Armando Conagin

Modifications for the tukey test procedure and evaluation of the power and efficiency of multiple comparison procedures

Multiple pairwise comparison tests of treatment means are of great interest in applied research. Two modifications for the Tukey test were proposed. The power of unilateral and bilateral Student, Waller-Duncan, Duncan, SNK, REGWF, REGWQ, Tukey, Bonferroni, Sidak, unilateral Dunnet statistical tests and the modified tests, Sidak, Bonferroni 1 and 2, Tukey 1 and 2, has been compared using the Monte Carlo method. Data were generated for 600 experiments with eight treatments in a randomized block design, of which 400 had four and 200 eight blocks. The differences between the treatment means in relation to the control were 30%, 20%, 15%, 10%, 5%. Two extra treatments did not differ from the control. A coefficient of variation of 10% and a probability Type I error of α = 0.05 were adopted. The power of all the tests decreased when the differences to the control, decreased. The unilateral and bilateral Student t, Waller-Duncan and Duncan tests showed greater number of significative differences, followed by unilateral Dunnett, modified Sidak, modified Bonferroni 1 and 2, modified Tukey 1, SNK, REGWF, REGWQ, modified Tukey 2, Tukey, Sidak and Bonferroni. There is great loss of efficiency for all tests in relation to the unilateral Student t test for each difference of the treatment to the control, when the differences between means decrease. The modified tests were always more efficient than their original ones.

Escala de valores para a avaliação da qualidade da bebida do café

O presente artigo relata os resultados obtidos com o emprego de uma escala de valores, na analise de resultados de provas de bebida de cafe. A escala foi construida a partir de amostras das diferentes bebidas-padrao, de cafe exportavel, tendo sido empregada uma equipe de degustadores previamente selecionados e treinados durante tres anos. Os resultados obtidos representam medias de aproximadamente 160 determinacoes. O metodo sera utilizado na avaliacao da qualidade da bebida do cafe nas experiencias realizadas no Instituto Agronomico.

Delineamento (1/5) (5 x 5 x 5) em blocos

No presente trabalho, os tratamentos do delineamento fatorial fracionado (1/5) (5x5x5), obtido pela superposicao de tres quadrados latinos ortogonais, sao colocados em cinco blocos, com a utilizacao de um quarto quadrado latino ortogonal. Um modelo quadratico em X foi usado para estudo da superficie de resposta, sendo considerados polinomios ortogonais linear e quadratico para cada um dos fatores e para blocos, uma vez que, em ensaios de campo, a maior parte do gradiente de fertilidade ou de outras causas sistematicas pode ser eliminada com a estimacao desses dois efeitos; foram ainda colocadas no modelo as interacoes lineares de dois fatores. Somente os efeitos lineares sao estimados independentemente, e foram dadas, para cada fator e para blocos, as matrizes para calculo dos efeitos quadraticos ajustados. Quando e eliminada do modelo uma das interacoes de dois fatores, o efeito quadratico do fator restante passa a ser estimado independentemente. Se o quarto indice for utilizado como outro fator, tem-se o delineamento (1/25) (5 x 5 x 5 x 5), completamente casualizado; este permite o estudo simultâneo de quatro fatores em cinco niveis, com apenas vinte e cinco pontos experimentais; o modelo contem efeitos lineares e quadraticos dos quatro fatores e as interacoes lineares desses fatores dois a dois. Se nos delineamentos (1/51 (5 x 5 x 5), divididos em cinco blocos, e (1/25) (5x5x5x5) completamente casualizado, todas as interacoes de dois fatores forem nao-significativas, o modelo ficara so com os termos lineares e quadraticos puros, e estes poderao ser estimados independentemente, a semelhanca do que ocorre com o (1/5) (5x5x5) completamente casualizado.

Efeito da falta de normalidade em testes de homogeneidade das variâncias

The mean and standard deviation of distributions with five different levels of assimetry and kurtosis were used to simulate 6,000 experiments, in a randomized complete block design with five treatments and six replications, considering two levels of precision and three levels of block effects. The tests of homogeneity of variance proposed by Han and Shukla, for randomized block design, and those of Bartlett, Cochran and Hartley, developed for one-way classification were applied to the simulated data. The last three tests were also used after correcting for block effects. The amount of rejection of the null hypothesis increased with the levels of assimetry and kurtosis in all tests. The percentage of rejection of the hypothesis of homogeneity of variances using Shuklas test and those of Bartlett, Cochran and Hartley, without block correction, were strongly affected by non-normality mainly when the block effect was small. The rejection of the null hypothesis when used Hans test or those of Bartlett, Cochran and Hartley tests, adjusted for block effects, were larger than 5% when the coefficients of assimetry and kurtosis were higher than 1.11 and 4.04 respectively.

