation study is used to compare the method with a non-parametric alternative (Mann-Whitney U test) in a variety of scenarios and the method is applied to a real example in neurosurgery.Results: The method attained a nominal power value in simulation studies and was favourable in comparison to a Mann-Whitney U test and a two-sample t-test of untransformed outcomes. In addition, the method can be adjusted and used in some situations where the outcome distribution is not strictly log-normal.Conclusions: We recommend the use of this sample size calculation approach for outcome data that are expected to be positively skewed and where a two group comparison on a log-transformed scale is planned. An advantage of this method over usual calculations based on estimates on the log-transformed scale is that it allows clinical efficacy to be specified as a difference in medians and requires a variance estimate on the untransformed scale. Such estimates are often easier to obtain and more interpretable than those for log-transformed outcomes. [ABSTRACT FROM AUTHOR]

The first probabilistic definition of the geometric mean of a non negative random variable under certain assumptions was given in Feng et al. (2013). In this paper, we generalize the definition to a larger class of random variables. We also show the basic properties of the geometric mean and point out its discontinuity and instability. Some convergence properties are studied as well, for which we emphasize its link to the positive moments of the random variable. A discussion of potential applications of the new definition in biomedical research and open questions to complete the theory of geometric mean is highlighted. [ABSTRACT FROM PUBLISHER]

In many fields of research variables are often both continuous and restricted to be positive. We analyzed 70 endpoints that contained continuous and positive dependent variables from 6 clinical and 3 preclinical trials. The impact of data transformation and adjustment for baseline on the fit of the model was studied. On average, including baseline as a covariate decreases the necessary sample size to achieve a particular precision in the treatment effect estimate by about 70% as compared to a model that ignores baseline, or by 20% to 33% as compared to models that only adjust for baseline in the response. Additionally, log transformation of the endpoint (either the direct outcome or a baseline-adjusted outcome) appears to decrease the sample size needed on average by 20% to 35%. We draw three conclusions from this work. First, if a baseline is available, use of baseline as a covariate should always be undertaken. Second, although we recommend exploration of data from previous studies, percent change from baseline analyses should not be undertaken unless there is strong empirical evidence that for that endpoint it is preferred. Finally, and again with the caveat that nothing replaces exploration of data from previous studies, log transformation ought to be the default analysis of positive data unless exploration of previous data provides convincing evidence that the natural scale is preferred. [ABSTRACT FROM AUTHOR]

Background: Meta-analysis is very useful to summarize the effect of a treatment or a risk factor for a given disease. Often studies report results based on log-transformed variables in order to achieve the principal assumptions of a linear regression model. If this is the case for some, but not all studies, the effects need to be homogenized.Methods: We derived a set of formulae to transform absolute changes into relative ones, and vice versa, to allow including all results in a meta-analysis. We applied our procedure to all possible combinations of log-transformed independent or dependent variables. We also evaluated it in a simulation based on two variables either normally or asymmetrically distributed.Results: In all the scenarios, and based on different change criteria, the effect size estimated by the derived set of formulae was equivalent to the real effect size. To avoid biased estimates of the effect, this procedure should be used with caution in the case of independent variables with asymmetric distributions that significantly differ from the normal distribution. We illustrate an application of this procedure by an application to a meta-analysis on the potential effects on neurodevelopment in children exposed to arsenic and manganese.Conclusions: The procedure proposed has been shown to be valid and capable of expressing the effect size of a linear regression model based on different change criteria in the variables. Homogenizing the results from different studies beforehand allows them to be combined in a meta-analysis, independently of whether the transformations had been performed on the dependent and/or independent variables. [ABSTRACT FROM AUTHOR]

The logarithmic transformation of the dependent variables formodels developed using regression analysis induces bias that should be corrected,regardless its magnitude. The simplest correction for bias was proposed by Sprugel (1983), which basically multiplies the back-transformed estimates with the constant value of exponential of half the variance of the errors of the logarithmically transformed variable. While this correction is fast and easy to implement does not supplies estimates of the variability existing in the original data. Consequently, a procedure based on generated data was developed to provide unbiased estimates for both attribute of interest and variability existing along the model. The procedure revealsthat valid estimates can be obtained if large number of values is generated(e.g., 5000 values/x). The procedures supplies accurate estimates for the attribute of interest and its variability, but encounters significant data processing difficulties for models with more than one predictor variable. Nevertheless, irrespective the number of predictor of variables and magnitude of the correction factor computed by Sprugel, the estimates determined using logarithmic transformations should be corrected for bias, to avoid cumulated errors or chaotic effects associated with nonlinear models.

