Análise comparativa do modelo de Cobb-Douglas com erro aditivo e multiplicativo

This paper dis cusses the fitting of a Cobb-Doug las response curve Yi = αXβi, with additive error, Yi = αXβi + e i, instead of the usual multiplicative error Yi = αXβi (1 + e i). The estimation of the parameters A and B is discussed. An example is given with use of both types of error

Experiments in square lattice with a common treatment in all blocks

O Instituto Agronômico de Campinas vem, há muitos anos, utilizando, nos seus ensaios de milho, reticulados quadrados com k² tratamentos em blocos de k + 1 parcelas, sendo a parcela extra de cada bloco cultivada com um cultivar padrão (variedade ou híbrido), não incluído entre os k² tratamentos originais. Conclui-se, pois, que esses delineamentos incluem k² + 1 tratamentos, em blocos de k + 1 parcelas. O presente trabalho deduz fórmulas para a análise da variância desses delineamentos, e para a estimação das médias ajustadas de tratamentos. Fórmulas para a variância de diversos contrastes são deduzidas. Finalmente, apresenta-se um exemplo, detalhadamente analisado, de um ensaio em reticulado quadrado com k² = 25, e 4 repetições ortogonais, instalado corn 26 cultivares, em blocos de 6 parcelas.This paper deals with a generalization of square lattice designs, with k² treatments in blocks of k + 1 plots, the extra plot in each block receiving a standard treatment, the same for all blocks. The new design leads to lower variances for contrasts between adjusted treatment mean

The problem of plot size in experiments with trees

Este trabalho desenvolve uma teoria sobre a determinação do tamanho ótimo de parcelas baseada no coeficiente de correlação intraclasse (ρ) entre unidades (subparcelas) dentro das parcelas do experimento. Essa abordagem tem a vantagem de utilizar uma estatística bem conhecida, que varia dentro de limites previamente conhecidos, que são: [- 1/(k - 1) < ρ < C 1], onde k é o número de subparcelas dentro da parcela. Considera-se ótimo o número de subparcelas (k), que dá a variância mínima da média de um tratamento, quando se fixa a área total relativa a esse tratamento. Discute-se detalhadamente a influência de bordadura completa ou de meia bordadura, e ainda da ausência de bordadura. A teoria se aplica especialmente ao caso de experimentos com árvores, e conduz a conclusões de grande generalidade.This paper develops a theory on the determination of optimum plot size, based on the intraclass correlation coefficient (ρ). This method has the advantage of using a well known statistic, which belongs always to the closed interval [- 1/(k - 1) < ρ < 1], where k is the number of units (subplots) within each plot. The plot taken as optimum is that with k units, which leads to minimum variance of treatment means, when the total area per treatment is constant. Guard rows are taken in consideration in the solution. The theory is specially appropriate for research on plot size in experiments with trees, with or without guard rows

