Distance-based tests for homogeneity of multivariate dispersions

Summary The traditional likelihood‐based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero‐inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non‐Euclidean dissimilarity would be more appropriate. Distance‐based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene's test, with P‐values obtained either using the traditional F‐distribution or using permutation of either least‐squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Niño. Monte Carlo simulations from the real data sets show that the distance‐based tests are robust and powerful for relevant alternative hypotheses of real differences in spread.     

Analysis of Proportions in One- or Two-Way Tables with Spoiled Data

This paper discusses the analysis of data on proportions in contingency tables. The X² ‘index of dispersion test’ (e.g. Fisher, 1954) is developed in these situations and compared with the use of the ‘logit’ transformation. An example using Osborn's (1979) data is given, illustrating the estimation of one or more missing observations.     

Efficiency in the Use of Hotellings T2

Alternative scale models are compared with regard to the Pitman efficiency of Hotelling's T² in tests for means. A basic decomposition identifies subspaces of the parameters in which one model is more efficient than another, or the two models have equal efficiency. Local and global bounds for relative Pitman efficiencies are given with reference to these subspaces. Applications include efficiency comparisons of marginal and conditional tests in a given model, and a comparison of the sensitivities of selected T² tests regarding psychological profiles in treated and control groups of children.     

Effect of Intracluster Correlation on the R-Square Statistic

R²-statistic is a popular and very widely used statistic in regression analysis to estimate the square multiple correlation (SMC), ρ², between a response variable Y and p predictor variables, _X1, …, _Xp. Numerous articles are available in the statistical literature on the properties of R² as an estimator of ρ² when the observations are uncorrelated. However, relatively little is known about the behavior of R² when the available observations are correlated such as the data that result from complex sampling schemes. In this paper, we study the behavior R² in the presence of two-stage sampling data. An approximate expressions for the variance and the bias of R² in the presence of two-stage cluster sampling data with positive intracluster correlation (ρ*) are obtained. It is evident from these formulas and from a simulation study that R² is a poor estimator of ρ² except when ρ* is small. As such, we consider several alternative estimators of ρ² and evaluate their theoretical properties and finite sample performance using a simulation study.     

A coefficient of determination (R2) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R²) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance‐covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.     

Robustness of Sequential Tests for Means

Three sequential tests of the null hypothesis, μ = μ₀, versus an alternative of the form (μ ? μ₀)²= =σ²d² are compared for different forms of violation of the underlying normal assumption. 10000 samples were simulated for d=0.6; 1.0 and 1.6 (σ² = 1), four (α, β)-combinations and seven alternative distributions. The results show that for small d-values one test is robust for α and another for β. For large d all tests can be used.     

Modeling of Pathogen Indicator Organisms in a Small-Scale Agricultural Catchment Using SWAT

Degradation of water quality from microbial contaminants associated with agricultural activities has significant implications for source protection of potable water. Novel environmental approaches must be adopted to assess risks from waterborne pathogenic microbes. The objective of this study was to evaluate applicability of the Soil and Water Assessment Tool (SWAT) to predict daily concentrations of E. coli in a small-scale agricultural catchment in Ireland. The study area is based on the Kilshanvey catchment located in the west of Ireland. E. coli data (n = 25) from June 2006 to June 2007 were utilized for comparison with the model's predictions. Statistical analysis indicates an unsatisfactory to fair level of correlation for the model's predictions (R² = 0.03–0.35, NSE = –0.42–0.29). A sensitivity analysis identified direct stream deposition and die-off rates for E. coli as having a significant impact on the model's predictions. Our results suggest that the model is adequate to assess the magnitude of various microbial sources within catchments but capability to replicate daily observations is uncertain. However, model outputs could provide adequate data to develop a human exposure assessment to pathogen indicator organisms in surface water and assist policy-makers in developing appropriate risk management strategies.     

A Note on Measures of Multivariate Kurtosis

We propose a measure of multivariate kurtosis suggested from Mardia's measure of multivariate skewness b₁,p, and examine its relationship both to Mardia's measure of multivariate kurtosis b₂,p, and to a smooth test of multivariate kurtosis ǔ₄².     

