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Investigation of multicollinearity allows parameters in multivariate analysis to be estimated with higher precision and with biological interpretation. In order to generate reliable estimates of the degree of multicollinearity, it is necessary to use appropriate sample size. Thus, the objectives of this study were to determine the sample size (number of plants) necessary to estimate the indicators of the degree of multicollinearity - condition number (CN), correlation matrix determinant (DET), and variance inflation factor (VIF) - in morphological traits of rye and to verify the variability of the sample size between the indicators. Five and three uniformity trials were conducted with the cultivars BRS Progresso and Temprano, respectively. Eight morphological traits were evaluated in 780 plants in eight trials. For each trial, 22 cases were selected among the 28 formed by the combination of eight traits, taken six by six, totaling 176 cases. In each case, 197 sample sizes were planned (20, 25, 30, ..., 1,000 plants) and in each size 2,000 resampling procedures with replacement were performed, CN, DET, and VIF were determined and the average among 2,000 estimates was calculated. For each case and indicator (CN, DET, and VIF), the sample size was determined through three models: modified maximum curvature method and linear and quadratic segmented models with plateau response. There is variability between sample sizes between indicators, with larger sample sizes required for DET, followed by CN and VIF, in that order, with at least 180, 116 and 85 plants, respectively. A investigação da multicolinearidade permite que parâmetros em análises multivariadas sejam estimados com maior precisão e com interpretação biológica. Para ter confiabilidade nas estimativas do grau de multicolinearidade, é necessário utilizar adequado tamanho de amostra. Assim, os objetivos deste trabalho foram determinar o tamanho de amostra (número de plantas) necessário para a estimação dos indicadores do grau de multicolinearidade - número de condição (NC), determinante da matriz de correlação (DET) e fator de inflação da variância (FIV) - em caracteres morfológicos de centeio e verificar a variabilidade do tamanho de amostra entre os indicadores. Foram conduzidos cinco e três ensaios de uniformidade com as cultivares BRS Progresso e Temprano, respectivamente. Foram avaliados oito caracteres morfológicos em 780 plantas em oito ensaios. Para cada ensaio, foram selecionados 22 casos entre os 28 formados pela combinação de oito caracteres, tomados seis a seis, totalizando 176 casos. Para cada caso, foram planejados 197 tamanhos de amostra (20, 25, 30, ..., 1.000 plantas) e para cada tamanho foram realizadas 2.000 reamostragens, com reposição, determinados o NC, DET e FIV e calculada a média das 2.000 estimativas. Após, para cada caso e indicador, foi determinado o tamanho de amostra, por meio de três modelos: método da máxima curvatura modificado e modelos linear e quadrático segmentados com resposta em platô. Há variabilidade entre os tamanhos de amostra entre os indicadores, com necessidade de maiores tamanhos de amostra para DET, seguido de NC e FIV, nessa ordem, com no mínimo de 180, 116 e 85 plantas, respectivamente.

The objective of this work was to model and identify the best models for estimating the leaf area, determined by digital photos, of buckwheat (Fagopyrum esculentum Moench) of the cultivars IPR91-Baili and IPR92-Altar, as a function of length (L), width (W) or length x width product (LW) of the leaf blade. Ten uniformity trials (blank experiments) were carried out, five with IPR91-Baili cultivar and five with IPR92-Altar cultivar. The trials were performed on five sowing dates. In each trial and cultivar, expanded leaves were collected at random from the lower, middle and upper segments of the plants, totaling 1,815 leaves. In these 1,815 leaves, L and W were measured and the LW of the leaf blade was calculated, which were used as independent variables in the model. The leaf area of each leaf was determined using the digital photo method (Y), which was used as a dependent variable of the model. For each sowing date, cultivar and thirds of the plant, 80% of the leaves (1,452 leaves) were randomly separated for the generation of the models and 20% of the leaves (363 leaves) for the validation of the models of leaf area estimation as a function of linear dimensions. For buckwheat, IPR91-Baili and IPR92-Altar cultivars, the quadratic model (Ŷ = 0.5217 + 0.6581LW + 0.0004LW2, R2 = 0.9590), power model (Ŷ = 0.6809LW1.0037, R2 = 0.9587), linear model (Ŷ = 0.0653 + 0.6892LW, R2 = 0.9587) and linear model without intercept (Ŷ = 0.6907LW, R2 = 0.9587) are indicated for the estimation of leaf area determined by digital photos (Y) based on the LW of the leaf blade (x), and, preferably, the linear model without intercept can be used, due to its greater simplicity.

