Critical Values and Some Properties of a New Test Statistic for Analyzing Unreplicated Factorial Experiments

Critical values of the test statistic proposed by Al‐Shiha and Yang (1999) for analyzing unreplicated factorials are estimated by fitting an appropriate linear model. Some important properties of the test are also provided.     

Assessing Equivalence Tests with Respect to their Expected p‐Value

Monte‐Carlo simulation methods are commonly used for assessing the performance of statistical tests under finite sample scenarios. They help us ascertain the nominal level for tests with approximate level, e.g. asymptotic tests. Additionally, a simulation can assess the quality of a test on the alternative. The latter can be used to compare new tests and established tests under certain assumptions in order to determinate a preferable test given characteristics of the data. The key problem for such investigations is the choice of a goodness criterion. We expand the expected p‐value as considered by Sackrowitz and Samuel‐Cahn (1999) to the context of univariate equivalence tests. This presents an effective tool to evaluate new purposes for equivalence testing because of its independence of the distribution of the test statistic under null‐hypothesis. It helps to avoid the often tedious search for the distribution under null‐hypothesis for test statistics which have no considerable advantage over yet available methods. To demonstrate the usefulness in biometry a comparison of established equivalence tests with a nonparametric approach is conducted in a simulation study for three distributional assumptions.     

On the Analysis of Variance for Time Sequenced Samples

The 3 way nested ANOVA model y_ijk = μ + a_i + B_ij + γ_k + (αγ)_ik + epsilon_ijk With α (treatment or group effects) and γ (time) both being fixed effects and B (the individual effects) random and nested within α, is introduced and explored. The problems associated with the usual approach are explained. The alternative model Is developed and a method of evaluation via the method of linear contrasts is recomended. The test statistic has the distribution of a convolution of F-distributions. Further, a method of investigating the assumptions of the model is offered and a further generalization using path spaces (of dim. K) is developed. Here again the appropriate test statistic has the distribution of a convolution of F-distributions. This combined with the method of linear contrasts offers an elegant solution to the BEHRENS-FISHER problem. y_ijk = f_ik + B_ij + epsilon_ijk     

Nonparametric All‐Pairs Multiple Comparisons

Nonparametric all‐pairs multiple comparisons based on pairwise rankings can be performed in the one‐way design with the Steel‐Dwass procedure. To apply this test, Wilcoxon's rank sum statistic is calculated for all pairs of groups; the maximum of the rank sums is the test statistic. We provide exact calculations of the asymptotic critical values (and P‐values, respectively) even for unbalanced designs. We recommend this asymptotic method whenever large sample sizes are present. For small sample sizes we recommend the use of the new statistic according to Baumgartner , Weiss , and Schindler (1998, Biometrics 54 , 1129–1135) instead of Wilcoxon's rank sum for the multiple comparisons. We show that the resultant procedure can be less conservative and, according to simulation results, more powerful than the original Steel‐Dwass procedure. We illustrate the methods with a practical data set.     

Cluster Randomization Trials: A Simulation Study

A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel‐Haenszel chi‐square statistic (χ²_MH), the adjusted Mantel‐Haenszel chi‐square statistics of Rao and Scott using both an unpooled design effect (χ²_RSN) and a pooled design effect (χ²_RSP), the adjusted Mantel‐Haenszel chi‐square statistic of Donald and Donner (χ²_DD), the chi‐square statistic using the GEE approach (χ²_GEE), the adjusted Mantel‐Haenszel chi‐square statistic of Begg (χ²_B), the Wald (χ²_W), the robust Wald (χ²_RW), the score (χ²_S), the robust score (χ²_RS), and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χ²_RS and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intracluster correlation is zero or the cluster sizes are balanced. χ²_RS performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.     

Decontamination of a hard surface contaminated with Bacillus anthracisΔSterne and B. anthracis Ames spores using electrochemically generated liquid-phase chlorine dioxide (eClO2)

