Recovery Of Interblock Information Research Articles

Comparison of analyses types in carrot experiment: square lattice versus randomized blocks design

ABSTRACT The square lattice 4x4 design was compared to a randomized block design, for carrot F1 hybrids. Sixteen experimental carrot hybrids were evaluated in Brasília, in 2014/15 and 2015/16 agricultural years. A square lattice 4x4 design with three replications was used. The experimental plot consisted of 1.5 m2 useful area. The experimental area was installed on the second half of November 2014 and 2015. Cultural practices were the usually given to the carrot crop in Brazilian savannah region. The incidence of leaf blight was evaluated 90 days after sowing date and, after 100 days, roots were harvested and yield components evaluated. We evaluated the three possible analyses in lattice: 1) as randomized block design; 2) intrablock analysis with adjusted treatments and blocks within unadjusted repetitions; 3) analysis with recovery of interblock information with adjusted treatments. The analysis in lattice permitted to reduce the mean squares of error and coefficients of variation; moreover, these were more efficient than the randomized block design experiments for most evaluated characters. Thus, use of the analysis in lattice is preferred in experiments with carrot when evaluating large number of treatments.

Association among agro-industrial traits and simultaneous selection in sweet sorghum.

Sweet sorghum has emerged as an alternative crop for ethanol yield. The breeding of this crop is performed to obtain cultivars with high ethanol yield, which necessarily requires associating favorable phenotypes for multiple traits. Therefore, the aims of this study were to investigate the association between agro-industrial traits related to ethanol yield and identify the promising genotypes considering multiple traits in sweet sorghum. For this purpose, we evaluated 45 genotypes using a 9 x 5 alpha-lattice experimental design with three replications. The traits measured were flowering time, plant height, tons of stalk per hectare, total soluble solids, tons of brix per hectare, juice extraction, total recoverable sugars, and ethanol yield. Analyses were performed after the recovery of inter-block information. The interrelation of the traits was described by genotype-by-trait biplot. For simultaneous selection, the Modified Mulamba and Mock index was used. For almost all of the agro-industrial traits, except for juice extraction, selective accuracy was above 70%. There were significant differences among genotypes for all the traits. The genotype-by-trait biplot evidenced a positive association between most of the traits related to ethanol yield, except for juice extraction, indicating the possibility of indirect selection to obtain more productive genotypes. Some genotypes proved to be promising based on the selection index, as they accumulated phenotypes favorable for the traits of interest.

Inter-block information: to recover or not to recover it?

Comparing standard errors of treatment differences using fixed or random block effects with the approximation of Kackar and Harville helps in choosing the preferable assumption for blocks in the analysis of field experiments. Blocked designs are common in plant breeding field trials. Depending on the precision of variance estimates, recovery of inter-block information via random block effects may be worthwhile. A challenge in practice is to decide when recovery of information should be pursued. To investigate this question, a series of sugar beet trials laid out as α-designs were analysed assuming fixed or random block effects. Additionally, small trials laid out as α-designs or partially replicated designs were simulated and analysed assuming fixed or random block effects. Nine decision rules, including the Kackar-Harville adjustment, were used for choosing the better assumption regarding the block effects. In general, use of the Kackar-Harville adjustment works well and is recommended for partially replicated designs. For α-designs, using inter-block information is preferable for designs with four or more blocks.

