Physical Sciences and Mathematics Commons^™

Trial By Jury Or Judge: Transcending Empiricism, Kevin M. Clermont, Theodore Eisenberg

Cornell Law Faculty Publications

Pity the civil jury, seen by some as the sickest organ of a sick system. Yet the jury has always been controversial. One might suppose that, with so much at stake for so long, we would all know a lot about the ways juries differ from judges in their behavior. In fact, we know remarkably little. This Article provides the first large-scale comparison of plaintiff win rates and recoveries in civil cases tried before juries and judges. In two of the most controversial areas of modern tort law--product liability and medical malpractice--the win rates substantially differ from other cases' win …

The Need For The Analysis Of Treatment X Period Interaction In Animal Experiments, L. A. Goonewardene, L. Z. Florence

Conference on Applied Statistics in Agriculture

Many growth experiments, in which weights are taken at different times on the same animals, involve the comparison of factorial main effects and interactions but exclude time (period) as an effect. The objective of this paper is to show that more information can be obtained by analysing the data as a repeated measures design. As an example, feedlot cattle being prepared for market are often on growth implants and provided different diets depending on the stage of growth and maturity. Growth promoting implants, either single or double, may be slow or fast acting. During the growing period, a diet with …

A Comparison Of Double Sampling Regression Estimators, Dennis L. Clason, G. Morris Southward

Conference on Applied Statistics in Agriculture

We investigate three alternative models for estimating the mean of a population using double sampling survey techniques. One estimator was found in the range science literature (Cook and Stubbendieck, 1986), another is the estimator presented by Cochran (1977). The third estimator uses method-of-moments estimators with measurement error regression models. Simulation studies suggest that the measurement error model does not work well when the slope is appreciably different from unity. Delta method variance estimators of the measurement error model may give negative variance estimates under these circumstances. The other estimators have better small sample performance (both are approximately unbiased, and have …

Simplified Data Analysis For Generally Balanced But Messy Experimental Designs, Richard E. Lund

Conference on Applied Statistics in Agriculture

Johnson posted the essential elements of a 'messy' experimental design and challenged participants at the 1991 KSU Conference on Applied Statistics in Agriculture to provide an analysis. Subsequently, he proposed an analysis using SAS. The experiment was laid out by a soil scientist and involved six classifying factors in an intricate crossing and nesting arrangement which lead to a need to consider eight error terms. My objective at the poster session was to show by live computer demonstration that the analysis can be setup and conducted more easily by use of software applying Wilkinson's methodology.

Soil Properties And Landtypes--Classification And Identification With Discriminant Analysis, R. David Hammer, John W. Philpot

Conference on Applied Statistics in Agriculture

Intensive land use is requiring more detailed information about patterns and magnitudes of soil variability than can be acquired through traditional soil survey techniques. Discriminant analysis is a mathematical method of numerical classification which could be used to identify discrete populations of soils in their natural settings. The hypothesis of this study was that discriminant analysis could be used to group soils on landtypes on the Mid-Cumberland Plateau. A large data set (132 observations of 29 soil variables) was collected from three landtypes at two Cumberland Plateau locations. Discriminant analysis was used to classify the soil observations into landtypes. Canonical …

Regression Modeling Using Principal Components, Shahar Boneh, Gonzalo R. Mendieta

Conference on Applied Statistics in Agriculture

In this paper we present a new stepwise method for selecting predictor variables in linear regression models and its application to agricultural data analysis. This method is an extension of principal component regression, and it consists of iteratively selecting original predictor variables one at a time from repeatedly selected subsets of principal components. The reasoning behind the method and its implementation are discussed, and an example of applying the method to agricultural data is given. The example also demonstrates the advantages of the proposed method over some known methods.