Aims: To evaluate the inactivation of Bacillus anthracisΔSterne and Ames spores using electrochemically generated liquid‐phase chlorine dioxide (eClO₂) and compare two sporulation and decontamination methods with regard to cost, safety and technical constraints. Methods and Results: Spores were prepared via agar and broth methods and subsequently inoculated and dried onto clean, autoclave‐sterilized glass coupons. Bacillus anthracis spore inactivation efficacy was evaluated using the modified three‐step method (AOAC 2008.05) and a single‐tube extraction method. Spores (7·0 ± 0·5 logs) were inactivated within 1 min at room temperature using freshly prepared eClO₂. Bacillus anthracisΔSterne spores decreased in size after eClO₂ treatment as measured using a Beckman Coulter Multisizer. Conclusions: eClO₂ saturation of a hard surface was an effective B. anthracis sporicide. Broth sporulation and the single‐tube extraction method required less time and fewer steps, yielded a higher percentage of phase‐bright spores and showed higher spore recovery efficiency compared with AOAC 2008.05, making it more amenable to biosafety level 3 (BSL3) testing of virulent spores. Significance and Impact of the Study: Two test methods demonstrated the sporicidal efficacy of eClO₂. A new single‐tube extraction test protocol for decontaminants was introduced.     

Quantifying the lag time to detect barriers in landscape genetics

Understanding how spatial genetic patterns respond to landscape change is crucial for advancing the emerging field of landscape genetics. We quantified the number of generations for new landscape barrier signatures to become detectable and for old signatures to disappear after barrier removal. We used spatially explicit, individual‐based simulations to examine the ability of an individual‐based statistic [Mantel’s r using the proportion of shared alleles’ statistic (Dps)] and population‐based statistic (F_ST) to detect barriers. We simulated a range of movement strategies including nearest neighbour dispersal, long‐distance dispersal and panmixia. The lag time for the signal of a new barrier to become established is short using Mantel’s r (1–15 generations). F_ST required approximately 200 generations to reach 50% of its equilibrium maximum, although G’_ST performed much like Mantel’s r. In strong contrast, F_ST and Mantel’s r perform similarly following the removal of a barrier formerly dividing a population. Also, given neighbour mating and very short‐distance dispersal strategies, historical discontinuities from more than 100 generations ago might still be detectable with either method. This suggests that historical events and landscapes could have long‐term effects that confound inferences about the impacts of current landscape features on gene flow for species with very little long‐distance dispersal. Nonetheless, populations of organisms with relatively large dispersal distances will lose the signal of a former barrier within less than 15 generations, suggesting that individual‐based landscape genetic approaches can improve our ability to measure effects of existing landscape features on genetic structure and connectivity.     

Unbiased and Locally Efficient Estimation of Genetic Effect on Quantitative Trait in the Presence of Population Admixture

Summary Population admixture can be a confounding factor in genetic association studies. Family‐based methods ( Rabinowitz and Larid, 2000 , Human Heredity 50, 211–223) have been proposed in both testing and estimation settings to adjust for this confounding, especially in case‐only association studies. The family‐based methods rely on conditioning on the observed parental genotypes or on the minimal sufficient statistic for the genetic model under the null hypothesis. In some cases, these methods do not capture all the available information due to the conditioning strategy being too stringent. General efficient methods to adjust for population admixture that use all the available information have been proposed ( Rabinowitz, 2002 , Journal of the American Statistical Association 92, 742–758). However these approaches may not be easy to implement in some situations. A previously developed easy‐to‐compute approach adjusts for admixture by adding supplemental covariates to linear models ( Yang et al., 2000 , Human Heredity 50, 227–233). Here is shown that this augmenting linear model with appropriate covariates strategy can be combined with the general efficient methods in Rabinowitz (2002) to provide computationally tractable and locally efficient adjustment. After deriving the optimal covariates, the adjusted analysis can be carried out using standard statistical software packages such as SAS or R . The proposed methods enjoy a local efficiency in a neighborhood of the true model. The simulation studies show that nontrivial efficiency gains can be obtained by using information not accessible to the methods that rely on conditioning on the minimal sufficient statistics. The approaches are illustrated through an analysis of the influence of apolipoprotein E (APOE) genotype on plasma low‐density lipoprotein (LDL) concentration in children.     

