Balancing the number and size of sites: An economic approach to the optimal design of cluster samples

The design of randomized controlled trials entails decisions that have economic as well as statistical implications. In particular, the choice of an individual or cluster randomization design may affect the cost of achieving the desired level of power, other things being equal. Furthermore, if cluster randomization is chosen, the researcher must decide how to balance the number of clusters, or sites, and the size of each site. This article investigates these interrelated statistical and economic issues. Its principal purpose is to elucidate the statistical and economic trade-offs to assist researchers to employ randomized controlled trials that have desired economic, as well as statistical, properties. (C) 2003 Elsevier Inc. All rights reserved.

Efeito da restrição hídrica sobre o crescimento de clones de eucalipto

O estabelecimento e o crescimento inicial de espécies florestais no campo são fortemente afetados pela disponibilidade de água no solo e pela época de plantio, por isso, o presente trabalho estuda o impacto do déficit hídrico no crescimento de mudas de dois clones do híbrido Eucalyptus grandis x Eucalyptus urophylla, ambos submetidos a 4 níveis de déficit hídrico, em duas épocas de plantio. O estudo foi realizado na área experimental do Núcleo de Estudos e Difusão de Tecnologia em Florestas, Recursos Hídricos e Agricultura Sustentável (NEDTEC), do Centro de Ciências Agrárias da Universidade Federal do Espírito Santo (CCA-UFES), localizado no município de Jerônimo Monteiro. O trabalho foi realizado em duas épocas distintas, sendo a primeira no período de 09 de fevereiro a 09 de junho de 2009 e a segunda no período de 11 de julho a 07 de novembro de 2009, visando à realização das observações em diferentes condições de regime de radiação, déficit de pressão do vapor do ar, temperatura, umidade relativa do ar e velocidade do vento. O delineamento experimental utilizado foi o inteiramente ao acaso em parcelas subdivididas 2 x 4, alocando-se os 4 níveis de déficits hídricos na parcela principal e as 2 épocas nas subparcelas, com três repetições. Os manejos hídricos aplicados foram: Déficit 0 (D0) sem déficit, Déficit 1(D1) corte da irrigação aos 30 dias de experimentação, permanecendo até o final do experimento, Déficit 2 (D2) corte da irrigação aos 30 dias de experimentação, suspensão da irrigação por 60 dias e posterior retomada da irrigação por mais 30 dias; Déficit 3 (D3) corte da irrigação aos 60 dias de experimentação, prolongando até o final do experimento. Os dados experimentais foram submetidos à análise de variância, e quando significativas, as médias foram comparadas pelo teste de média Tukey a 5% de probabilidade, para cada clone estudado. Com este trabalho, foi possível avaliar o impacto de diferentes déficits hídricos, no crescimento inicial das plantas, em duas épocas do ano e avaliar o incremento no desenvolvimento das plantas durante a aplicação dos tratamentos, com retiradas de amostras médias de cada tratamento a cada 30 dias. As variáveis medidas nos dois experimentos foram altura total da planta, diâmetro ao nível do coleto, número de folhas, área foliar, matéria seca de folhas, matéria seca de haste e ramos, matéria seca de raízes e matéria seca total. Foram avaliadas as variáveis climáticas durante todo o período experimental, nas duas épocas, a fim de determinar a condição do clima em cada época. Para os dois clones estudados, em geral, os déficits hídricos promoveram a redução das variáveis morfológicas estudadas e a época experimental foi o fator que mais influenciou a redução do crescimento das plantas. Sendo que a Época 1 foi a que proporcionou resultados superiores, e a Época 2 foi a que prejudicou mais o desenvolvimento das plantas, reduzindo significativamente todas as variáveis morfológicas em todos os déficits hídricos, inclusive o D0.

