Physical Sciences and Mathematics Commons^™

Can Simple Random Sampling Confidence Intervals Be Used On Transect Sampling Data?, William Noble

Conference on Applied Statistics in Agriculture

When sampling geographic regions, transect sampling may be easier and cheaper than simple random sampling. However, transect sampling data is more difficult to analyze. In the past, transect sampling data has sometimes been analyzed as if it was the result of simple random sampling. The purpose of this note is to present simulation results which show that this can lead to vastly inaccurate conclusions when one is calculating confidence intervals. In particular, an example is given of a purported 95% confidence interval which is actually a 49% confidence interval.

Binomial Variation In The Sex Composition Of Pig Families, Thomas Kirchoff, D. F. Cox

Conference on Applied Statistics in Agriculture

Given the known mechanisms for sex determination, the number of males in families of pigs should follow a binomial distribution. A report of deviations from binomial expectation prompted an investigation of 33,176 pig records from two breeds collected on a single farm. Two methods of assessing the agreement with the binomial distribution found no evidence of significant lack of fit.

A Permutation Test For A Repeated Measures Design, James J. Higgins, William Noble

Conference on Applied Statistics in Agriculture

Multivariate permutation tests have advantages over conventional methods in analyzing repeated measures designs. The tests are exact for all sample sizes regardless of the underlying population distribution from which the observations are selected. More importantly the tests do not require a priori assumptions about the form of the correlation structure, obviating the need to check Huynh-Feldt conditions. An example is given of how a multivariate permutation test may be conducted in a context frequently encountered in agricultural research. The SAS program corresponding to this example is also given.

Litter Mate Correlations In The Weight Of Pigs, Thomas Kirchoff, D. F. Cox

Conference on Applied Statistics in Agriculture

Competition may influence the weights of animals confined to litters or pens, if conditions occur that limit the space and the feed provided, by inducing a negative correlation among the weights within the groups. An example of the phenomenon appeared in the birthweight of pigs where the intra-class correlation declined in a linear manner with increasing litter size. The data consisted of records on 33,165 pigs from 3282 litters raised on a single farm.

Overcoming Resistance To Multivariate Analysis Over Time, April J. Milliken, Anne M. Parkhurst

Conference on Applied Statistics in Agriculture

One aspect of statistical consulting is assessing a clients needs. Sometimes the need for simplicity beclouds the information contained in the experiment. As an example, an experiment was performed as a multivariate study with repeated measures, yet the client preferred numerous univariate analyses that ignored time. The challenge was to show how a more sophisticated analysis provided additional insight into the biological process. Various covariance structures were employed to illustrate the usefulness of progressively more complex analyses. Multivariate methods were performed to utilize the correlation among variables to illuminate biological concepts. To complicate the whole process, an additional problem occurred …

A Comparison Of Algorithms For Selecting An Optimum Sample From H Strata Using K Variables, M. Williams, H. T. Schreuder

Conference on Applied Statistics in Agriculture

In stratified sampling with k different variables and H strata it is often of interest to minimize the survey cost with respect to variance restrictions on each of the k variables. This problem has previously been solved using compromise solutions or using a linear approximation to this nonlinear problem. In this paper a nonlinear optimization routine is tested on this problem. The formulation of the problem in its original form proved problematic. For the test cases run, the transformation t_h = l/n_h, where n_h is the number of samples in stratum h, performed best when k …

Imputing Characteristic Values Of Agricultural "Seed-Stock", Bbryan E. Melton, W. Arden Colette, Richard L. Willham

Conference on Applied Statistics in Agriculture

Statistical methods of regression and mathematical (linear) programming are employed to combine principles of economics and genetics in a conceptual, multi-step, model of valuation for biotechnical change. The resulting model has the capacity to estimate the value of changes in specific characteristics for specific production environments, whether those changes are accomplished by traditional plant and animal breeding methods or by genetic engineering. The application of the model is illustrated with an example of commercial cow-calf production under conditions typical of the Texas Panhandle using a total of 32 breed groups.