An Example Of Path Analysis Applied To Classification Variables Applied To Classification Variables, Richard E. Lund, Albert L. Scharen

Conference on Applied Statistics in Agriculture

Path analysis was originally proposed to decompose and interpret causal linear relationships among a set of continuous stochastic variables. Research designs necessarily employed the natural variation in the system rather than the technique of controlling independent variables by selection of levels and categories which is emphasized in many experimental designs. Path coefficients are closely related to correlation coefficients, the size of which will be controlled when variation in the system is controlled. We examine a data set produced by research related to worldwide occurrence of a wheat pathogen and describe techniques for applying path analysis to its variables, some of …

When Should Random Effects Be Included In Estimable Functions And When They Should Not?, David C. Blouin

Conference on Applied Statistics in Agriculture

In the mixed model, the behavior of linear functions of the fixed and random effects is examined. It is found that inclusion of certain functions of random effects can lead to estimators which are equivalent to those under a fixed effects model and are inconsistent with the inherent structure of the mixed model. Three examples are presented which illustrate the behavior of linear functions of the fixed and random effects. These functions represent the broad, narrow and intermediate inference spaces as introduced by McLean, Sanders and Stroup (1991). Which random effects should be included in the model is discussed. Random …

Analyzing Split-Plot Andrepeated-Measures Designsusing Mixed Models, Russ Wolfinger, Nancy Miles-Mcdermott, Jenny Kendall

Conference on Applied Statistics in Agriculture

We first introduce the general linear mixed model and provide a justification for using REML to fit it. Then, for an irrigation example, we present several mixed models of increasing complexity. The initial model corresponds to a typical split-plot analysis. Next, we present covariance structures that directly describe the variability of repeated measures within whole plots. Finally, we combine the above types into more complicated mixed models, and compare them using likelihood-based criteria.

Analysis Of Mixed Models Without Mixed Models Software, George A. Milliken

Conference on Applied Statistics in Agriculture

The recent development of mixed model software has expanded the use of mixed models analysis, but mixed models have been analyzed using non-mixed models software for many years. The purpose of this paper is to discuss the differences, similarities, advantages and disadvantages of the two approaches. Section 1 introduces the mixed model with two examples. The analysis of the mixed model using mixed models software is presented in Section 2 and the analysis of the mixed model using non-mixed models software is described in Section 3. Finally, an 'example' is used to compare the two methodologies.

Options For Analyzing Unbalanced Split-Plot Experiments: A Case Study, Marta D. Remmenga, Dallas E. Johnson

Conference on Applied Statistics in Agriculture

Unbalanced split-plot experiments present many analysis problems. This paper discusses some of the difficulties by comparing the results of the analysis recommended by Milliken and Johnson (1984) to a set of minimal sufficient statistics using a small experiment from Milliken and Johnson as a case study. The estimators used by Milliken and Johnson are not necessarily the best (smallest variance) estimators. A set of minimal sufficient statistics is used to show that the whole plot error term suggested by Milliken and Johnson does not have a distribution that is proportional to an exact chi-square distribution and is not always independent …

The Analysis Of Tree Ring Chronologies Using A Mixed Linear Model, O. Brian Allen, Daniel A.J. Ryan, David L. Mclaughlin

Conference on Applied Statistics in Agriculture

The analysis of a tree's annual growth rings can provide a great deal of information about the environment in which the tree has grown. In this paper we propose statistical methodology for analysing the incremental growth of sugar maple sampled throughout southern and central Ontario, by the Ontario Ministry of the Environment. Two trees, ranging in age from 75 to 150 years, were sampled from each of 42 stands in 6 regions. The data were analysed using a mixed linear model, incorporating age of tree, region, year, a year by region interaction and average monthly air temperature and total seasonal …

Estimating Variance Functions For Weighted Linear Regression, Michael S. Williams, Hans T. Schreuder, Timothy G. Gregoire, William A. Bechtold

Conference on Applied Statistics in Agriculture

For linear models with heterogeneous error structure, four variance function models are examined for predicting the error structure in two loblolly pine data sets and one white oak data set. An index of fit and a simulation study were used to determine which models were best. The size of coefficients for linear and higher order terms varied drastically across different data sets, thus it is not desirable to recommend a general model containing both linear and higher order terms. The unspecified exponent model σ²v_i = σ²⁽D_i² H_i)^{k 1} is recommended …

Planning A Safety Study Of An Agricultural Product: Effects Of Land Application Of Phosphogypsum On Radon Flux, Ramon C. Littell, Sudeep Kundu

