Mathematical Analysis of a Five Periods Crossover Design for Two Treatments

Introduction: A cross-over design is a repeated measurements design such that each experimental unit receives different treatments during different time periods. Lower order cross-over designs such as the two treatments, two periods and two sequences C (2, 2, 2) design have been discovered to be inefficient and erroneous in their analysis of treatments efficacy. In this regard, higher order cross-over designs have been recommended and developed like: the two treatments, three periods and four sequence C (2, 3, 4) design; and the two treatments, four periods and four sequence C (2, 4, 4) designs. However, there still exists more efficient higher order cross-over designs for two treatments which can be used in bioequivalence experiments. This study gives a new design and analysis for two treatments, five periods and four sequence C (2, 5, 4) cross-over design that gives more precise estimates and provides estimates for intra subject variability. Method: A hypothetical case study was considered on 160 experimental units which are assumed to be randomly selected from a given population. A cross over design of two treatments (A, B) in five periods whose sequences are given by BABAA, ABABB, BAABA and ABBAB were used. Each of the experimental units was used as its own control. The estimates for both direct treatments and treatments carry-over effects were obtained using best linear unbiased estimation method (BLUE). We simulated data for two treatments in five periods and four sequences and used it to test the null hypotheses of no significant differences in both the direct treatments and treatments carry-over effects using the

Reinventing quantitative genetics for plant breeding: something old, something new, something borrowed, something BLUE

The goals of quantitative genetics differ according to its field of application. In plant breeding, the main focus of quantitative genetics is on identifying candidates with the best genotypic value for a target population of environments. Keeping quantitative genetics current requires keeping old concepts that remain useful, letting go of what has become archaic, and introducing new concepts and methods that support contemporary breeding. The core concept of continuous variation being due to multiple Mendelian loci remains unchanged. Because the entirety of germplasm available in a breeding program is not in Hardy–Weinberg equilibrium, classical concepts that assume random mating, such as the average effect of an allele and additive variance, need to be retired in plant breeding. Doing so is feasible because with molecular markers, mixed-model approaches that require minimal genetic assumptions can be used for best linear unbiased estimation (BLUE) and prediction. Plant breeding would benefit from borrowing approaches found useful in other disciplines. Examples include reliability as a new measure of the influence of genetic versus nongenetic effects, and operations research and simulation approaches for designing breeding programs. The genetic entities in such simulations should not be generic but should be represented by the pedigrees, marker data, and phenotypic data for the actual germplasm in a breeding program. Over the years, quantitative genetics in plant breeding has become increasingly empirical and computational and less grounded in theory. This trend will continue as the amount and types of data available in a breeding program increase.

Faktor-faktor Yang Mempengaruhi Permintaan Bawang Merah Di Kota Medan

Shallot is a horticultural commodity classified as vegetable spices that serve as a seasoning for food and traditional medicine. The importance of shallot for cooking makes the demand for shallot continue to increase every year. This research aims to see what factors influence the demand for shallot in Medan City. This research was conducted in Medan Deli Market and Kemiri Market. Sampling used this research used the Accidental Sampling method, which determines the sample based on people who are accidentally encountered in the study area. The number of samples examined in this research is 40 samples of shallot consumers. This research uses Best Linear Unbiased Estimation and Multiple Linear Regression methods. The variables studied were the price of shallot, the income of consumers, the number of family members and the price of yellow onion. The result of this research indicates that the factor that influences the demand for shallot is the price of shallot, the income of consumers and the number of family members, while those that do not affect is the price of yellow onion.

Best linear unbiased estimation for varying probability with and without replacement sampling

When sample survey data with complex design (stratification, clustering, unequal selection or inclusion probabilities, and weighting) are used for linear models, estimation of model parameters and their covariance matrices becomes complicated. Standard fitting techniques for sample surveys either model conditional on survey design variables, or use only design weights based on inclusion probabilities essentially assuming zero error covariance between all pairs of population elements. Design properties that link two units are not used. However, if population error structure is correlated, an unbiased estimate of the linear model error covariance matrix for the sample is needed for efficient parameter estimation. By making simultaneous use of sampling structure and design-unbiased estimates of the population error covariance matrix, the paper develops best linear unbiased estimation (BLUE) type extensions to standard design-based and joint design and model based estimation methods for linear models. The analysis covers both with and without replacement sample designs. It recognises that estimation for with replacement designs requires generalized inverses when any unit is selected more than once. This and the use of Hadamard products to link sampling and population error covariance matrix properties are central topics of the paper. Model-based linear model parameter estimation is also discussed.

A Compensation Method for Airborne SAR with Varying Accelerated Motion Error

Motion error is one of the most serious problems in airborne synthetic aperture radar (SAR) data processing. For a smoothly distributing backscatter scene or a seriously speed-varying velocity platform, the autofocusing performances of conventional algorithms, e.g., map-drift (MD) or phase gradient autofocus (PGA) are limited by their estimators. In this paper, combining the trajectories measured by global position system (GPS) and inertial navigation system (INS), we propose a novel error compensation method for varying accelerated airborne SAR based on the best linear unbiased estimation (BLUE). The proposed compensating method is particularly intended for varying acceleration SAR or homogeneous backscatter scenes, the processing procedures and computational cost of which are much simpler and lower than those of MD and PGA algorithms.