Fuzziness In Forest Survey Design Optimization, George Gertner, Xiangchi Cao

Conference on Applied Statistics in Agriculture

When using optimization techniques to optimize a sampling with partial replacement design, it is often assumed that the following parameters are known exactly: 1) desired level of sampling error or total sampling cost for the survey; 2) variable costs; and 3) population variance and correlation coefficients. In practice, however, these parameters needed for finding the optimal design are only educated guesses. The parameters can be considered to be fuzzy. In this paper, brief consideration is given to the optimization of a sampling with partial replacement design using nonlinear programming techniques with fuzzy parameters. The basis of this method is to …

The Effect Of Weather Station Density On Crop Yield Forecasts, M. Denice Mccormick

Conference on Applied Statistics in Agriculture

The National Agricultural Statistics Service (NASS) uses regression models to forecast yield for crops such as corn, soybeans and winter wheat. Analyses were conducted on the use of precipitation data in these regression models (McCormick and Birkett 1992, and McCormick 1993). Precipitation data are obtained from two sources. The National Climatic Data Center (NCDC) supplies historic precipitation data used for developing regression model parameters. The Climate Analysis Center (CAC) supplies current year precipitation data that are used as regression model input. CAC weather station density is sparse across the U.S. in many major agricultural areas compared to NCDC weather station …

Tests And Estimators Of Multiplicative Models For Variety Trials, P. L. Cornelius, J. Crossa, M. S. Seyedsadr

Conference on Applied Statistics in Agriculture

Some recently obtained results on cross validation, hypothesis test and estimation procedures for multiplicative models applied to multi-site crop variety trials are presented. The PRESS statistic is more sensitive to overfitting and choice of model form than data-splitting cross-validation. Because of their extreme liberality, Gollob F-tests should not be used to test multiplicative terms. FGH tests effectively control Type I error, but are conservative for tests of terms for which the previous term is small. "Simulation tests" have greater power than FGH tests, but still effectively control Type I error rates. Simulation results and cross validation in two examples suggest …

Designing Alfalfa Yield Trials For Comparing Long-Term Yields, G. B. Schaalje, S. N. Acharya

Conference on Applied Statistics in Agriculture

An aspect of experimental design that must be taken into consideration for variety trials of perennial crops is the number of years to continue the trial. By tradition, alfalfa forage yield trials are harvested for three or four production years, but the consumers of information from these trials, the producers, often keep their stands in production for more than four years. This study developed a statistical efficiency measure for evaluating the adequacy of forage trial designs with specified numbers of years and replicates, based on a multivariate linear model. The measure was applied to data from four long-term trials grown …

On Multivariate Analyses Of Crossover Designs, Dallas E. Johnson, Carla Goad

Conference on Applied Statistics in Agriculture

In crossover experiments, treatments are assigned to experimental units in successive periods. Traditional analyses of crossover designs with three or more periods assume that the observations in successive periods satisfy conditions similar to those utilized in the analysis of many repeated measures experiments. The successive measurements are assumed to satisfy conditions known as the Huynh-Feldt conditions. This paper gives a test for the Huynh-Feldt conditions and discusses possible analyses of crossover experiments, including tests for carryover, when the Huynh-Feldt conditions are not satisfied.

The Estimation Of Fixed Effects In A Mixed Linear Model, F. Nabugoomu, O. B. Allen

Conference on Applied Statistics in Agriculture

The estimation of fixed effects is considered for small, unbalanced, mixed linear models. The two-stage estimator, in which the variance components are first estimated by ML or REML, is compared to the intra-block (IB) estimator, the ordinary least squares (OLS) estimator (ignoring the random effects) and the Gauss-Markov (GM) estimator. Comparison is made, based on 100 simulated data sets each, for 6 designs (3 BIBD's and 3 unbalanced designs). In comparing loss of information, relative to the GM lower bound, the two-stage procedures (using either ML or REML) are recommended for all but the smallest and least balanced design. The …

Simple Estimations Of The Variance Components And The Fixed And Random Effects In Mixed, Three-Stage, Hierarchal Models, C. Philip Cox

Conference on Applied Statistics in Agriculture

FRR (Fixed, Random, Random) hierarchal models in which the first-stage" elements are fixed and the second and third-stage elements are random, are used in analyses of comparative experiments and, extensively, in animal breeding contexts where, in the latter, estimates of the second-stage elements and of combinations of them with first-stage elements, are of practical interest. The two procedures, i) empirical BLUP (Best Linear Unbiased Prediction) and ii) a Bayesian approach, used when the ratio of the within-second-stages and the within-third-stages variances is unknown are 'computationally intensive'. When the ratio of the second- to the third-stage variances is large, an alternative …

Mixed Models Combined Analysis Of Independent Grazing Trials, H. A. Fribourg, J. C. Waller, R. W. Thompson, W. L. Sanders