Conference on Applied Statistics in Agriculture

Traditional agricultural research has been concerned largely with demonstrating that new products or new practices increase yield from plants or animals; i.e. that a change has occurred. Concepts of experimental design have been effectively employed in production-agriculture research planning to control extraneous variation and thereby reduce experimental error. Good data analysis practices have been employed to control type 1 error rate and to correctly compute errors of estimation. In recent years, increased emphasis has been placed on food safety and environmental impact of agricultural products. Studies of these issues are concerned with measuring small effects with required precision or establishing …

A Simple Alternative To The Standard Statistical Model For The Analysis Of Field Experiments With Latin Square Designs, C. Philip Cox, Jeff B. Meeker

Conference on Applied Statistics in Agriculture

Latin Square (LS) designs have long been advocated for field crop experiments on the grounds that '. . . soil fertility and other variations in two directions are controlled.' As counter-evidence, the published standard analyses of eight LS experiments showed that in only two did the sum of squares for both between-rows and between-columns account for appreciable background variability.

Regarding the background concomitant variability as a continuous surface to which treatment effects are additive, it is suggested that a contributory shortcoming of the standard model is that it admits only a restricted class of surfaces because parameters for warp, or …

Designed Experiments In The Presence Of Spatial Correlation, David B. Marx

Conference on Applied Statistics in Agriculture

Soil heterogeneity is generally the major cause of variation in plot yield data and the difficulty of its interpretation. If a large degree of variability is present at a test site, some method of controlling it must be found. Controlling experimental variability can be achieved either by good experimental design or by analysis procedures which account for the spatial correlation. Classical designs are only moderately equipped to adjust for spatially correlated data. More complex designs including nearest neighbor designs, Williams designs, and certain restricted Latin square designs are developed for field experimentation when spatial correlation causes classical designs to be …

Confidence Intervals For Soil Properties Based On Differing Statistical Assumptions, Fred J. Young, R. David Hammer, Jon M. Maatta

Conference on Applied Statistics in Agriculture

Agricultural soil management is becoming increasingly precise as technology advances and as environmental concerns increase. Soil surveys are a readily available source of soils information, but soil properties are reported as generalized values or generic ranges. A need exists to define the central tendencies of soil properties in a rigorous, quantified fashion. Statistically, the central tendency is best expressed as confidence intervals about means or medians. Transect sampling was used to collect data on soil properties within a soil survey map unit. Key questions for data analysis include assumptions of independence within transects and normality. The choice of statistical method …

A Markov Chain Model To Assess Resistance Of Cattle To Horn Flies, Edward Gbur, C. Dayton Steelman

Conference on Applied Statistics in Agriculture

The horn fly is an economically important external permanent parasite of cattle. As part of a research project focused on alternatives to chemical control of the horn fly, a study was conducted to determine the degree of innate resistance of individual cattle to the horn fly. A fly resistant cow was defined as one whose horn fly counts were in the lower quartile of the weekly fly count distributions for a herd more often than would be expected by chance. A Markov chain model was formulated and a small sample test for fly resistance was developed. The model and procedure …

Statistical Analysis Of Genotype-By-Environment Interaction Using The Ammi Model And Stability Estimates, Bahman Shafii, William J. Price

Conference on Applied Statistics in Agriculture

Understanding the implication of genotype-by-environment (GE) interaction structure is an important consideration in plant breeding programs. A significant GE interaction for a quantitative trait such as yield can seriously limit efforts in selecting superior genotypes for both new crop introduction and improved cultivar development. Traditional statistical analyses of yield trials provide little or no insight into the particular pattern or structure of the GE interaction. The Additive Main Effects and Multiplicative Interaction (AMMI) statistical model incorporates both additive and multiplicative components of the two-way data structure which can account more effectively for the underlying interaction patterns. Integrating results obtained from …

Utilization Of The Line-Intercept Method To Estimate The Coverage, Density, And Average Length Of Row Skips In Cotton And Other Row Crops, Jeffrey L. Willers, Sreenivasa R. Yatham, Michael R. Williams, Dennis C. Akins