A Note on Non-Parametric Tests for the Interaction in Two-Way Layouts

A suggestion is given of how to prove main and interaction effects in two-way layouts independent of each other even if the data are just ordinally scaled. Starting from HILDEBRAND'S (1980a, b) non-parametric approach which presupposes interval-scaled data, transformations of ranks are settled before analysis per analogy to the H-test takes place. That is, the same formula of an asymptotically X²-distributed test-statistic results but mean ranks are used instead of mean scores in order to partialize, for instance, main effects while testing interaction effect. Finally an allusion is given of how to handle ties as well as unequal sample sizes.     

Light interception as a source of variation for nitrogen fixation in groundnut genotypes

The ability of several chemical soil N availability indexes to predict the N supplying capability (NSC) of soils to maize in the field was evaluated in 49 field experiments over 3 years in Pennsylvania. Two recently proposed indexes based on the amount of NH₄ ⁺ released by treating soil with 2 M KCl at 100°C for 4 hr or with a pH 11.2 phosphate-borate buffer for 8 min were not good predictors of NSC (r=0.484 and 0.254, respectively). The absorbance of a 0.01 M NaHCO₃ extract at 260 nm was also poorly correlated with field-measured NSC (r=0.412). The pre-sidedress soil NO₃ ⁻ test (PSNT), the soil NO₃ ⁻ concertration in the surface 20 cm of soil at planting, and the UV absorbance at 200 nm of a 0.01 M NaHCO₃ extract of at planting soils were all moderately well correlated with NSC (r=0.672, 0.750, and 0.737, respectively). The latter two indexes are very simple, rapid, and inexpensive to perform and offer the possibility of improving the prediction of NSC in heavily manured fields. Paper No 8211 of the Journal series of The Pennsylvania Agricultural Experimental Station.     

Photoracemization of Blestriarene C and Its Analogs

Two analogs of blestriarene C (4,4'‐dimethoxy‐1,1'‐biphenanthrene‐2,2',7,7'‐tetraol) bearing no 7,7'‐dihydroxy ( 3 ) and 4,4'‐dimethoxy groups 4 were prepared. Unlike blestriarene C ( 1 ), compounds 3 and 4 , as well as 1,1'‐biphenanthrene‐2,2'‐diol ( 5 ), do not racemize under fluorescent lamp illumination. Cyclic voltammetry analysis reveals that compound 1 has a lower half‐wave potential (E_1/2) than compounds 3 , 4 , 5 , suggesting that a redox cycle is involved in the racemization. Compound 1 racemizes by absorbing UV light corresponding to the ¹L_b band. During the reaction, no side products are observed. The racemization is significantly inhibited under nitrogen. Based on these observations, we propose a feasible mechanism for the easy racemization of compound 1 , which is mediated by a cation radical generated in situ by a reversible photo‐induced oxygen oxidation. Chirality 27:479–486, 2015. © 2015 Wiley Periodicals, Inc.     

Estimation of vegetation photosynthetic capacity from space‐based measurements of chlorophyll fluorescence for terrestrial biosphere models

Photosynthesis simulations by terrestrial biosphere models are usually based on the Farquhar's model, in which the maximum rate of carboxylation (V_cmax) is a key control parameter of photosynthetic capacity. Even though V_cmax is known to vary substantially in space and time in response to environmental controls, it is typically parameterized in models with tabulated values associated to plant functional types. Remote sensing can be used to produce a spatially continuous and temporally resolved view on photosynthetic efficiency, but traditional vegetation observations based on spectral reflectance lack a direct link to plant photochemical processes. Alternatively, recent space‐borne measurements of sun‐induced chlorophyll fluorescence (SIF) can offer an observational constraint on photosynthesis simulations. Here, we show that top‐of‐canopy SIF measurements from space are sensitive to V_cmax at the ecosystem level, and present an approach to invert V_cmax from SIF data. We use the Soil‐Canopy Observation of Photosynthesis and Energy (SCOPE) balance model to derive empirical relationships between seasonal V_cmax and SIF which are used to solve the inverse problem. We evaluate our V_cmax estimation method at six agricultural flux tower sites in the midwestern US using spaced‐based SIF retrievals. Our V_cmax estimates agree well with literature values for corn and soybean plants (average values of 37 and 101 μmol m^?2 s^?1, respectively) and show plausible seasonal patterns. The effect of the updated seasonally varying V_cmax parameterization on simulated gross primary productivity (GPP) is tested by comparing to simulations with fixed V_cmax values. Validation against flux tower observations demonstrate that simulations of GPP and light use efficiency improve significantly when our time‐resolved V_cmax estimates from SIF are used, with R² for GPP comparisons increasing from 0.85 to 0.93, and for light use efficiency from 0.44 to 0.83. Our results support the use of space‐based SIF data as a proxy for photosynthetic capacity and suggest the potential for global, time‐resolved estimates of V_cmax.     