Efeito da restrição hídrica sobre o crescimento de clones de eucalipto

O estabelecimento e o crescimento inicial de espécies florestais no campo são fortemente afetados pela disponibilidade de água no solo e pela época de plantio, por isso, o presente trabalho estuda o impacto do déficit hídrico no crescimento de mudas de dois clones do híbrido Eucalyptus grandis x Eucalyptus urophylla, ambos submetidos a 4 níveis de déficit hídrico, em duas épocas de plantio. O estudo foi realizado na área experimental do Núcleo de Estudos e Difusão de Tecnologia em Florestas, Recursos Hídricos e Agricultura Sustentável (NEDTEC), do Centro de Ciências Agrárias da Universidade Federal do Espírito Santo (CCA-UFES), localizado no município de Jerônimo Monteiro. O trabalho foi realizado em duas épocas distintas, sendo a primeira no período de 09 de fevereiro a 09 de junho de 2009 e a segunda no período de 11 de julho a 07 de novembro de 2009, visando à realização das observações em diferentes condições de regime de radiação, déficit de pressão do vapor do ar, temperatura, umidade relativa do ar e velocidade do vento. O delineamento experimental utilizado foi o inteiramente ao acaso em parcelas subdivididas 2 x 4, alocando-se os 4 níveis de déficits hídricos na parcela principal e as 2 épocas nas subparcelas, com três repetições. Os manejos hídricos aplicados foram: Déficit 0 (D0) sem déficit, Déficit 1(D1) corte da irrigação aos 30 dias de experimentação, permanecendo até o final do experimento, Déficit 2 (D2) corte da irrigação aos 30 dias de experimentação, suspensão da irrigação por 60 dias e posterior retomada da irrigação por mais 30 dias; Déficit 3 (D3) corte da irrigação aos 60 dias de experimentação, prolongando até o final do experimento. Os dados experimentais foram submetidos à análise de variância, e quando significativas, as médias foram comparadas pelo teste de média Tukey a 5% de probabilidade, para cada clone estudado. Com este trabalho, foi possível avaliar o impacto de diferentes déficits hídricos, no crescimento inicial das plantas, em duas épocas do ano e avaliar o incremento no desenvolvimento das plantas durante a aplicação dos tratamentos, com retiradas de amostras médias de cada tratamento a cada 30 dias. As variáveis medidas nos dois experimentos foram altura total da planta, diâmetro ao nível do coleto, número de folhas, área foliar, matéria seca de folhas, matéria seca de haste e ramos, matéria seca de raízes e matéria seca total. Foram avaliadas as variáveis climáticas durante todo o período experimental, nas duas épocas, a fim de determinar a condição do clima em cada época. Para os dois clones estudados, em geral, os déficits hídricos promoveram a redução das variáveis morfológicas estudadas e a época experimental foi o fator que mais influenciou a redução do crescimento das plantas. Sendo que a Época 1 foi a que proporcionou resultados superiores, e a Época 2 foi a que prejudicou mais o desenvolvimento das plantas, reduzindo significativamente todas as variáveis morfológicas em todos os déficits hídricos, inclusive o D0.

Growth and nutrient uptake of coffee seedlings cultivated in nutrient solution with and without silicon addition

In recent years, the application of silicon (Si) in crops, including coffee, has become a common practice. The objective of this study was to assess the silicon uptake by coffee seedlings and its effects on plant growth, water and macro and micronutrient uptake. The research was conducted using nutrient solution in a greenhouse at the Departamento de Fitotecnia da Universidade Federal de Viçosa, in a completely randomized design with two treatments (with and without silicon) and three replications. Each plot consisted of three plants grown in a 800 mL vessel containing the treatment solutions. At every three days, water consumption, the concentration of OH - and the depletion of Si and K were assessed in the nutrient solutions. After 33 days, the plants were assessed with regard to their fresh and dry weight of leaves, roots and stem, shoot height and total length of the plant (shoot and root). Number of leaves and internodes, and the content and accumulation of silicon, macro, and micronutrients were also determined. The consumption of water, the amount of potassium uptake and, biomass accumulation were greater in plants grown in solution without silicon addition. However, the concentration of OH- in the solution and the amount of silicon uptake were greater in plants grown in solution with added silicon. Silicon accumulation was greater in leaves than in stem and roots. Silicon decreased coffee plant accumulation of phosphorus, potassium, calcium, zinc, copper and iron.

Growth and yield of Coffea arabica L. in Northwest Fluminense: 2nd harvest

In recent years, several new coffee cultivars recommended for different regions have been released. However, the performance of these varieties in many traditionally producing regions is unknown. Difference of climate and soil may jeopardize the productivity of the new cultivars and cause losses to farmers. The objective of this study is to evaluate the vegetative growth and productive genotypes of C. arabica in the conditions of the Northwestern Rio de Janeiro State, Brazil. The experiment was settled in 2007, in Panorama 1 Farm, located in the municipality of Varre Sai, RJ. Twenty-five genotypes of C. arabica were planted in a spacing of 2.5 × 0.8 m, using a completely randomized design with five replications and eight plants per plot. There were eight measurements of vegetative growth represented by plant height, stem diameter and number of plagiotropic branches. Assessments of productivity were also performed in years 2009 and 2010. There was a positive phenotypic correlation among vegetative characteristics and between vegetative characteristics and yield in the first harvest, while in the second harvest only the number of plagiotropic branches was positively correlated with yield. Up to date, the genotypes Catucaí amarelo 2 SL, Catiguá MG 02, Acauã, Palma II, Sabiá 398, IPR 103/ Iapar, IPR 100/Iapar, H 419-10-6-2-12-1, Catucaí amarelo 24 / 137, Iapar 59, Catucaí amarelo 20/15, H 419-10-6-2-5-10-1 and H 419-10-6-2-5-1 had the highest average yield after two harvests.