Conference on Applied Statistics in Agriculture

The mixed models procedure (MMP) was used to analyze pooled data sets from 12 independent studies over 13 yr at 9 locations in 7 states to provide combined estimates of daily gains by beef steers grazing tall fescue pastures with different levels of infestation by Acremonium coenophialum, with and without clover. Spring, summer, and combined spring + summer data were analyzed separately. The MMP permitted estimation of the fixed effects of treatments over a broad inference space of future years and different tall fescue pastures over a wide geographic range, detected some relationships not apparent in the individual studies, …

Spatial Analysis Of Yield Trials Using Separable Arima Processes, M. O. Grondona, J. Crossa, P. N. Fox, W. H. Pfeiffer

Conference on Applied Statistics in Agriculture

Spatial analysis procedures based on one-dimensional and two-dimensional (separable) ARIMA (Auto Regressive Integrated Moving Average) processes were used to analyze several yield trials. Two criteria were used to determine the best spatial model: 1) standard error of the treatment difference (SED) and 2) mean squared error (MSE) of prediction based on a cross-validation approach. It is found that spatial models with two-dimensional exponential covariance functions are frequently the best models regarding SED and MSE. Differenced models are frequently the best models regarding SED and the worst with respect to MSE.

Spatial Statistical Analysis For The Area-Of-Influence Experiments, Bahman Shafii, William J. Price, Don W. Morishita

Conference on Applied Statistics in Agriculture

The area-of-influence (AOI) approach to quantifying crop/weed competition involves measuring the effect of individual weed plants on crop growth and yield at specified distances away from the weed plant. AOI experiments are often analyzed using classical statistical techniques based on the assumption that successive observations on crop response are independent in spite of their distribution in space. However, as the distance varies along the row, the competitive ability will vary spatially so that observations located nearby are expected to be more alike than those separated by large distances. Analyses based on spatial dependencies will therefore provide a more comprehensive understanding …

Analysis Of Spatial Variability Using Proc Mixed, David B. Marx, Walter W. Stroup

Conference on Applied Statistics in Agriculture

Many data sets in agricultural research have spatially correlated observations. Examples include field trials conducted on heterogeneous plots for which blocking is inadequate, soil fertility surveys, ground water resource research, etc. Such data sets may be intended for treatment comparisons or for characterization. In either case, linear models with correlated errors are typically used. Geostatistical models such as those used in "kriging" are often used to estimate the error structure .

SAS PROC MIXED allows the estimation of the parameters of mixed linear models with correlated errors. Fixed and random effects are estimated by generalized least squares. Variance and covariance …

Distance Measures In Post Hoc Comparisons Of Temperature Germination Quadratic Response Surfaces, D. E. Palmquist, S. N. Bagchi, J. A. Young, R. D. Davis

Conference on Applied Statistics in Agriculture

Generalized quadratic response surface models are used to describe seed germination at diurnally alternating cold and warm incubation temperatures for three Great Basin exotic plant species. The method of the F-statistic SS_drop is applied to determine whether the response surface models are equal. Two proposed distance measures are used as modified multiple comparison techniques for determining differences between surfaces. These measures prove useful in distinguishing between the species showing the highest germination response and the one showing the lowest response to the incubation temperature ranges studied.

Tools For The Construction Of Effective Experimental Designs, M. F. Franklin, R. W. Payne

Conference on Applied Statistics in Agriculture

Experimenters should be able to choose between competing designs the one which yields the required information clearly and efficiently at the desired precision. One way to achieve this is to allow interaction between design and analysis but few statistical analysis packages include more than rudimentary design facilities. We review some of the theory and tools for design construction with a view to providing the statistician and experimenter with a tool-kit for building the most effective design. Examples in the design process are techniques for determining aliases and patterns of confounding, algorithms for constructing fractional factorial and incomplete block designs and …

Confidence Intervals For Variance Components In One-Way Unbalanced Designs, Franklin A. Graybill, Rana S. Fayyad

Conference on Applied Statistics in Agriculture

Consider the one way unbalanced components of variance model given by Y_ij = μ + A_i + E_ij, (i = l, ... ,a, j = l, ... ,b_i) where μ is an unknown constant parameter, A_i and E_ij are independent normal random variables with zero means and variances σ²_A and σ²_E respectively,

The problem is to obtain a confidence interval for σ²_A with confidence coefficient greater than or equal to a specified 1 - α. Three new procedures for obtaining confidence intervals for σ²_{A …}

Editor's Preface, Table Of Contents, And List Of Attendees, William Noble

Conference on Applied Statistics in Agriculture

These proceedings contain papers presented in the fifth annual Kansas State University Conference on Applied Statistics in Agriculture, held in Manhattan, Kansas, April 25 through 27, 1993.