Spreadsheets at this site for the analysis of controlled trials, post-only cross-overs and pre-post crossovers have been modified to allow adjustment for, and estimation of, the effect of two covariates (predictor variables). The user of the spreadsheet now has to specify a "custom" effect by inserting weighting factors to make any combination of each subject's repeated measurements. There is provision for estimating the custom effect as a trend in some or all of the repeated measurements representing a time series. Adjustment for a single covariate is obtained as previously, using the FORECAST function to fit a simple linear relationship between the covariate and the custom effect and thereby to predict the value of the custom effect at the mean or some other chosen value of the covariate. Adjustment for two covariates is achieved by predicting the value of the custom effect at chosen values of each predictor using the regression coefficients provided by the LINEST function. The standard error of the predicted value, which is required for inferential statistics, is not provided by LINEST but was derived from the standard errors of the regression coefficients by accounting for the correlation between the predictors. As before, individual responses to treatments are estimated by comparing variances of custom effects in experimental and reference (control) groups or treatments; in the case of post-only crossovers, two treatments are assumed to be repeats of a control or reference treatment, and these are now assigned to a separate spreadsheet to allow comparison of the variance of their change scores with the variance of change scores between reference and active treatments. The spreadsheets provide the usual analyses of the raw and log-transformed dependent variable, along with non-clinical and clinical magnitude-based inferences for smallest important effects defined by raw, percent, factor and/or standardized differences in the dependent variable. Values of the trial(s) or treatment(s) chosen to provide the standard deviation for standardizing are automatically selected as the values of one of the covariates, but these values can be replaced with those of another covariate. Accuracy of the computations in the spreadsheets was checked by analysing simulated datasets with the spreadsheets and with mixed modeling in the University Edition of the Statistical Analysis System (SAS Studio). [ABSTRACT FROM AUTHOR]

Pooling biospecimens prior to performing laboratory assays is a useful tool to reduce costs, achieve minimum volume requirements and mitigate assay measurement error. When estimating the risk of a continuous, pooled exposure on a binary outcome, specialized statistical techniques are required. Current methods include a regression calibration approach, where the expectation of the individual-level exposure is calculated by adjusting the observed pooled measurement with additional covariate data. While this method employs a linear regression calibration model, we propose an alternative model that can accommodate log-linear relationships between the exposure and predictive covariates. The proposed model permits direct estimation of the relative risk associated with a log-transformation of an exposure measured in pools. Published 2016. This article is a U.S. Government work and is in the public domain in the USA. [ABSTRACT FROM AUTHOR]

A new approach is proposed for the numerical solution of boundary value one-dimensional problem of advection-diffusion equation which arises, among others, in air pollution modeling. Since the problem is posed in an unbounded interval we use a log-transformation to confine the computational region. We discuss the well-posedness of the new problem and the properties of its solution. We derive a positive finite volume difference scheme. Some results from computational experiments are presented. [ABSTRACT FROM AUTHOR]

Heino et al. () identified the weak explanatory power of abundance data as an important limitation of macroinvertebrate trait analysis. This limitation may be an artefact of analytical design., The widespread practice of combining logarithmically transformed abundance data with trait frequencies, log(x + 1)*(trait frequency), represents a nonlinear abundance weighting of trait frequencies, as opposed to an expression of trait abundances per se. Because the addition of logarithmic data is equivalent to multiplication on an arithmetic scale, summing these abundance-weighted frequencies provides an inconsistent scaling of trait abundance that may confound quantitative comparison., We provide examples of the options for estimating trait abundance from data on macroinvertebrate abundance and trait frequencies and discuss the meaning of numerical data in the context of analytical objectives., In the light of the contrasting methods that have been employed to analyse trait data for benthic macroinvertebrates, the conclusion that the explanatory power of trait abundance is inferior to that of taxonomic abundance may be premature. [ABSTRACT FROM AUTHOR]

