Analysis of covariance: an alternative to nutritional indices

Some statistical problems are added to the growing list of cautionary tales regarding the use of the conventional, ratio-based nutritional indices (RCR, RGR, ECI, AD and ECD). Analysis of ratios is based on the, probably unrealistic, assumption of an isometric relationship between denominator and numerator variables. Analysis of covariance (ANCOVA) makes less restrictive assumptions, and additionally provides important information about the data which is lost by using ratio variables. We demonstrate, using computer-generated data sets, some of the pitfalls of statistical analysis of ratios and illustrate how these may be avoided using ANCOVA. Some possible consequences of such statistical iniquities for biological interpretations are discussed.     

A Method for Analyzing Nonlinear Models When the Data are from a Split-plot or Repeated Measures Design

Statistical methods are described which can be used to compare treatments where the response model is nonlinear and the experimental design includes split-plots or repeated measures. The nonlinear analysis of covariance is described for a two-way treatment structure in a split-plot design structure, the usual split-plot experimental design. Evaluating heat tolerance in common beans as a function of temperature is used as an example to demonstrate the methodology.     

Rank Covariance Methods for the Analysis of Survival Data

A procedure for comparing survival times between several groups of patients through rank analysis of covariance was introduced by WOOLSON and LACHENBRUCH (1983). It is a modification of Quade' rank analysis of covariance procedure (1967) and can be used for the analysis of right-censored data. In this paper, two additional modifications of Quade' original test statistic are proposed and compared to the original modification introduced by Woolson and Lachenbruch. These statistics are compared to one another and to the score test from Cox' proportional hazards model by way of a limited Monte Carlo study. One of the statistics, Q_R2, is recommended for general use for the rank analysis of covariance of right-censored survivorship data.     

Foundations of spatial ecology: the reification of patches through quantitative description of patterns and pattern repetition

Insect populations tend to be patchy, and the nature of the patches is a critical component of ecology. Predator-prey interactions, coexistence of competing species, survival of rare species as habitat is destroyed, and damage to crops are just a few examples of spatially-dependent ecological processes. For want of tractable quantitative approaches, understanding of spatial ecology has lagged far behind recognition of its importance. We assert that a quantitative foundation of a spatial ecology involves the reification of patches as objects of study. We introduce two new measures of patch dynamics: total covariance for comparing degrees of patchiness between populations, and quantile variance for quantifying the constancy of dispersion patterns through time. These new measures, in combination with the long-established spatial covariance from geostatistics, comprise a rudimentary toolbox for reification of patches and empirical field studies in spatial ecology.     

Further comments on analysis of covariance in insect dietary studies

Raubenheimer & Simpson (1992) recently discussed the advantages of using analysis of covariance in insect dietary studies as an alternative to the more conventional ratio-based nutritional indices. We expand on some interpretations of Raubenheimer & Simpson and illustrate our points with examples from published and unpublished data sets. Specifically, we show that an ANCOVA on biomass gain incorporating initial biomass as a covariate provides information not immediately available using the analysis suggested by Raubenheimer & Simpson (ANCOVA on final biomass incorporating initial biomass as a covariate). Second, we show that dietary studies in which the covariate (food consumption) is affected by diet can provide information about the relative importance of preingestive effects (e.g., deterrence) and postingestive effects (e.g., antibiosis) on performance. Cautions about this latter use of ANCOVA are discussed.     

基于最小自由能和协变信息预测带伪结RNA二级结构的迭代化方法

多数RNA分子的结构在进化中是高度保守的, 其中很多包含伪结。而RNA伪结的预测一直是一个棘手问题, 很多RNA 二级结构预测算法都不能预测伪结。文章提出一种基于迭代法预测带伪结RNA 二级结构的新方法。该方法在给潜在碱基对打分时综合了热力学和协变信息, 通过基于最小自由能RNA折叠算法的多次迭代选出所有的碱基对。测试结果表明: 此方法几乎能预测到所有的伪结。与其他方法相比, 敏感度接近最优, 而特异性达到最优。     

Model misspecification in proportional hazards regression

The proportional hazards model is frequently used to evaluatethe effect of treatment on failure time events in randomisedclinical trials. Concomitant variables are usually availableand may be considered for use in the primary analyses underthe assumption that incorporating them may reduce bias or improveefficiency. In this paper we consider two approaches to includingcovariate information: regression modelling and stratification.We focus on the setting where covariate effects are nonproportionaland we compare the bias, efficiency and coverage propertiesof these approaches. These results indicate that our intuitionbased on linear model analysis of covariance is misleading.Covariate adjustment in proportional hazards models has littleeffect on the variance but may significantly improve the accuracyof the treatment effect estimator.     