Scaling Vo2 Peak in Obese and Non‐obese Girls

Objective: The conventional ratio method (milliliters O₂ per mass) typically is used to express Vo ₂ peak. The goal of the current study was to compare Vo ₂ peak of obese girls with normal‐weight girls by ratio and allometric scaling methods. Research Methods and Procedures: We compared Vo ₂ peak by ratio and allometric methods in 46 obese and 47 normal‐weight girls. Indirect calorimetry was used to measure Vo ₂ peak during either treadmill running or walking. Regression analysis was used to determine coefficients for mass and stature for each group with ANOVA used to compare data between groups. Results: The obese girls were taller and had higher values of body fatness (p ≤ 0.05). Absolute Vo ₂ peak (liters per minute) was similar between groups ; however Vo ₂ peak relative to mass was 50% lower (p ≤ 0.05) in the obese girls. When Vo ₂ peak (milliliters per minute per kilogram) and mass were correlated, r = ?0.48 was found in the obese group. Allometric scaling of logarithmic transformed stature and mass reduced this to r = ?0.002, thus eliminating the bias associated with the ratio method. Adjusting Vo ₂ peak allometrically scaled for mass, stature, and the combination of mass and stature reduced the difference between groups from 50% (ratio method) to 10% to 11% (p ≤ 0.05) with higher values found in the normal‐weight girls. Discussion: These results demonstrate the bias associated with the ratio method when comparing Vo ₂ peak in obese girls with Vo ₂ peak in normal‐weight girls. Allometric scaling eliminated the bias and thus may reflect a truer comparative response.     

Interactions between hydrogen sulphide and nitric oxide regulate two soybean citrate transporters during the alleviation of aluminium toxicity

Hydrogen sulphide (H₂S) is emerging as an important signalling molecule involved in plant resistance to various stresses. However, the underlying mechanism of H₂S in aluminium (Al) resistance and the crosstalk between H₂S and nitric oxide (NO) in Al stress signalling remain elusive. Citrate secretion is a wide‐spread strategy for plants against Al toxicity. Here, two citrate transporter genes, GmMATE13 and GmMATE47, were identified and characterized in soybean. Functional analysis in Xenopus oocytes and transgenic Arabidopsis showed that GmMATE13 and GmMATE47 mediated citrate exudation and enhanced Al resistance. Al treatment triggered H₂S generation and citrate exudation in soybean roots. Pretreatment with an H₂S donor significantly elevated Al‐induced citrate exudation, reduced Al accumulation in root tips, and alleviated Al‐induced inhibition of root elongation, whereas application of an H₂S scavenger elicited the opposite effect. Furthermore, H₂S and NO mediated Al‐induced GmMATE expression and plasma membrane (PM) H⁺‐ATPase activity and expression. Further investigation showed that NO induced H₂S production by regulating the key enzymes involved in biosynthesis and degradation of H₂S. These findings indicate that H₂S acts downstream of NO in mediating Al‐induced citrate secretion through the upregulation of PM H⁺‐ATPase‐coupled citrate transporter cotransport systems, thereby conferring plant resistance to Al toxicity.     

How to assess the prediction accuracy of species presence–absence models without absence data?

It is very common that only presence data are available in ecological niche modeling. However, most existing methods for evaluating the accuracy of presence–absence (binary) predictions of species require presence–absence data. The aim of this study is to present a new method for accuracy assessment that does not rely on absence data. Two new statistics F_pb and F_cpb were derived based on presence–background data. With generated six virtual species, we used DOMAIN, generalized linear modeling (GLM), and maximum entropy (MAXENT) to produce different species presence–absence predictions. To investigate the effectiveness of the new statistics in accuracy assessment, we used F_pb, F_cpb, the traditional F‐measure (F), kappa coefficient, true skill statistic (TSS), area under the receiver operating characteristic curve (AUC), and the contrast validation index (CVI) to evaluate the accuracy of predictions, and the behaviors of these accuracy measures were compared. The effectiveness of F_pb for threshold selection and estimation of species prevalence was also investigated. Experimental results show that F_cpb is an estimate of F. The Pearson's correlation coefficient (COR) between F_cpb and F is 0.9882, with a root‐mean‐square error (RMSE) of 0.0171. In general, F_pb, F_cpb, F, kappa coefficient, TSS, and CVI can sort models by the accuracy of binary prediction, but AUC is not appropriate to evaluate the accuracy of binary prediction. For DOMAIN, GLM, and MAXENT, finding the threshold by maximizing F_pb and by maximizing F result in similar accuracies. In addition, the estimation of species prevalence based on binary output with maximizing F_pb as the thresholding method is significantly more accurate than simply averaging the original continuous output. The best estimate of prevalence is provided by the binary output of MAXENT, with an RMSE of 0.0116. Finally, we conclude that the new method is promising in accuracy assessment, threshold selection, and estimation of species prevalence, all of which are important but challenging problems with presence‐only data. Because it does not require absence data, the new method will have important applications in ecological niche modeling.     

