W. B. Smith

Scoring under ordered constraints in contingency tables

Methods are developed for analyzing contingency tables which have ordered categoriesa priori. A correspondence analysis is extended to incorporate this a priori ordering. An exact represention is obtained when differences in the scores of the categories are known.

A Simple Method for Obtaining the Information Matrix for a Multivariate Normal Distribution

The purpose of this note is to present a simple method for finding the informnation matrix, and its inverse, for the p-variate normal distribution, N(O,2). Corresponding matrices for N(,u,) are easily obtained since they are block diagonal and the portion corresponding to , presents no difficulty. The simplicity of the technique presented here arises froin the fact that both the information matrix and its inverse can be expressed as the product of a diagonal matrix with a matrix whose elements are given by a simple set of formulas. The basic technique is extended to the case in which some observations on one of the variates are missing, and is illustrated by an example.

Combinatoric classification of multivariate normal variates

Consider classifying an n × I observation vector as coming from one of two multivariate normal distributions which differ both in mean vectors and covariance matrices. A class of dis-crimination rules based upon n independent univariate discrim-inate functions is developed yielding exact misclassification probabilities when the population parameters are known. An efficient search of this class to select the procedure with minimum expected misclassification is made by employing an algorithm of the implicit enumeration type used in integer programming. The procedure is applied to the classification of male twins as either monozygotic or dizygotic.

Properties of profile parallelism tests in repeated measures designs

Properties of several test statistics for profile parallelism in repeated measures designs are evaluated by simulation. The procedures were derived to test secondary hypotheses in the presence of significant time by treatment interactions. Statistical techniques commonly available in computer packages are found to be inferior to the recommended test statistics.

Normal combinatoric classification: The sample case

Combinatoric classification of multivariate observation vectors is a procedure which can be applied to two normal populations with known parameters. Exact probabilities of misclassification can be obtained in this known parameter case. This paper extends combinatoric classification to the unknown parameter case by substituting appropriate estimates for the unknown parameters Simulation results are given for the specific trivariate case where the mean vectors are equal and the covariance matrices are of a special form.

A note on homogeneity tests of covariance matrices

In this note we propose two procedures for testing homogeneity of co-variance matrices that are both extensions of Hartleys (1940) test for equality of variances. The first is a two-stage procedure where the first step is a simple test for equality of the largest eigenvalues, and corresponding eigenvectors, of the covariance matrices. The second is based on projection pursuit and seems harder to apply in practice.

Effects of rotating antibiotic and ionophore feed additives on volatile fatty acid production, potential for methane production, and microbial populations of steers consuming a moderate-forage diet

Ionophores and antibiotics have been shown to decrease ruminal methanogenesis both in vitro and in vivo but have shown little evidence toward a sustainable means of mitigation. Feed additive rotation was proposed and investigated for methane, VFA, and microbial population response. In the present study, cannulated steers ( = 12) were fed a moderate-forage basal diet in a Calan gate facility for 13 wk. In addition to the basal diet, steers were randomly assigned to 1 of 6 treatments: 1) control, no additive; 2) bambermycin, 20 mg bambermycin/d; 3) monensin, 200 mg monensin/d; 4) the basal diet + weekly rotation of bambermycin and monensin treatments (B7M); 5) the basal diet + rotation of bambermycin and monensin treatments every 14 d (B14M); and 6) the basal diet + rotation of bambermycin and monensin treatments every 21 d (B21M). Steers were blocked by weight in a randomized complete block design where the week was the repeated measure. Rumen fluid was collected weekly for analysis ( = 13), and results were normalized according to individual OM intake (OMI; kg/d). Potential activity of methane production was not significantly different among treatments ( > 0.05). However, treatment tended to affect the CH-to-propionate ratio ( = 0.0565), which was highest in the control and lowest in the monensin, B21M, and B14M treatments (0.42 vs. 0.36, 0.36, and 0.33, respectively). The CH:propionate ratio was lowest in wk 2 and 3 ( < 0.05) but the ratio in wk 4 to 12 was not different from the ratio in wk 0. Week also affected total VFA, with total VFA peaking at wk 3 and plummeting at wk 4 (4.02 vs. 2.86 m/kg OMI; < 0.05). A significant treatment × week interaction was observed for the acetate-to-propionate (A:P) ratio, where bambermycin- and rotationally fed steers did not have a reduced A:P ratio compared with monensin-fed steers throughout the feeding period ( < 0.0001). Microbial analysis revealed significant shifts, but several predominant classes showed adaptation between 4 and 6 wk after additive initiation. There was no significant evidence to suggest that rotations of monensin and bambermycin provided additional benefits to steers consuming a moderate-forage diet at the microbial/animal and environmental level versus those continuously fed.

Prebiotic and Probiotic Approaches to Improving Food Safety on the Farm and Their Implications on Human Health

Human health is a broad category that encompasses the entirety of the food produc‐ tion system. Livestock production practices have important effects on human health because livestock not only are a primary food source but also can be the source of pathogenic bacteria that may enter the food chain indirectly. As government regula‐ tion and public scrutiny restrict the prophylactic use of antibiotic and antimicrobial interventions, other techniques must be used to reduce the burden of animal‐borne pathogenic bacteria entering the food system. Prebiotics (isolated compounds that enhance natural microflora and thereby decrease pathogens) and probiotics (live microbes that are administered to livestock to enhance microbial diversity and crowd out pathogens) represent two unique opportunities for alternative measures in pathogen reduction. This review addresses the link between animal production and human health, the agricultural sources of pathogenic organisms, and the probiotic and prebiotic approaches that have been evaluated in an effort to reduce carriage of foodborne pathogenic bacteria by livestock.

Inference with overlapping 2×2 tables

Exact probabilities (under a Markov-like assumption) are calculated for overlapping 2×2 contingency tables. These contingency tables often arise in biological and legal situations that yield dichotomous responses, including the evaluation of clinical trials and the determination of prima facie evidence of employer discrimination. In this note, probabilities, means and variances are derived and comparisons are made with results when assuming no overlap exists.

Profile parallelism in repeated measures designs

Three statistics are developed to test tor treatment by time interaction after a certain point in repeated measures designs under several covariance matrix configurations, viz., unstructured, spherically symmetric and autoregressive. An example is fully developed.