A Multivariate Analysis of Hybridization when Covariance Matrices are Unequal

Numerous occurrences of natural hybridization have been known in many groups of animals. It has a bearing on growth, nomenclature, speciation, genetics and wildlife management. It is well recognised that demonstration of intermediacy based on several characters makes the identification of hybrids more certain than that based on just a single character, and that differences among the hybrids and the parental populations should be analysed for variations due to the additive genetic (A) and the non-additive genetic (NA) factors separately. In the present paper (i) it is pointed out that sometimes the assumption that covariance matrices of the hybrids and the parental populations are equal, may not be valid, and (ii) a multivariate method of testing hypotheses analysing differences between the hybrids and the parents, qualified by the A and the NA factors, when covariance matrices are not equal, is submitted.     

Testing the rate isomorphy hypothesis using five statistical methods

Abstract Organisms are said to be in developmental rate isomorphy when the proportions of developmental stage durations are unaffected by temperature. Comprehensive stage‐specific developmental data were generated on the cabbage beetle, Colaphellus bowringi Baly (Coleoptera: Chrysomelidae), at eight temperatures ranging from 16°C to 30°C (in 2°C increments) and five analytical methods were used to test the rate isomorphy hypothesis, including: (i) direct comparison of lower developmental thresholds with standard errors based on the traditional linear equation describing developmental rate as the linear function of temperature; (ii) analysis of covariance to compare the lower developmental thresholds of different stages based on the Ikemoto‐Takai linear equation; (iii) testing the significance of the slope item in the regression line of versus temperature, where p is the ratio of the developmental duration of a particular developmental stage to the entire pre‐imaginal developmental duration for one insect or mite species; (iv) analysis of variance to test for significant differences between the ratios of developmental stage durations to that of pre‐imaginal development; and (v) checking whether there is an element less than a given level of significance in the p‐value matrix of rotating regression line. The results revealed no significant difference among the lower developmental thresholds or among the aforementioned ratios, and thus convincingly confirmed the rate isomorphy hypothesis.     

Discriminant functions for linear comparisons of means when covariance matrices are unequal

Situations exist, as in the biological example of discriminant analysis for natural hybridization, cited in the text, where (a) not all populations have equal variances, and (b) comparisions based on single degrees of freedom must be planned. This paper presents a statistical methodology of estimating discriminant functions for linear comparisons among k(<2) multivariate normal populations, and of testing their significance, when these populations have unequal covariance matrices.     

The relative merits of open- and closed-path analysers for measurement of eddy fluxes

Theoretical and practical aspects of measuring eddy fluxes of trace gases using open-and closed-path analysers are presented. Trace gas fluxes measured with an open-path analyser require the concurrent measurement of sensible and latent heat fluxes to correct for density fluctuations in trace gas concentration caused by these fluxes. A closed-path analyser eliminates the corrections due to sensible heat flux, but not for water vapour, provided temperature fluctuations are completely removed without significantly reducing fluctuations in the trace gas mixing ratio. Theory for the design of heat exchangers and for the attenuation of concentration fluctuations during air flow through tubes is used to provide design criteria for closed-path systems. Spectral transfer functions are used to estimate flux losses caused by flow through the sampling tube and gas analyser. Other factors considered include cross-sensitivity of infrared CO₂ analysers to water vapour, and deterioration of system performance caused by contaminants on the walls of sampling tubes. Of two open-path, infrared CO₂ analysers tested, one showed a strong interaction between CO₂ and water vapour, while the other showed little sensitivity to the presence of water vapour, other than caused by dilution. A commercial closed-path CO₂ analyser also showed little cross-sensitivity to water vapour. Compared to results for a clean sampling tube, the spectral bandwidth for water vapour fluctuations decreased significantly after several weeks of sampling. No such deterioration in bandwidth was observed for CO₂. These findings are attributed to differential adsorption/desorption of water vapour by dust or salt on the tubing walls. Rain and dust must be removed from open-path analysers to obtain satisfactory measurements. Careful system design and maintenance is required for both open- and closed-path systems to ensure satisfactory long-term measurement of trace gas fluxes. With these precautions, both approaches will provide satisfactory flux measurements.