Genetic divergence of tomato subsamples

Understanding the genetic variability of a species is crucial for the progress of a genetic breeding program and requires characterization and evaluation of germplasm. This study aimed to characterize and evaluate 101 tomato subsamples of the Salad group (fresh market) and two commercial controls, one of the Salad group (cv. Fanny) and another of the Santa Cruz group (cv. Santa Clara). Four experiments were conducted in a randomized block design with three replications and five plants per plot. The joint analysis of variance was performed and characteristics with significant complex interaction between control and experiment were excluded. Subsequently, the multicollinearity diagnostic test was carried out and characteristics that contributed to severe multicollinearity were excluded. The relative importance of each characteristics for genetic divergence was calculated by the Singh's method (Singh, 1981), and the less important ones were excluded according to Garcia (1998). Results showed large genetic divergence among the subsamples for morphological, agronomic and organoleptic characteristics, indicating potential for genetic improvement. The characteristics total soluble solids, mean number of good fruits per plant, endocarp thickness, mean mass of marketable fruit per plant, total acidity, mean number of unmarketable fruit per plant, internode diameter, internode length, main stem thickness and leaf width contributed little to the genetic divergence between the subsamples and may be excluded in future studies.

Rooting of hardwood cuttings of Roxo de Valinhos fig (Ficus carica L.) with different propagation strategies

The objective of this study was to evaluate the substrate, cuttings collection time, the position and the cutting depth, and the propagation environment on rooting of 'Purple Valinhos' fig tree cuttings in Southwestern Paraná, Brazil. Two experiments were carried out at UTFPR, Câmpus Dois Vizinhos, with hardwoods cuttings from Roxo de Valinhos fig tree. The first experiment used a randomized block design, in 3 x 3 x 2 factorial (substrate x environment x collection time), with four replications of 10 cuttings per plot. The cuttings were collected in the first fifteen days of July and August. The substrates were sand, soil and the mixture of these [1:1 (v / v)]. The environments used were open sky, tunnel with plastic cover and tunnel with half-shade black net cover. The second experiment used a randomized block design, 2 x 2 x 3 factorial (shoot cutting position x soil cover x shoot cutting depth), with four replications of 12 cuttings per plot. In the factor position, the vertically (0 º inclination) and inclined (45 º inclination) shoot cuttings were evaluated. Soil cover was tested with mulching plastic cover or not. The tested depths were 1/3, 1/2 and 2/3 in relation to the total length of the shoot cutting. In both experiments, the following were analyzed: rooting and mortality indices, number of leaves and primary shoots, length of the three largest roots per cutting. It was conclude that, the protected environment with plastic cover on sand as substrate must recommended for the rooting of fig estaca, collecting them in the first half of July. The inclination position and cutting depth of the estaca and the substrate coverage with plastic mulching did not influence the results.

Effect of the number of shells on the pressure and energy of two-dimensional free bubble clusters

We have performed Surface Evolver simulations of two-dimensional hexagonal bubble clusters consisting of a central bubble of area lambda surrounded by s shells or layers of bubbles of unit area. Clusters of up to twenty layers have been simulated, with lambda varying between 0.01 and 100. In monodisperse clusters (i.e., for lambda = 1) [M.A. Fortes, F Morgan, M. Fatima Vaz, Philos. Mag. Lett. 87 (2007) 561] both the average pressure of the entire Cluster and the pressure in the central bubble are decreasing functions of s and approach 0.9306 for very large s, which is the pressure in a bubble of an infinite monodisperse honeycomb foam. Here we address the effect of changing the central bubble area lambda. For small lambda the pressure in the central bubble and the average pressure were both found to decrease with s, as in monodisperse clusters. However, for large,, the pressure in the central bubble and the average pressure increase with s. The average pressure of large clusters was found to be independent of lambda and to approach 0.9306 asymptotically. We have also determined the cluster surface energies given by the equation of equilibrium for the total energy in terms of the area and the pressure in each bubble. When the pressures in the bubbles are not available, an approximate equation derived by Vaz et al. [M. Fatima Vaz, M.A. Fortes, F. Graner, Philos. Mag. Lett. 82 (2002) 575] was shown to provide good estimations for the cluster energy provided the bubble area distribution is narrow. This approach does not take cluster topology into account. Using this approximate equation, we find a good correlation between Surface Evolver Simulations and the estimated Values of energies and pressures. (C) 2008 Elsevier B.V. All rights reserved.

Can varying the number of teams in a shift schedule constitute a preventive strategy?