Abstract: Formation of disinfection by-products (DBPs) in ten drinking source waters located in the United States was examined in this study. DBP generation was interpreted in the context of halogenation-induced changes of log-transformed absorbance spectra of dissolved organic matter (DOM) present in the waters. This approach allows probing the behavior of relatively minor structures that can be highly sensitive towards any process of interest, notably DOM halogenation. This concept was applied to examine effects of chlorination time on the kinetics of chlorine consumption and release of several DBP groups such as total trihalomethanes (THM4, including CHCl3, CHCl2Br, CHClBr2 and CHBr3), haloacetic acids (HAA9, including MCAA, MBAA, DCAA, TCAA, BCAA, DBAA, BDCAA, DBCAA and TBAA), haloacetonitriles (THAN4, including TCAN, DCAN, BCAN and DBAN), haloketones (HK2, including DCP and TCP), chloral hydrate (CH) and chloropicrin (CPN). Two alternative parameters, namely the differential logarithm of DOM absorbance at 350 nm (DLnA350) and change of the spectral slope in the range of wavelengths 325–375 nm (DSlope325-375) were introduced to quantify individual DBP species formed and Cl2 consumption. DLnA350 and DSlope325-375, especially DLnA350 were determined to be more reliable than differential absorbance at 272 nm that was utilized in prior applications of differential spectroscopy to characterize DBP formation. Strong linear relationships between DLnA350 values and concentrations of major groups of and individual DBP species (e.g. THM4, HAA9, HAN4 and CPN were found to exist (mostly, R 2 > 0.95) and the intercept of these correlations with the y-axis was near zero for the examined water sources. Correlations between DLnA350 values and concentrations of CH and HK2 were also strong but they were nonlinear. The slope of the correlations between the concentrations of major groups of DBP species vs -DLnA350 were also well correlated with SUVA254 and LnA350 for all the examined source waters. It indicates that log-transformations of the absorbance spectra of surface water and parameters based on such transformations (e.g., DLnA350 and DSlope325-375) have a potential to provide an alternative reliable approach to monitor the halogenation of DOM and attendant formation of individual DBP species. [Copyright &y& Elsevier]

The concentrations of 48 trace elements (Li, Be, Sc, V, Cr, Co, Ni, Cu, Zn, Ga, As, Br, Rb, Sr, Y, Zr, Nb, Mo, Ag, In, Cd, Sn, Sb, I, Cs, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Tl, Pb, Bi, Th and U) in 14 soils derived from limestone, sampled at three sites, are compared with the concentrations in 500 soil samples derived from a variety of other parent materials. The 500 samples were collected from 75 sites nationwide in order to include the wide range of common soil types in Japan. Most analytical results were obtained by inductively coupled plasma mass spectrometry (ICP-MS), but Cr, As, Br, Zr, Sn, and I concentrations were determined by energy dispersive X-ray fluorescence spectrometry (EDXRF), because the acid dissolution techniques employed in this study were found to be incapable of recovering these elements completely. In order to examine the reliability of analyses, the concentrations of many elements were also determined by EDXRF, inductively coupled plasma-atomic emission spectrometry (ICP-AES), and atomic absorption spectrometry (AAS). Box and whisker diagrams (Tukey plots), constructed using log-transformed values of each element, show clearly that geometric means of nearly all the trace elements in soils derived from limestone are higher than those in soils derived from other parent materials. The only exceptions are Sr, Ag and Eu, though statistical analysis (Student’st-test) shows that the differences for these three elements were not significant atp< 0.05. Similarly, the observed differences of geometric means for Sc, Br and Ba between limestone soils and other types of soils were also not significant atp< 0.05. It can be concluded, therefore, that the concentrations of the above-mentioned 48 trace elements in soils derived from limestone are significantly higher than those in other types of soils, with the exception of Sc, Br, Sr, Ag, and Ba, though it was necessary to exclude 81 soil samples, developed on scoriaceous (basaltic) volcanic ash from Mt. Fuji, as an exceptional group for comparisons of V and Cu, as these soils contain higher levels of these two elements. The above results can be attributed to the gradual accumulation of trace elements in the limestone soils due to the intense weathering processes. [ABSTRACT FROM PUBLISHER]

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. [ABSTRACT FROM AUTHOR]