Cultivo de café em latossolo vermelho-amarelo da região de Batatais, SP

This paper presents the results of an experiment of coffee fertilization on a Red Yellow Latosol of extremely low fertility. This soil was formerly considered improper for economical agriculture. Three treatments based on the application of barnyard manure and four treatments employing only mineral fertilizers were used. The effects of the treatments were studied for the period 1960 to 1969. The yields showed that the use of mineral fertilizers plus lime and micronutrients and this same mineral misture plus a dose of barnyard manure gave the best responses. The application of borax and zinc sulphate as soil dressings corrected efficiently the deficiencies of boron and zinc and increased the production when applied together with dolomite. The application of dolomite was highly efficient for correction of magnesium deficiency and increased significantly the yields. The results showed that it is possible to cultivate coffee successfully on a Red Yellow Latosol of extremely low fertility using exclusively mineral fertilizers.

Rotação de culturas: análise estatística de um experimento de longa duração em Campinas (SP)

With the goal of determining the crop rotation effects on cotton, peanut, rice, sugar cane and maize yields, a rotation experiment was established in Campinas, State of Sao Paulo, Brazil, for eleven years (1963/64 to 1974/75). The residual effect was determined by planting maize on all experimental plots in the following year (1975/76). The experimental design was randomized blocks with twenty treatments and four replications, spanning all treatments in all years in order to have an efficient and faster evaluation of the crop rotation effects. The results showed that the continuous cropping with mineral fertilizer applied annually led to a significant decrease of crop yield. However, when this continuous cropping received an initial liming, the average crop yield was maintained throughout the years. The crop rotation effect, with initial liming and mineral fertilization resulted in a significant increase in crop yields when compared with the individual crop that received only mineral fertilization.

Fontes e doses de nitrogênio na adubação química do cafeeiro em latossolo roxo e podzólico vermelho-amarelo orto

Ammonium nitrate limestone (ANL), ammonium sulphate, Chilean nitrate and urea at rates of 75, 150, 225 and 300 kilograms of nitrogen per hectare, splitted in 1, 2, 3 and 4 applications were used in field experiments with coffee trees, in two soils: in a Red Latosol in Ribeirao Preto and in a Red Yellow Ortho-Podzolic in Mococa, Sate of Sao Paulo, Brazil. In Ribeirao Preto, the experiment was set up in December 1957 and the grain yields were recorded from 1960 to 1969. In Mococa, the experiment was set up in 1960 and the grain yields were recorded from 1962 to 1971. The grain yields of coffee increased with the increases in the nitrogen rates applied. The yield responses to high nitrogen rates were greater in the Red Yellow Ortho-Podzolic soil than in the Red Latosol. Ammonium sulphate and ANL resulted in better yields than Chilean nitrate in the Red Yellow Ortho-Podzolic soil. Urea increased coffee yields above those obtained with Chilean nitrate, but the differences were not significant. No significant effects of nitrogen sources were observed in the Red Latosol. The practice of splitting the total quantities of nitrogen did not affect the grain yields of coffee in the Red Latosol. In the Red Yellow Ortho-Podzolic soil, grain yields were higher when nitrogen was splitted in four applications.

Delineamentos (1/5)(5³)