Tables of the critical values for simultaneous and sequential Bonferroni-z-tests

Simultaneous and sequential BONFERRONI -tests (HOLM , 1979) are going to replace the traditional global tests (ANOVA, PEARSON -χ²). To facilitate (sequential) BONFERRONI -evaluation, BONFERRONI -test limits for the normal distribution are tabulated for r = 1(1)100, 100(2)300, 300(5)800, 800(10)1600, 1600(20)3200, 3200(50)10000 tests and for some conventional alphas in one- and two-sided alternatives.     

Albedo estimates for land surface models and support for a new paradigm based on foliage nitrogen concentration

Vegetation albedo is a critical component of the Earth's climate system, yet efforts to evaluate and improve albedo parameterizations in climate models have lagged relative to other aspects of model development. Here, we calculated growing season albedos for deciduous and evergreen forests, crops, and grasslands based on over 40 site‐years of data from the AmeriFlux network and compared them with estimates presently used in the land surface formulations of a variety of climate models. Generally, the albedo estimates used in land surface models agreed well with this data compilation. However, a variety of models using fixed seasonal estimates of albedo overestimated the growing season albedo of northerly evergreen trees. In contrast, climate models that rely on a common two‐stream albedo submodel provided accurate predictions of boreal needle‐leaf evergreen albedo but overestimated grassland albedos. Inverse analysis showed that parameters of the two‐stream model were highly correlated. Consistent with recent observations based on remotely sensed albedo, the AmeriFlux dataset demonstrated a tight linear relationship between canopy albedo and foliage nitrogen concentration (for forest vegetation: albedo=0.01+0.071%N, r²=0.91; forests, grassland, and maize: albedo=0.02+0.067%N, r²=0.80). However, this relationship saturated at the higher nitrogen concentrations displayed by soybean foliage. We developed similar relationships between a foliar parameter used in the two‐stream albedo model and foliage nitrogen concentration. These nitrogen‐based relationships can serve as the basis for a new approach to land surface albedo modeling that simplifies albedo estimation while providing a link to other important ecosystem processes.     

Technical note: A linear model for predicting δ13Cprotein

Objective : Development of a model for the prediction of δ¹³C_protein from δ¹³C_collagen and Δ¹³C_ap‐co. Model‐generated values could, in turn, serve as “consumer” inputs for multisource mixture modeling of paleodiet. Methods : Linear regression analysis of previously published controlled diet data facilitated the development of a mathematical model for predicting δ¹³C_protein (and an experimentally generated error term) from isotopic data routinely generated during the analysis of osseous remains (δ¹³C_co and Δ¹³C_ap‐co). Results : Regression analysis resulted in a two‐term linear model (δ¹³C_protein (%) = (0.78 × δ¹³C_co) ? (0.58× Δ¹³C_ap‐co) ? 4.7), possessing a high R‐value of 0.93 (r² = 0.86, P < 0.01), and experimentally generated error terms of ±1.9% for any predicted individual value of δ¹³C_protein. This model was tested using isotopic data from Formative Period individuals from northern Chile's Atacama Desert. Conclusions : The model presented here appears to hold significant potential for the prediction of the carbon isotope signature of dietary protein using only such data as is routinely generated in the course of stable isotope analysis of human osseous remains. These predicted values are ideal for use in multisource mixture modeling of dietary protein source contribution. Am J Phys Anthropol 157:694–703, 2015. © 2015 Wiley Periodicals, Inc.     