Spatial and temporal variation of genetic diversity and estimation of effective population sizes in Atlantic salmon (Salmo salar, L.) populations from Asturias (Northern Spain) using microsatellites

Rivers in Asturias (northern Spain) constitute the southern limit of the distribution of Atlantic salmon (Salmo salar L.) in Europe, a biological resource facing one of the more serious challenges for conservation today. In this work, eight microsatellite loci have been used to analyse samples collected in 1993 and 1999 from four Asturian rivers (Esva, Narcea, Sella, and Cares), obtaining information about the temporal and the spatial genetic variation in these populations and, in addition, estimations of their effective population sizes. The temporal analysis revealed a general decrease in all the estimated genetic variability parameters when samples from 1993 (mean A ₍₁₉₉₃₎ = 6.47, mean H _O(1993) = 0.472, mean H _E(1993) = 0.530) were compared with those obtained in 1999 (mean A ₍₁₉₉₉₎ = 6.16, mean H _O(1999) = 0.460, mean H _E(1999) = 0.490). This reduction was particularly notable for the case of the Esva river. Our results pointed to a pattern of spatial genetic differentiation inside the Asturian region (F _{ST (1993)} = 0.016 P < 0.01; F _{ST (1999)} = 0.023 P < 0.01). Using the standard Temporal Method we found estimates of N _e^{^} _(Esva) = 75.1 (33.2–267.2); N _e^{^} _(Cares) = 96.6 (40.0–507.5), N _e^{^} _(Sella) = 106.5 (39.1–9396.4) and N _e^{^} _(Narcea) = 113.9 (42.0–3693.3). The use of likelihood-based methods for the N _e^{^} estimations improved the results (smaller CIs) for the Esva and Cares rivers (N _e^{^} _(Esva) = 63.9 (32.3–165.3); N _e^{^} _(Cares) = 76.4 (38.8–202.0) using a Maximum likelihood approach) and suggested the presence of larger populations for the Sella and Narcea rivers (N _e^{^}≈200). These results showed that the Asturian Atlantic salmon populations (in particular Esva and Cares river populations) could be close to the conservation genetic borderline for avoiding inbreeding depression although we discuss some implications of the analysis of temporal genetic change in populations with overlapping generations.     

On the exact null distribution of the generalised likelihood ratio test for analysing unreplicated factorial designs

Al-Shiha and Yang (1999) proposed a multistage procedure for analysing unreplicated factorial experiments, which is based on the statistic that is derived from the generalised likelihood ratio test statistic under the assumption of normality. It was shown by their simulation study that the method is quite competitive with Lenth's (1989) method. In their paper, because of the difficulty of determining the null distribution analytically, the quantiles of the null distribution were empirically simulated. In this paper, we give the exact null distribution of their test statistic, which makes it possible to calculate the critical values of the test.     

Inversion of net ecosystem CO2 flux measurements for estimation of canopy PAR absorption

The fractional absorption of photosynthetically active radiation (f_PAR) is frequently a key variable in models describing terrestrial ecosystem–atmosphere interactions, carbon uptake, growth and biogeochemistry. We present a novel approach to the estimation of the fraction of incident photosynthetically active radiation absorbed by the photosynthetic components of a plant canopy (f_Chl). The method uses micrometeorological measurements of CO₂ flux and incident radiation to estimate light response parameters from which canopy structure is deduced. Data from two Ameriflux sites in Oklahoma, a tallgrass prairie site and a wheat site, are used to derive 7‐day moving average estimates of f_Chl during three years (1997–1999). The inverse estimates are compared to long‐term field measurements of PAR absorption. Good correlations are obtained when the field‐measured f_PAR is scaled by an estimate of the green fraction of total leaf area, although the inverse technique tends to be lower in value than the field measurements. The inverse estimates of f_Chl using CO₂ flux measurements are different from measurements of f_PAR that might be made by other, more direct, techniques. However, because the inverse estimates are based on observed canopy CO₂ uptake, they might be considered more biologically relevant than direct measurements that are affected by non‐physiologically active components of the canopy. With the increasing number of eddy covariance sites around the world the technique provides the opportunity to examine seasonal and inter‐annual variation in canopy structure and light harvesting capacity at individual sites. Furthermore, the inverse f_Chl provide a new source of data for development and testing of f_PAR retrieval using remote sensing. New remote sensing algorithms, or adjustments to existing algorithms, might thus become better conditioned to ‘biologically significant’ light absorption than currently possible.     