A adubação do milho em Lavras

O estudo de 38 ensaios de adubação de milho, espalhados em fazendas da Seccional de Lavras, Minas Gerais, Brasil, conduziu às seguintes conclusões: 1. Em experimentos com produção da testemunha abaixo de 2000 Kg/ha houve respostas significativas para N, R, K e calcário. Se tomarmos o preço de 100 kg de milho como equivalente ao de 10 kg de N, 12 de P2O5 ou 30 de K2O, as doses recomendáveis de adubação são: 38 kg/ha de N, zero de P2O5 e 88 kg/ha de K2O. 2. Em experimentos com produção da testemunha não inferior a 2000 kg/ha somente os efeitos de N e de R foram significativos, mas parece preferível usar fertilização completa, que, com os preços adotados, seria recomendável aos níveis de 44kg/ha de N, 75 de P2O5 e 51 de K2O. 3. Nos experimentos em solos de cerrado, foram significativas as respostas a N, R, K e calcário. As doses recomendáveis, para os preços adotados, foram: 51 kg/ha de N, 40 de P2O5 e 99 de K2O. 4. Para solos com teor conhecido de matéria orgânica, as recomendações devem levar em conta se é ou não superior a 1,25%. Quando superior a 1,25%, a adubação nitrogenada recomendável é de 27 kg/ha de N, se igual ou inferior a 1,25%, devem-se usar 120 kg/ha de N. 5. No caso do fósforo e do potássio a análise do solo não parece adequada para estimar a resposta aos fertilizantes. 6. As respostas à calagem são maiores em solos com Ca + Mg não superior a 3,40 eq. mg/100 ml de terra, ou para pH não superior a 4,75, ou ainda para alumínio trocável acima de 0.566 eq. mg/100 ml de terra.The study of 38 trials on the fertilization of maize scattered in farms of the region of Lavras, State of Minas Gerais, Brasil, led to the following conclusions : 1. In experiments with control below 2000 kg./ha. there were significant responses for N, R, K and limestone. If we take the price of 100 kg. of maize as equivalent to that of 10 kg. of N, 12 of P2O5 or 30 of K2O, the recommended dressings are 38 kg./ha. of N, no phosphorus, and 88 kg./ha. of K2O. 2. In experiments with control not below 2000 kg./ha. only effects of N and R were significant, but it seems better to use a complete fertilizer. For the prices given above the recommended dressings are 44 kg./ha. of N, 75 of P2O5 and 51 of K2O. 3. In experiments carried out on cerrado soils significant responses were found for N, R, K and limestone. The recommended dressings, for the prices mentioned, are 51 kg./ha. of N, 40 of P2O5 and 99 of K2O. 4. For soils with known content of organic matter recommendations should take in account if it over 1.25% or not. When over 1.25%, the recommended dressing is 27 kg./ha. of N; if it is not over 1.25%, one should use 120 kg./ ha. of N. 5. For R and K soil analysis does not seem suitable to estimate responses to fertilization. 6. Responses to limestrone are higher in soils with Ca + Mg not above 3.40 meq./100 ml. of soil, or for pH not above 4,75, or else for exchangeable Al over 0.566 meq./100 ml. of soil

Inconvenientes do uso do valor médio do diâmetro para determinação da área basal

This paper discusses the use of the arithmetic mean of diameters in the computation of basal area in forestry. This use, proposed in the Serviço Florestal of the Secretary of Agriculture of the State of São Paulo, leads to several difficulties, to be shown presently. Let be the diameter of a tree, with i = 1 referring to trees to be cut, and i = 2 to trees to be left uncut. If Nd is the number of trees to be cut, Nr the nummber of trees to be left uncut, and Np = Nd + Nr is the total number of trees, then the basal area of the total population (Ap) is Ap = (&#960;/4) &#931;/i,j D²ij , and the basal area of trees to be cut and to be left uncut are, respectively, Ad = (&#960;/4) &#931;/j D²lj , Ar = (&#960;/4) &#931;/j D²2j , The similar estimates A'p; A'd, A'r, computed with the aritmetic means of diameters, are: A'p = (&#960;/4) D²../Np , A'p = (&#960;/4) D²1./Nd , A'p = (&#960;/4) D²2/Nr , It is shown that A'p A'd - A'r = - (&#960;/4) [ sum of square of contrast cut thees v. uncut trees ] so that, since the contrast in question may be taken as alwys non-zero, we have A'p < A'd + A'r , which is certainly absurd from the point of view of the theory of measure. But indeed, in some cases we may even have A'p < A'r , which is really an absurd. On the other hand it is proved that Ap = A'p + .(&#960;/4) [ sum of square of deviations of diameters in population ] so that the difference A'p, Ap - increases with the heterogeneity of diameteres of the trees.Através do estudo matemático do problema, o autor demonstra que o uso do valor médio do diâmetro (GOMES, 1957), obtido através da média aritmética dos diâmetros das árvores, não convém para o cálculo da área basal de um povoamento florestal, pois não satisfaz aos postulados da Teoria da Medida

Amostragem no mamão para a determinação do brix

The present paper deals with sampling methods to be employed in the determination of the total sugar content obtained from brix measurements in Carica papaya L., given by Zeiss hand refractometer. The results obtained led to the conclusion that, rather than using several samples per fruit, it is better to get a large number of fruits, taking just one sample per fruit. The sample in each fruit should be taken always from the same region