Rank Tests for Complete Block Designs

In this article a general univariate K-sample rank test for complete block designs with proportional cell frequencies is derived. It is shown that the test statistic has under H₀ and for arbitrary scores asymptotically a X²-distribution with K — 1 degrees of freedom. Special cases of this test are the Kruskal-Wallis test and the Friedman test. The test is compared with the Benard-van-Elteren test, the Mack-Skillings test and a test proposed by Downton. Finally the application of the test is illustrated by two examples.     

Predictive Configural Frequency Analysis Evaluated by Simultaneous Berchtold-Corrected Fourfold X2-Tests

For testing against outlying cells in r × c contingency tables in predictive configural frequency analysis, it is suggested not to replace the usual PEARSON fourfold X²-test by YATES ' discontinuity corrected test but by BERCHTOLD'S test correcting for skewed hypergeometric distributions. In general, the BERCHTOLD correction is most efficient for tables involving three small and one large fourfold frequency. The correction is illustrated by configural frequency analysis of data from psychotherapy research.     

Red cabbage anthocyanin extract alleviates copper-induced cytological disturbances in plant meristematic tissue and human lymphocytes

Red cabbage is a source of health beneficial substances with antioxidant and antigenotoxic properties. HPLC analysis specifying the content of the investigated extract indicated that mainly anthocyanins (ATH) were responsible for its abilities. Cytological research was conducted with two experimental models: plant tissues—meristematic cells of Vicia faba, and animal tissue elements—human lymphocytes. Positive influence of ATH extract on mitotic activity of Vicia cells exposed to Cu²⁺ stress, and inhibitory effect of ATH on cytotoxic actions of Cu²⁺ on lymphocytes were demonstrated. In all experimental series with ATH application in combinations with Cu²⁺, mitotic index (MI) were higher than those obtained for only Cu²⁺ stressed tissues. Preincubation in ATH before Cu²⁺ stress had the best effect. Similarly, after ATH applications in all tested series decrease in frequency of micronuclei (MN) appearance was noticed in comparison with only Cu²⁺ stressed material. In the case of Vicia cells ATH acted effectively even applied after Cu²⁺ stress. It suggests that this ATH mixture not only prevents and limits but also heals the cytological injury caused by Cu²⁺ stress.     

Adenosine accumulation causes metabolic disorders in testes and associates with lower testosterone level in obese mice

Overweight and obese men face numerous health problems, including type 2 diabetes, subfertility, and even infertility. However, few studies have focused on the effects of nutritional status and obesity‐related regulatory signals on fertility deficiency. Our previous observations have shown that the elevation of plasma 5'‐adenosine monophosphate (5'‐AMP) and the accumulation of adenosine in liver and muscle of obese diabetic db/db mice are related to insulin resistance. Here, we found that adenosine accumulation in testis is a common marker of both genetic obesity and high‐fat‐diet induced obese mice. An messenger RNA sequencing analysis indicated that 78 upregulated genes and 155 downregulated genes in the testis of 5'‐AMP‐treated mice overlapped with the same genes in the testis of ob/ob mice, and these genes belonged to the clusters of steroid metabolic process and regulation of hormone levels, respectively. Serum testosterone was reduced in ob/ob and 5'‐AMP‐treated mice. Metabolomic analysis based on ¹H nuclear magnetic resonance showed that the testicular metabolic profiles of ob/ob mice were similar to those of 5'‐AMP treated mice. Exogenous 5'‐AMP inhibited the phosphorylation of AKT and mammalian target of rapamycin signal transduction and reduced the proliferating cell nuclear antigen expressions in testes. Our results suggest that the accumulation of adenosine causes metabolic disorders in testes and associates lower testosterone level in obese mice.     

Minimum Sample Size Ensuring Validity of Classical Confidence Intervals for Means of Skewed and Platykurtic Distributions

COCHRAN (1953) and BARTCH (1957) gave formulae for the magnitude of the sample size (n) ensuring the validity of the limiting normal distribution of the sample mean x(ⁿ) obtained from a non-normal distribution with marked asymmetry and kurtosis. These formulae have been checked empirically in this paper using (a) simulated data with given asymmetry and kurtosis and (b) real data gathered from a coronary heart disease study. We find that our results are in general agreement with Bartch's formula. However, in a number of cases, the asymptotic normal distribution is attained for smaller sample size than that required by Bartch's formula.