Acceptance testing procedure equivalence

This article addresses the issues of comparing different acceptance testing systems in an industrial setting, specifically in the dairy industry. The issues were two-fold: how to demonstrate that two different product testing systems were equivalent; and how to ensure that testing done by a customer or consumer on delivery of the product does not reject product deemed acceptable by the producer's testing system. Our comparison of sampling systems was focused around Operating Characteristic curves. Our results suggest that previous approaches are sound when data are normally distributed, although some refinement is possible. When data are not distributed normally, especially with multi-parameter distributions, the usual one dimensional Operating Characteristic curve method fails. In such cases, test methods can be compared by comparing acceptance surfaces in three dimensional plots. To address discrepancies between producer and consumer testing systems, especially if these arise because of different levels of variability between the two systems, an approach involving confidence intervals has the most appeal. References L. J. Bain and M. Engelhardt. Introduction to Probability and Mathematical Statistics. Duxbury Press, 2000. N. N. Cencov. Statistical Decision Rules and Optimal Inference. American Mathematical Society, 2000. J. Cohen. A coefficient of agreement for nominal scales. Educational and Psychological Measurement. 20, 1960, 37--46. D. R. Cox and D. V. Hinkley. Theoretical Statistics. Chapman and Hall/CRC, 1979. P. Grzegorzewski. Acceptance sampling plans by attributes with fuzzy risks and quality levels. In: P-Th. Wilrich and H. J. Lenz, editors, Frontiers in statistical quality control, Vol. 6, pages 36--46. Physica-Verlag, 2001. K. Gwet. Handbook of Inter-Rater Reliability. Advanced Analytics, LLC., 2010. A. Hald. Statistical theory of sample inspection by attributes. Academic, 1981. {ISO 8196-1:2009} Milk---Definition and evaluation of the overall accuracy of alternative methods of milk analysis. {ISO 8196-2:2000} Milk---Definition and evaluation of the overall accuracy of indirect methods of milk analysis. N. A. Nechval, K. N. Nechval, E. K. Vasermanis. Statistical decision equivalence principle and its applications. Proceedings of International Conference RelStat04, 2004, 81--89. S. K. Niazi. Handbook of Bioequivalence Testing. Informa Healthcare, 2007. NIST/SEMATECH e-Handbook of Statistical Methods. http://www.itl.nist.gov/div898/handbook/pmc/section2/pmc21.htm H. D. Patterson and R. Thompson. Recovery of inter-block information when block sizes are unequal. Biometrika, 58 (3), 1971, 545--554. http://www.ams.org/mathscinet-getitem?mr=0319325 S. Wellek. Testing Statistical Hypotheses of Equivalence. Chapman and Hall/CRC, 2002. P.-Th. Wilrich. Single sampling plans for the inspection by variables in the presence of measurement error. Allgermeines Statistisches Archiv, 84, 2000, 239--250. P.-Th. Wilrich. Statistical concepts of capability of detection. Appl. Stochastic Models Bus. Ind. 18, 2002, 339--346. http://www.ams.org/mathscinet-getitem?mr=1932646

Statistical Tests for Mixed Linear Models

Nature of Exact and Optimum Tests in Mixed Linear Models. Balanced Random and Mixed Models. Measures of Data Imbalance. Unbalanced One-Way and Two-Way Random Models. Random Models with Unequal Cell Frequencies in the Last Stage. Tests in Unbalanced Mixed Models. Recovery of Inter-Block Information. Split-Plot Designs Under Mixed and Random Models. Tests Using Generalized P-Values. Multivariate Mixed and Random Models. Appendix. General Bibliography. Indexes.

Alternativas de análise de ensaios em látice no melhoramento vegetal

Compararam-se diferentes formas de análise de experimentos em blocos incompletos, abordadas como casos particulares de modelos mistos, quais sejam: (a) análise intrablocos, em que apenas o efeito do erro experimental é suposto aleatório; (b) análise interblocos (látice), com efeitos de blocos supostos aleatórios; (c) análise BLUP, com os efeitos de tratamentos supostos aleatórios, e (d) modelo aleatório. Além disso, montou-se a ANAVA, considerando duas alternativas: (e) usando o quadrado médio de tratamentos ajustados para blocos e o quadrado médio do erro efetivo do látice; (f) tomando as repetições como blocos completos. Um exemplo de análise de um teste de progênies de Eucalyptus grandis (Hill) Maiden ilustra as implicações da escolha dos modelos para fins de seleção e de caracterização genética de populações. Observou-se que em geral o ordenamento dos tratamentos sofreu maiores alterações ao se mudar a alternativa de análise do que as estimativas do progresso esperado pela seleção. Tendência que se reforça com a seleção mais intensa. As formas de análise que consideram a restrição da casualização (blocos incompletos) foram as mais precisas, e dentre estas, a análise BLUP de tratamentos é conceitualmente a melhor, pois os tratamentos eram progênies de polinização livre, sendo a que mais difere da análise usual do látice. Isto indica ser possível minorar os erros de seleção nas análises de blocos incompletos no melhoramento vegetal.

Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if the design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.

Analysis of experiments in square lattice with emphasis on variance components. i. Individual analysis

This paper focused on four alternatives of analysis of experiments in square lattice as far as the estimation of variance components and some genetic parameters are concerned: 1) intra-block analysis with adjusted treatment and blocks within unadjusted repetitions; 2) lattice analysis as complete randomized blocks; 3) intrablock analysis with unadjusted treatment and blocks within adjusted repetitions; 4) lattice analysis as complete randomized blocks, by utilizing the adjusted means of treatments, obtained from the analysis with recovery of interblock information, having as mean square of the error the mean effective variance of this same analysis with recovery of inter-block information. For the four alternatives of analysis, the estimators and estimates were obtained for the variance components and heritability coefficients. The classification of material was also studied. The present study suggests that for each experiment and depending of the objectives of the analysis, one should observe which alternative of analysis is preferable, mainly in cases where a negative estimate is obtained for the variance component due to effects of blocks within adjusted repetitions.

Nonparametric recovery of interblock information in clinical trials with a surrogate endpoint

For clinical trials involving (a treatment-wise) incomplete block design and a surrogate variable as a substitute for the primary endpoint, recovery of interblock information in nonparametric analysis of covariance models based on a suitable aligned rank statistics is explored through a combined inference scheme based on intra as well as interblock rank statistics incorporating both the surrogate replicates and the validation samples. Related nonparametrics are presented in detail.

Properties of superimposed BIBDs

Superimposed designs in the sense to be considered in this paper arise in the following manner. First, a balanced incomplete block design is implemented to compare a set of treatments T 1. At some later time, it is desired to compare a second set of treatments T 2 using the same experimental units. If the effects of the treatments T 1 are thought to still be present, either in a direct fashion as part of an on-going experiment, or as residual effects of a prior experiment, then they effectively become another blocking factor to be accounted for in the estimation of contrasts for T 2. What then is the optimal assignment for the set T 2 to the units? Among the results proven here are (i) a BIBD for T 2 that achieves bottom-stratum orthogonality with respect to T 1 is optimal for the usual analysis, and (ii) most of the known BIBDs that achieve this orthogonality are also optimal for the analysis with recovery of interblock information, even if not achieving block-stratum orthogonality, provided the number of replicates is not too large.

A formula for a missing plot in a general incomplete block design, when recovery of interblock information is used

In this paper, Yate's missing plot technique is used to derive the formula for substitution in a missing plot in a general incomplete block design, where blocks are assumed to be independent normal. The use of penalized normal equations, using BLUPS, makes this task simpler.

The randomization model for experiments in block designs and the recovery of inter-block information

A general randomization model for experiments in block designs and conditions for obtaining the best linear unbiased estimators of treatment parametric functions under the model are re-examined. It is shown how the best linear unbiased estimators under the overall randomization model can be obtained when the variance components are known. Furthermore, a general method of estimating these, usually unknown, variance components is described and properties of the resulting estimators of treatment parametric functions are considered. In connection with this the recovery of inter-block information in a general block design is discussed.

Recovery of inter-block information: extensions in a two variance component model

For a two variance component mixed linear model, it is shown that under suitable conditions there exists a nonlinear unbiased estimator that is better than a best linear unbiased estimator defined with respect to a given singular covariance matrix. It is also shown how this result applies to improving on intra-block estimators and on estimators like the unweighted means estimator in a random one-way model.

The basic contrasts of a block design with special reference to the recovery of inter-block information

The basic contrasts of a block design with special reference to the recovery of inter-block information