Conference on Applied Statistics in Agriculture

In row crops, a skip is a length of row within the drill where the crop has failed to establish. If the number of skips and their mean length per acre becomes too high, then considerable losses in crop yield occur. Frequently, farmers are faced with the decision to replant a crop which has row skips. To make the best decision, reliable estimates of the stand loss due to skips must be available. In making this decision, three parameters are useful: the percent of the area per acre that is skipped, the number of individual skips (that is, density) per …

Prevalence Rate Differences Based On Herdmate Comparisons, Jerome M. Sacks, Randall C. Cutlip, Amy L. Weaver, Howard D. Lehmkuhl

Conference on Applied Statistics in Agriculture

A non-random survey of ovine progressive pneumonia (OPP) seropositive prevalence rates among 16,827 sheep in 29 states in the United states revealed large breed differences, a higher prevalence rate among older sheep and an unexplainable female rate that was more that three times the male rate. The herdmate comparison procedure, successfully used in evaluating dairy bulls, was adapted to compare the prevalence of a breed to the rate of its herdmates within herds. Likewise, sex and age differences in OPP prevalence were compared within herds that contained animals of both sexes and several ages. Using herdmate comparisons, breed and age …

Studying Herbicide Resistance Using Treatment Area Dynamics Model, Agam N. Sinha, Dale L. Shaner

Conference on Applied Statistics in Agriculture

Repeated use of a herbicide or herbicides with the same mode of action on a particular crop over a number of years may cause the selection of herbicide resistant weed populations. As a result effective weed control is lost which can seriously affect crop yield and quality. The selection of herbicide resistant weed populations is a concern not only for crop-growers, but also the manufacturers of the affected herbicides. In the present paper a two-step procedure is developed to identify the herbicide resistant activity in a particular crop growing region by estimating the resistant areas (in acres/hectares) in a given …

Co-Effect Analysis Of Variance: A New Method For Unbalanced Data, Andre Plante

Conference on Applied Statistics in Agriculture

For fixed-effect models one can always, according to the Gauss-Markov Theorem, uniquely determine independent variables called source identifiers, each corresponding to a source of variation. When linearly combined, source identifiers can generate all possible expected values for the response variable. The co-effect method uses regression of the response variable on source identifiers. Corresponding regression coefficients are, by definition, unbiased estimates of co-effects, and satisfy the same restrictions as those imposed on main effects and interaction effects in standard analysis of variance. with balanced data, co-effect analysis gives results identical to those of the standard method; with unbalanced data, however, results …

Beyond Linearity And Independence, J. Stuart Hunter

Conference on Applied Statistics in Agriculture

This brief lecture discusses statistical problems associated with postulating and fitting models in engineering and the sciences. Particular emphasis is placed on the two-model problem: the employment of both deterministic and stochastic components within a model. Further, the use of empirical versus theoretical models on the part of both statisticians and experimenters is examined.

Editor's Preface, Table Of Contents, And List Of Attendees, George A. Milliken

Conference on Applied Statistics in Agriculture

These proceedings contain papers presented at the fourth annual Kansas State University Conference on Applied Statistics in Agriculture, held in Manhattan, Kansas, April 26 through 28, 1992.

Inside The Quiet Revolution In Products Liability, Theodore Eisenberg, James A. Henderson Jr.

Cornell Law Faculty Publications

"A bullet in the head of products liability reform." Thus did a lobbyist orally characterize our article in this law review, The Quiet Revolution in Products Liability, describing declining plaintiff success in products liability cases in the 1980s. From the coverage and criticism the Quiet Revolution received around the country and around the world, the trends we discovered struck many as surprising enough to be newsworthy and others as sufficiently threatening to warrant a special response. Products liability's sustained presence on state and federal legislative agendas warrants continuing and expanding the study begun in the Quiet Revolution.

This …

Book Review, Thomas G. Field Jr.

RISK: Health, Safety & Environment (1990-2002)

Review of the following book: THOMAS GILOVICH, How WE KNOW WHAT ISN'T SO: THE FALLIABILITY OF REASON IN EVERYDAY LIFE. (The Free Press 1991) [216 pp.] Index, notes. CIP: 90-26727; ISBN: 0-02-911705-4. [Cloth $19.95. 866 Third Ave. New York, NY 10022.]

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Yi Li

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Yi Li

No abstract provided.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.