Analysis of Partially Balanced Incomplete Block Designs with Standards

The paper presents a detailed analysis of variance of PBIB designs supplemented by one or more standard treatments. Comparisons were carried out of treatment effects within the group of standard and test treatments and between the two groups. The analysis is supplemented by an example.     

Construction of Partially Balanced Incomplete Block Designs with Nested Rows and Columns

A number of methods of construction of partially balanced incomplete block designs with nested rows and columns are developed and new balanced incomplete block designs with nested rows and columns are obtained as a by-product.     

Experiment with Split-Plot Generated by PBIB Designs

The paper refers to the construction of two-factor experiments carried out in incomplete split-plot design in which levels of both factors occur as treatments in PBIB designs. It presents also the analysis of variance of these experiments based on partial analyses in the so called strata. These strata are connected with the variability between subplots inside wholeplots, between the wholeplots inside blocks and between blocks inside the total experiment.     

Analysis of Diallel Table for Experiments in Block Designs

In this paper the analysis of genotypes obtained in diallel crossing system, including parents, one set of F₁s and reciprocal F₁'s, is given. This analysis is presented for data obtained from the experiments laid out in block designs. The analysis of variance, estimator of reciprocal effects, estimators of general and specific combining abilities as well as statistics for testing of hypotheses concerning those parameters are given.     

Analysis of Triangular Diallel Table for Experiments in Block Designs

In this paper the analysis of genotypes obtained in diallel crossing system, including one set of F₁′s and parents, arranged in triangular table is given. This analysis is presented for data obtained from the experiments laid out in block designs. The analysis of variance, estimators of general and specific combining abilities as well as statistics for testing of hypotheses concerning those parameters are given.     

Randomization of Neighbour Balanced Designs

This paper is a simulation study on the influence of interference between treatments in field trials. The considerations in the paper are based on a simple model which includes additive neighbour effects of treatments. We use uniformity data where neighbour effects are added, to demonstrate the influence that these effects have on the validity of comparisons between treatments. The simulations illustrate that the influence of the neighbour effects is reduced if a neighbour balanced or a partially neighbour balanced design is used.     

Universal Optimality of Nearest Neighbour Balanced Block Designs using Second Order Correlated Models

Block designs for observations correlated in one dimension are investigated. Santharam and Ponnusamy (1995) investigated the universal optimality of Nearest Neighbour balanced block designs (NNBD) using first order correlated models (AR(1), MA(1) and ARMA(1,1)). In this article we have investigated the universal optimality of NNBD using second order correlated models (ar(2), and MA (2)).     

On the Effect of Correlation Between Plots in Randomized Block Experiments

Correlation between adjacent plots in field experiments are common. In this paper the effect of correlation on the usual analysis of variance in a randomized block design is studied. A generalised analysis of variance where correlation is taken into consideration, and the analysis of covariance where the residuals of the neighbouring plots are used as covariates, is discussed. Uniformity trials are used as a basis of a Monte-Carlo study. The generalised analysis improved the power of the tests. The analysis of covariance method was not better than the usual analysis of variance method.     

Model Building and Analysis for Block Designs with Nested Rows and Columns

The paper deals with two main problems: it gives a unified approach to model building for observations obtained in a block design with nested rows and columns and it provides the analysis of variance for such data. Also, some statistical properties of the design are examined.     

On the Efficiency of Nearest Neighbour Balanced Block Designs with Correlated Error Structure

Nearest Neighbour Balanced Block Designs (NNBD) are widely used in biological and industrial experiments. In this article we examine the optimality and efficiencies of NNBD under various correlated error structure models. A numerical comparison of NNBD with regular block design (RBD) is also presented.     

A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA-estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the corresponding F-quotients and the approximate confidence intervals of variance components are received in a simple way.     

On the Application of the Analysis ct Variance in the Identification of Dadoxylon woods

This paper suggests that the analysis of variance could be used to the distinction of Da- doxylon-like woods and some quantitave characters of Dadoxylon taiyuanensis, Amyelon radicans, A. xui, A. equivius and Billigea resinosa, for example, diameter of ray cells and tracheids, height of rays, and diameter ratio of ray to tracheid, are compared and discussed. The comparision and discussion show quantitave character is more useful to identification of fossil plants than others if analysis Of variance is used.     

How to cope with negative estimates of components of variance in ecological field studies

Ecologists often need to estimate components of spatial or temporal variation. The most widely used method in ecology uses the observed and expected mean squares in an analysis of variance. A more general approach, which can be used for balanced and unbalanced designs, is based on residual maximal likelihood (REML). This method is less well known by ecologists and requires specialist software. If the design is balanced, the two methods are equivalent, except for one important respect: estimates from analysis of variance can be negative whereas REML estimates cannot. The purpose of this note is to point out a simple modification to the analyses of variance which yields the same estimates as REML for many of the designs commonly used in ecological studies. This modification has been available in the mathematical literature for over 30 years, but appears not to be well known amongst ecologists. It is useful in many cases of balanced analytical designs.     

The influence of aberrant values on the statistics related to a selection program

Summary Examples are presented to illustrate some of the effects aberrant values, in particular, measurement errors, may have on estimates of the genetic parameters related to selection studies. It is shown that aberrant values may cause observed response to selection pressure to differ considerably from predicted response. Possible dangers of indiscriminate screening are also discussed.     

Responses of alloplasmic (cytoplasm=Triticum timopheevii) and euplasmic wheats (Triticum aestivum) to photoperiod and vernalization

Summary Heritability estimated from sire family variance components, ignoring dams, pools conventional paternal and maternal half sib estimates, in a way which is biased upward, and sub-optimal for minimizing the sampling variance. Standard error of a sire family estimate will be smaller than that of the equivalent paternal half sib estimate, but not as small as that of an estimate obtained by optimal pooling of paternal and maternal half sib estimates. If only additive genetic variance components are significant, the bias may be removed by use of a computed average genetic relationship for sire families, in place of a nominal R = 0.25. Average genetic relationship may be computed from mean and variance of dam family size within sire families. If dominance, epistatic, or maternal components are significant, this simple correction is not appropriate. In situations likely to be encountered in large domestic species such as sheep and cattle (dam family size small and uniform) bias will be negligible. The method could be useful where cost of dam identification is a limiting factor.