The statistical solutions for quadratic and square root polynomials for a group of special 1/5 (53) fractional factorial, aiming, primarily, its application to fertilizer experiments are reported. These factorial designs were originated by the superposition of three of the four existing orthogonal 5x5 latin squares. Three basic designs are obtained: I-II-III, I-II-IV, and I-III-IV; the last one is presented below. 111 245 324 453 532 222 351 435 514 143 333 412 541 125 254 444 523 152 231 315 555 134 213 342 421 The quadratic model of second order with ten parameters is: Yijk = b0x0 +blixli + bljxlj + blkxlk + b2ix2i + b2jx2j + b2kx2k + + bliljxlilj + blilkxlilk + bljlkxljlk + xijk where xlm = a1 + Xm, x2m = a2 + g2Xm + X2m , m= i,j,k; each factor varying from 1 to 5, with the orthogonality conditions: Sxlm=0, Sx2m=0, Sxlmx2m=0, giving Sxlm=-3+Xm e Sx2m= 7-6Xm+X2m, so: xl1=-2; xl2=-1; xl3=0; xl4=1; xl5=2; x21=2; x22=-1; x23=-2; x24=-1; x25=2 The linear regression coefficient for each factor can be estimated independently; the quadratic and the linear x linear interaction coefficients are estimated from a 6x6 full matrix. Consequently in the analysis of variance the linear sums of squares for each factor are independent but the quadratic and interactions sums of squares for all factors are entangled and should be jointly tested. If the contribution of a factor and its respective interaction with the others are negligible, independent estimators of the linear and quadratic regression of the other two factors and the correspondent interaction can be calculated, with correspondent parallelism in the analysis of variance. On the other hand, if the factors are important but its interactions are negligible, the linear and quadratic coefficients for each factor are estimated independently. The square root polynomial model may be represented as in (1) with the values: xlm= a1+ (Xm)1/2 and x2m= a2+ g2(Xm)1/2 +Xm, where m= i,j,k; Sxlm=0, Sx2m=0, Sxlmx2m=0, giving: xlm= -1,67646 + (Xm)1/2, x2m= 2,41157-3,22798 (Xm)1/2 +Xm; xl1=-0,67646; xl2=-0,26226; xl3=0,05554; xl4=0,32354; xl5=0,55964; x21=0,18359; x22=-0,15342; x23=-0,17928; x24=-0,04438 and x25=0,19349, for each factor i,j,k. Regarding this model, with the exclusion of b0, the coefficients for each factor and the square-root interactions are estimated from a full 9x9 symetric matrix. In consequence; with the exception of b0; the sums of squares correspondent to the other coefficients are tested together. Equivalent properties to the quadratic model hold true for the square root model, when the interactions or when one main factor and its interactions are negligible. Assuming no interaction, the Mitscherlich model Y=A [l _ 10 _ c(x+b) ], can be used for evaluation of each factor response from the corresponding marginal totals. An extra evaluation from the main diagonal of the design can be obtained, representing the response to increasing amounts of the three factors at equal levels. In case of fertilizer experiments, treatments like 000 should be added as extra points to the 25 used in this design, in order to allow the determination of the increment due to the use of macronutrient combinations and their costs. Using proper range of dosages (avoiding plateau responses), as it should be in npk fertilizer experiments, this group of designs allows a more efficient analysis of the curvature of the surface functions on the area of economical decision. If the models are used without interactions, the independent estimation of the parameters for the quadratic, square-root and Mitscherlich models can be very easily achieved. These properties are of great interest in the economical studies of fertilization programs for developing countries. With the help of a net of experiments of this type, economical studies of fertility nature with macronutrients as nitrogen, phosphorus, and potassium, for example, can be obtained with five different levels of each factor, with experiments of medium size.

ENSAIO DE ADUBAÇÃO N-P-K EM AMENDOIM(*)

The influence of nitrogen, phosphorus, and potassium on the yield of the wheat plant was studied in a greenhouse experiment carried out in Mitscherlich pots filled with soil of the Glacial type as found in the state of Sao Paulo. A 3 x 4 x 3 factorial design with 3 pots per treatment was used. The agronomical variety of wheat used was Frontana. The influence of the treatments was studied on the height of the plants, number of ears produced, and on the dry weight of these. The results showed that nitrogen did not affect the height of the plants, but increased greatly the number of ears and their weight. Potassium showed a favorable effect on the three characters studied, but its influence was smaller than that of nitrogen for number and weight of ears. Phosphorus induced the greatest yield response and its effect was very pronounced on the three factors considered. A detailed analysis of variance for the characters studied with decomposition of main effects and interactions is given.

Variedades de cavalos de videira e sua melhor época de enraizamento

The experiment reported in this paper was carried out to determine the most appropriate time to root cuttings of six of the most common rootstock varieties of grapes under field conditions in the state of Sao Paulo. The rootstocks tested were Rupestris du Lot, Riparia x Rupestris 101-14, Golia, Kobber 5BB, Mourvedre x Rupestris 1202, and Aramon x Rupestris Ganzin No. 1. The following rooting dates were compared: mid of May, June, July, August, September, and October. Cutting of all varieties tested gave good rootstocks when rooted in June, July, and August. Not only was the percentage of established rootstocks higher, but there was also a higher percentage of vigorously growing plants. Cuttings rooted in May, September, and October gave poor results. The good results obtained in June, July, and August were attributed in great part to the use of cuttings from completely lignified branches that had dormant buds, whereas those used in May were taken from branches still immature, and those for September and October, from matrices that were starting the new vegetative growth.