O problema técnico-econômico da adubação

The authors discuss from the economic point of view the use of a few functions intended to represent the yield y corresponding to a level xof the nutrient. They point out that under conditions of scarce capital what is actually most important is not to obtain the highest profit per hectare but the highest return per cruzeiro spent, so that we should maximize the function z = _R - C_ = _R_ - 1 , C C where R is the gross income and C the cost of production (fixed plus variable, both per hectare). Being C = M + rx, with r the unit price of the nutrient and Af the fixed cost of the crop, wo are led to the equation (M + rx)R' - rR = 0. With R = k + sx + tx², this gives a solution Xo = - Mt - &#8730; M²t² - r t(Ms - Kr)- _____________________ rt on the other hand, with R = PyA &#91;1 - 10-c(x + b)&#93;, x0 will be the root of equation (M + rx)cL 10 + r 10c(x + b) = 0 (12). Another solution, pointed out by PESEK and HEADY, is to maximize the function z = sx + tx² _________ m + rx where the numerator is the additional income due to the nutrient, and m is the fixed cost of fertilization. This leads to a solution x+ = - mt - &#8730;m²t² - mrst (13) _________________ rt However, we must have x+< _r_-_s_ I if we want to satisfy t _dy_ &gt; r. dx This condition is satisfied only if we have m < _(s__-__r)² (14), - 4 t a restriction apparently not perceived by PESEK and HEADY. A similar reasoning using Mitscherlich's law leads to equation (mcL 10 + r) + cr(L 10)x - r 10cx = 0 (15), with a similar restriction. As an example, data of VIEGAS referring to fertilization of corn (maize) gave the equation y - 1534 + 22.99 x - 0. 1069 x², with x in kg/ha of the cereal. With the prices of Cr$5.00 per kilo of maize, Cr$ 26.00 per kilo of P2O3,. and M = Cr$5,000.00, we obtain x0 = 61 kg/ha of P(2)0(5). A similar reasoning using Mitscherlich's law leads to x0 = 53 kg/ha. Now, if we take in account only the fixed cost of fertilization m = Cr$ 600.00 per hectare, we obtain from (13) x+ = 51 kg/ha of P2O5, while (14) gives x+ - 41 kg/ha. Note that if m = Cr$ 5,000.00, we obtain by formula (13) x+ = 88 kg/ha of P2O5, a solution which is not valid, since condition (14) is not satisfied

Substituição de subprodutos de trigo pelo sorgo moído na alimentação de pintos

Searching for a substitute of wheat bran and wheat standard middlings in chick mashes, three experiments were carried out using ground sorghums. In the first one, 30% of Atlas, Kafir e White Afrikan x Sumac (seed chops) were substituted for 30% of wheat by-products. All the rations with sorghum grain gave inferior results. In another experiment, 7, 14, 20 and 30% of sorghum substituted equal percentages of those wheat by-products, the best results having been obtained with 7% of Atlas and 23% of wheat by-products. Finally, in a third experiment, 5% of dried cow manure plus 10, 20 and 30% of ground Atlas sorghum were substituted for 5% of alfalfa hay meal plus, respectively, 10, 20 and 30% of wheat by-products. All results obtained from rations containing sorghum were as good as or better than that given by the ration including alfalfa hay meal and only wheat by-products. Under the conditions of this experiment, 5% of cow manure plus 12,25% of sorghum and 17,75% of wheat by-products is supposed to be the best combination to be recommended, this result having been attained through the study of the regression equation

Novas variedades de Cana-de-Açúcar

The authors carried out joint analyses of data referring to six experiments with varieties of sugar cane, carried out by SEGALLA and ALVAREZ in six locations in the State of S. Paulo, Brasil. The analyses showed that for cane or sugar yield, either for plant-cane or for plant-cane together with the first two ratoons, the best five varieties were CB 40-69, CB 41-76, CB 40-13, CB 40-19 and Co 419. The yield of sugar cane/for all varieties studied is given below, in metric tons produced in plant cane and the first two ratoons. Varieties Yield of sugar cane (tons/hectare) CB 40-69 205.2 CB 41-76 204.5 CB 40-13 199.4 CB 40-19 192.4 Co 419 192.1 CB 38-30 182.1 CB 41-70 181.5 Co 413 177.5 CB 38-22 174.4 CB 36-14 172.8 Co 290 166.6 CB 41-35 147.9 The least significant difference by Tukey's test, at the 5% level of probability, is A = 28.3 metric tons/hectare