Most modern population dynamics analyses of time series use simple population indices for ecological inference. These indices, collected for many years for various agricultural pests or game animals, are generally believed not to distort systematically feedback estimates because the assumption of linearity to population size roughly holds. To assess the relative importance of this assumption, we examined the effect of nonlinearity in a burrow index for voles on feedback estimates obtained through autoregressive modeling. We show that the issue of linearity is of less importance to ecological inference because the feedback estimates are routinely obtained on a logarithmic scale. Transforming data to logs has a strong linearization effect, removing most of the nonlinearity observed on the original scale. We conclude that the statistical tools for ecological inference, such as autoregressive log-linear models, are sufficiently robust to the systematic error imposed by index nonlinearity and that indices are valuable sources of ecological information even in situations when the assumed linear functional forms to population size were not exactly validated. We suggest that for time series modelers, the issue of a large sampling variation in small 'noisy' populations is by far a more burning one than the systematic error due to index nonlinearity. [ABSTRACT FROM AUTHOR]

Abstract: First, we propose a new method for estimating the conditional variance in heteroscedasticity regression models. For heavy tailed innovations, this method is in general more efficient than either of the local linear and local likelihood estimators. Secondly, we apply a variance reduction technique to improve the inference for the conditional variance. The proposed methods are investigated through their asymptotic distributions and numerical performances. [Copyright &y& Elsevier]

We present five new discriminant function diagrams based on an extensive database representative of basic and ultrabasic rocks from four tectonic settings of island arc, continental rift, ocean-island, and mid-ocean ridge. These diagrams were obtained after loge-transformation of concentration ratios of major-elements -- a technique recommended for a correct statistical treatment of compositional data. Higher % success rates (overall values from ∼83 to 97%) were obtained for proposing these new diagrams as compared to those (∼82 to 94%) obtained from the discriminant analysis of the raw major-element concentration data (i.e., without the loge-transformation and without taking ratios of the compositional data, but using exactly the same database to provide an unbiased comparison), suggesting that such a data transformation constitutes a statistically correct and recommended technique. The new diagrams also resulted in less mis-classification of basic and ultrabasic rocks from known tectonic settings than the diagrams obtained from the raw data. The use of these highly successful new discriminant function diagrams is illustrated using Miocene to Recent basic and ultrabasic rocks from three areas of Mexico with complex or controversial tectonic settings (Mexican Volcanic Belt, Los Tuxtlas volcanic field, and Eastern Alkaline Province), as well as older rocks from three areas (Deccan, Malani, and Bastar) of India. Additionally, the major-element data from two 'known' continental arc settings are used to show that they are similar to those from the island arc setting. Continental rift setting is inferred for all Mexican cases and for one cratonic area of India (Malani) and an IAB setting for the Bastar craton. The Deccan flood basalt province of India is used to warn against an indiscriminate use of those discrimination diagrams that do not explicitly include the likely setting of the area under evaluation. An Excel template is also provided for an easy application of these new diagrams for discriminating the four settings considered in this work. [ABSTRACT FROM AUTHOR]

Leaf shape and symmetry is of interest because of the importance of leaves in photosynthesis. Recently, a novel method was proposed to measure the extent of bilateral symmetry in leaves in which a leaf was divided into left and right sides by a straight line through the leaf apex and base, and a number of equidistant strips were drawn perpendicular to the straight line to generate an equivalent number of differences in area between the left and right parts. These areal differences are the basis for a measure of leaf bilateral symmetry, which was then examined to see how well it follows Taylor’s power law (TPL) using three classes of plants, namely, 10 geographical populations of Parrotia subaequalis (H.T. Chang) R.M. Hao et H.T. Wei, 10 species of Bambusoideae, and 10 species of Rosaceae. The measure of bilateral symmetry followed TPL for a single species or for a class of closely related species. The estimate of the exponent of TPL for bamboo plants was significantly larger than for the dicotyledonous trees, but its goodness of fit was the best among the three classes of plants. The heterogeneity of light falling on branches and leaves due to above-ground architectural patterns is an important contributor to leaf asymmetry. [ABSTRACT FROM AUTHOR]

The rank product statistic has been widely used to detect differentially expressed genes in replicated microarrays and a one-class setting. The objective of this article is to apply a rank product statistic to approximate the P-value of differential expression in a two-class setting, such as in normal and cancer cells. For this purpose, we introduce a simple statistic that compares the P-values of each class's rank product statistic. Its null distribution is straightforwardly derived using the change-of-variable technique.