OBJECTIVE: The study examines the implications for shiftworkers of applying different numbers of teams in the organization of shiftwork. METHODS: The participating operators came from five different companies applying continuous shift rotation systems. The companies shared the same product organization and a common corporate culture belonging to the same multinational company. Each company had a shift system consisting of four, five or six teams, with the proportion of shifts outside day work decreasing as the number of teams increased. Questionnaire and documentary data were used as data sources. RESULTS: Operators in systems with additional teams had more daywork but also more irregular working hours due to both overtime and schedule changes. Operators using six teams used fewer social compensation strategies. Operators in four teams were most satisfied with their work hours. Satisfaction with the time available for various social activities outside work varied inconsistently between the groups. CONCLUSIONS: In rotating systems the application of more teams reduces the number of shifts outside day work. This apparent improvement for shiftworkers was counteracted by a concomitant irregularity produced by greater organizational requirements for flexibility. The balance of this interaction was found to have a critical impact on employees.

Study of the influence of count’s number in myocardium in the determination of reproducible functional parameters in Gated-SPECT studies simulated with GATE

Myocardial Perfusion Gated Single Photon Emission Tomography (Gated-SPET) imaging is used for the combined evaluation of myocardial perfusion and left ventricular (LV) function. But standard protocols of the Gated-SPECT studies require long acquisition times for each study. It is therefore important to reduce as much as possible the total duration of image acquisition. However, it is known that this reduction leads to decrease on counts statistics per projection and raises doubts about the validity of the functional parameters determined by Gated-SPECT. Considering that, it’s difficult to carry out this analysis in real patients. For ethical, logistical and economical matters, simulated studies could be required for this analysis. Objective: Evaluate the influence of the total number of counts acquired from myocardium, in the calculation of myocardial functional parameters (LVEF – left ventricular ejection fraction, EDV – end-diastolic volume, ESV – end-sistolic volume) using routine software procedures.

Ensino da Matemática : Os Number Bonds de Singapura

(...) Os number bonds (esquemas todo-partes) constituem um dos procedimentos didáticos mais famosos do Método de Singapura. Estas representações auxiliam a compreensão numérica basilar, nomeadamente a capacidade de decompor quantidades e a álgebra fundamental (adições e subtrações). Neste artigo, analisaremos o que são, quais as vantagens e a forma de utilização destes esquemas no 1.º ano de escolaridade. (...)

Determining the number of clusters in categorical data

Cluster analysis for categorical data has been an active area of research. A well-known problem in this area is the determination of the number of clusters, which is unknown and must be inferred from the data. In order to estimate the number of clusters, one often resorts to information criteria, such as BIC (Bayesian information criterion), MML (minimum message length, proposed by Wallace and Boulton, 1968), and ICL (integrated classification likelihood). In this work, we adopt the approach developed by Figueiredo and Jain (2002) for clustering continuous data. They use an MML criterion to select the number of clusters and a variant of the EM algorithm to estimate the model parameters. This EM variant seamlessly integrates model estimation and selection in a single algorithm. For clustering categorical data, we assume a finite mixture of multinomial distributions and implement a new EM algorithm, following a previous version (Silvestre et al., 2008). Results obtained with synthetic datasets are encouraging. The main advantage of the proposed approach, when compared to the above referred criteria, is the speed of execution, which is especially relevant when dealing with large data sets.

The influence of count's number in myocardium in the determination of reproducible parameters in Gated-SPECT studies simulated with GATE

Myocardial Perfusion Gated Single Photon Emission Tomography (Gated-SPET) imaging is used for the combined evaluation of myocardial perfusion and left ventricular (LV). The purpose of this study is to evaluate the influence of the total number of counts acquired from myocardium, in the calculation of myocardial functional parameters using routine software procedures. Methods: Gated-SPET studies were simulated using Monte Carlo GATE package and NURBS phantom. Simulated data were reconstructed and processed using the commercial software package Quantitative Gated-SPECT. The Bland-Altman and Mann-Whitney-Wilcoxon tests were used to analyze the influence of the number of total counts in the calculation of LV myocardium functional parameters. Results: In studies simulated with 3MBq in the myocardium there were significant differences in the functional parameters: Left ventricular ejection fraction (LVEF), end-systolic volume (ESV), Motility and Thickness; between studies acquired with 15s/projection and 30s/projection. Simulations with 4.2MBq show significant differences in LVEF, end-diastolic volume (EDV) and Thickness. Meanwhile in the simulations with 5.4MBq and 8.4MBq the differences were statistically significant for Motility and Thickness. Conclusion: The total number of counts per simulation doesn't significantly interfere with the determination of Gated-SPET functional parameters using the administered average activity of 450MBq to 5.4MBq in myocardium.