Uniformity trial with lucerne grown for fodder

AbstractData on the yield of lucerne for individual cuts and the total for three cuts from a uniformity trial were analysed. It was observed that CV% values decreased with the increase in plot size, both for each cut and for total yield. The decrease was considerable up to a plot size of 8 to 16 m2. The plot shape did not show any consistent effect. Increasing the size of block resulted in increased CV values, but block shape had no consistent effect. The CV values were highest for the first cut and lowest for the second cut. A relationship between the average CV% and plot size was found. However, this relationship, or its modified form Y= a.X1−b1. X2−b2 taking into account the plot shape and considering the individual CV values, provide a good fit to the data for the cases where blocking was adopted. The coefficient of heterogeneity was less than 0·29, being lowest for first‐cut yields, followed by the total, the third cut and the second cut yields. This showed a high degree of positive correlation between yields of neighbouring plots. Blocking proved useful in increasing the efficiency of the experiment and it is suggested that block size may be kept at 8 or less plots per block. The relationship between average CV% and block size was of the from Y = a Xb. The present study suggests that, for field experiments with luceme, the plot size may be kept to a minimum that does not exceed 8 to 12 m2, in blocks of eight to nine plots with the shapes of plots and blocks being nearly square. Calculating the efficiencies of confounded factorial design and incomplete block design revealed that block size may be kept to a minimum. The recovery of interblock information was found useful and balancing may be attempted, but only, if necessary.

A Simple Procedure for Constructing Experiment Designs with Incomplete Blocks of Sizes 2 and 3

AbstractIn order to maximize control of heterogeneity within complete blocks, an experimenter could use incomplete blocks of size k = 2 or 3. In certain situations, incomplete blocks of this nature would eliminate the need for such spatial types of analyses as nearest neighbor. The intrablock efficiency factors for such designs are relatively low. However, with recovery of interblock information, FEDERER and SPEED (1987) have presented measures of design efficiency factors which demonstrate that efficiency factors approach unity for certain ratios of the intrablock and interblock variance components. Hence with recovery of interblock information, even incomplete block designs with k = 2 or 3 have relatively high efficiency factors. The reduction in the intrablock error variance over the complete block error variance in many situations will provide designs with high efficiency.A simple procedure for constructing incomplete blocks of sizes 2 and 3 is presented. It is shown how to obtain additional zero‐one association confounding arrangements when v = 4 t, t an integer, and for v = pk, k ≤ p. It is indicated how to do the statistical analysis for these designs.

Interblock information in multidimensional block designs

AbstractIn many experimental situations, d‐way heterogeneity among experimental units may be controlled through use of multiple blocking criteria. In some cases it is reasonable to regard some or all of the block effects as random. Then the model is mixed and observations within blocks are correlated. Very general estimators of treatment effects and their dispersion matrix with recovery of interblock information are provided. They apply to designs with d > 1 blocking criteria that may be crossed, nested, or a combination thereof. These general results may be specialized to provide analyses of new classes of MBD's or used directly for numerical analyses of designs in the general class, perhaps through use as the basis for very general computer programs. Estimation of variance components is discussed, and an example is provided to illustrate adaptation of the general results.

Recovery of information in BIBDs with interaction

Consider a Balanced Incomplete Blocks Design (BIBD) for a mixed two way model with interactions and p observations per cell. A sufficient condition is given under which recovery of interblock information is obtainable for inferences concerning treatment contrasts. The condition is considerably weaker than the previously known condition for analyzing such BIBDs given by Kapadia, Kvanli, and Lee (1988). The condition suffices to preserve the covariance structure of the observation vector when no interactions are present. The condition not only suffices to preserve the structure for BIBDs but also for any block design in which the mixed model is assumed. For the BIBD case a test for the presence of a random interaction is given. In addition, consider a K-random factor design under a mixed model which includes random interactions between blocking factors and treatments. Another set of sufficient conditions is given under which the covariance structure of the observation vector is preserved from the model with no interactions.

A note on the recovery of inter-block information in balanced incomplete block designs

Consider the recovery of interblock information in balanced incomplete block designs. It is shown that the recovery of interblock information through the estimated generalized least squares (EGLS) estimator may improve the estimation, provided (b-t) > 4 where b =number of blocks and t =number of treatments. An expression for the variance covariance matrix for the EGLS estimator is provided and its behaviour is studied.

Recovery of inter‐block information in cross‐over trials

For cross-over designs, we show that one can recover information on direct and/or residual treatment effects from an inter-block (patients as blocks) analysis as is done in an incomplete block design. By combining the intra- and inter-block estimates, we obtain the generalized least squares estimate. In analysing cross-over trials, we recommended this approach provided the between-patient variance component can be estimated efficiently.