Phosphorus alleviates aluminum-induced inhibition of growth and photosynthesis in Citrus grandis seedlings

Limited data are available on the effects of phosphorus (P) and aluminum (Al) interactions on Citrus spp. growth and photosynthesis. Sour pummelo (Citrus grandis) seedlings were irrigated for 18 weeks with nutrient solution containing 50, 100, 250 and 500 μM KH₂PO₄× 0 and 1.2 mM AlCl₃· 6H₂O. Thereafter, P and Al in roots, stems and leaves, and leaf chlorophyll (Chl), CO₂ assimilation, ribulose‐1,5‐bisphosphate carboxylase/oxygenase (Rubisco) and Chl a fluorescence (OJIP) transients were measured. Under Al stress, P increased root Al, but decreased stem and leaf Al. Shoot growth is more sensitive to Al than root growth, CO₂ assimilation and OJIP transients. Al decreased CO₂ assimilation, Rubisco activity and Chl content, whereas it increased or did not affect intercellular CO₂ concentration. Al affected CO₂ assimilation more than Rubisco and Chl under 250 and 500 μM P. Al decreased root, stem and leaf P, leaf maximum quantum yield of primary photochemistry (F_v/F_m) and total performance index (PI_tot,abs), but increased leaf minimum fluorescence (F_o), relative variable fluorescence at K‐ and I‐steps. P could alleviate Al‐induced increase or decrease for all these parameters. We conclude that P alleviated Al‐induced inhibition of growth and impairment of the whole photosynthetic electron transport chain from photosystem II (PSII) donor side up to the reduction of end acceptors of photosystem I (PSI), thus preventing photosynthesis inhibition through increasing Al immobilization in roots and P level in roots and shoots. Al‐induced impairment of the whole photosynthetic electron transport chain may be associated with growth inhibition.     

An Improved Goodness of Fit Statistic for Probability Prediction Models

We consider the general case of probability prediction models having two or more outcomes and propose an adjusted χ² statistic which can be used to assess the goodness of fit of these models. We present a simulation study to show that our proposed statistic has an approximate χ² distribution under the null hypothesis. Two applications are provided to illustrate the use of the new statistic. The first application examines the fit of a logistic regression model using both the proposed statistic and the popular Hosmer-Lemeshow statistic and we compare and contrast these two methods. The second application evaluates the goodness of fit of a polychotomous regression model.     

Bootstrap and Second‐Order Tests of Risk Difference

Summary Clinical trials data often come in the form of low‐dimensional tables of small counts. Standard approximate tests such as score and likelihood ratio tests are imperfect in several respects. First, they can give quite different answers from the same data. Second, the actual type‐1 error can differ significantly from nominal, even for quite large sample sizes. Third, exact inferences based on these can be strongly nonmonotonic functions of the null parameter and lead to confidence sets that are discontiguous. There are two modern approaches to small sample inference. One is to use so‐called higher order asymptotics ( Reid, 2003 , Annal of Statistics 31 , 1695–1731) to provide an explicit adjustment to the likelihood ratio statistic. The theory for this is complex but the statistic is quick to compute. The second approach is to perform an exact calculation of significance assuming the nuisance parameters equal their null estimate ( Lee and Young, 2005 , Statistic and Probability Letters 71 , 143–153), which is a kind of parametric bootstrap. The purpose of this article is to explain and evaluate these two methods, for testing whether a difference in probabilities p₂? p₁ exceeds a prechosen noninferiority margin δ₀ . On the basis of an extensive numerical study, we recommend bootstrap P‐values as superior to all other alternatives. First, they produce practically identical answers regardless of the basic test statistic chosen. Second, they have excellent size accuracy and higher power. Third, they vary much less erratically with the null parameter value δ₀ .     

A Truncated Proportional Hazards Test

We present two truncated proportional hazards tests. The first, which is applicable to those cases in which the time of action of an agent or treatment is known, was studied in two forms: One uses expected Fisher information and the other observed Fisher information. In this case the expected information statistic, C₁(a₀), had properties superior to the observed information statistic and is recommended. The use of the X² distribution with one degree of freedom for percentiles appears to be satisfactory. When the time of action is unknown, a statistic based on the maximum of the C₁(a) statistics is used. A simulation study gives empirical percentiles for the Max C₁(a) statistic which agree with those given in a study by Muenz, Green and Byar (1977).