The aim of this study was to determine the rate of node appearance (RNA), the final number of nodes (FNN) and the period of node emission (PNE) in two buckwheat cultivars (Fagopyrum esculentum Moench) for different sowing dates, and to check variability in the RNA, FNN and PNE between the cultivars and sowing dates. The IPR91-Baili and IPR92-Altar cultivars were evaluated for 29 and 31 sowing dates from October to May in the 2017/2018 and 2018/2019 agricultural years respectively. In each experiment, a completely randomised design with five replications was used. The number of nodes (NN) on the main stem was counted twice a week in each plant (replication), from emission of the first node until the end of the cycle. The linear regression (y = a + bx) of the number of nodes (NN, y) was adjusted for each plant based on the number of days after emergence (DAE, x). The rate of node appearance (RNA), in days node-1, was determined from the inverse of the slope of the linear regression between NN and DAE (RNA = 1/b). The RNA was calculated for the period of node emission (PNE, in days), i.e. from emergence to emission of the last node. The final number of nodes (FNN) was counted at the end of node emission. Variability was found in the rate of node appearance (RNA), the final number of nodes (FNN) and the period of node emission (PNE) between the cultivars and sowing dates. The rate of node appearance ranges between 2.20 and 8.23 days node-1, the final number of nodes between 2.20 and 17.20, and the period of node emission between 16.60 and 49.20 days. Plants of the IPR91-Baili and IPR92-Altar cultivars show better vegetative development (lower RNA, higher FNN and greater PNE) when sown in November, December, January and February, compared to those sown in October, March, April and May.

The objective of this work was to determine the optimal plot size to evaluate the fresh weight in buckwheat (Fagopyrum esculentum Moench) of the IPR91-Baili and IPR92-Altar cultivars, in scenarios formed by combinations of numbers of treatments, numbers of replicates, and levels of experimental precision. Sixteen uniformity trials (blank experiments) were carried out, eight with cultivar IPR91-Baili and eight with cultivar IPR92-Altar. The trials were performed in eight sowing dates. The fresh weight was evaluated in 576 basic experimental units (BEU) of 1 m × 1 m (36 BEU per trial). The soil heterogeneity index of Smith (1938) was estimated. The plot size was determined by the method of Hatheway (1961) in scenarios formed by combinations of i treatments (i = 5, 10, 15, and 20), r replicates (r = 3, 4, 5, 6, 7, and 8), and d precision levels (d = 10%, 11%, 12%, 13%, 14%, 15%, 16%, 17%, 18%, 19%, and 20%). To evaluate the fresh weight in buckwheat of the IPR91-Baili and IPR92-Altar cultivars, in experiments under completely randomized and randomized block designs, with 5 to 20 treatments and eight replicates, plots of 8 m2 of useful area are sufficient to identify significant differences between treatments, at 5% probability level, of 15% of the overall mean of the experiment. O objetivo deste trabalho foi determinar o tamanho ótimo de parcela para avaliar a massa de matéria fresca de trigo mourisco (Fagopyrum esculentum Moench) das cultivares IPR91-Baili e IPR92-Altar, em cenários formados por combinações de números de tratamentos, números de repetições e níveis de precisão experimental. Foram conduzidos 16 ensaios de uniformidade (experimentos em branco), sendo oito com a cultivar IPR91-Baili e oito com a cultivar IPR92-Altar. Os ensaios foram realizados em oito épocas de semeadura. Foi avaliada a massa de matéria fresca em 576 unidades experimentais básicas (UEB) de 1 m × 1 m (36 UEB por ensaio). Foi estimado o índice de heterogeneidade do solo de Smith (1938). Foi determinado o tamanho de parcela por meio do método de Hatheway (1961) em cenários formados pelas combinações de i tratamentos (i = 5, 10, 15 e 20), r repetições (r = 3, 4, 5, 6, 7 e 8) e d níveis de precisão (d = 10%, 11%, 12%, 13%, 14%, 15%, 16%, 17%, 18%, 19% e 20%). Para avaliar a massa de matéria fresca de trigo mourisco das cultivares IPR91-Baili e IPR92-Altar, nos delineamentos inteiramente casualizado e blocos completos ao acaso, com 5 a 20 tratamentos e oito repetições, parcelas de 8 m2 de área útil são suficientes para identificar diferenças significativas entre tratamentos, a 5% de probabilidade, de 15% da média geral do experimento.

The objectives of this study were to evaluate the agronomic performance of nine lettuce cultivars (Gloriosa, Pira Verde, Stella, Ceres, Grandes Lagos, Rubinella, Crocantela, Elisa and Vera), in three seasons (autumn-winter, spring and summer) and evaluate the effect of shade netting in spring and summer. Ten experiments were carried out, using the soilless cultivation systems in a sheltered environment. The experimental design was completely randomized, six benches were used in the autumn-winter season and four in both spring and summer, with 44 pots per bench. Lettuce seedlings were transplanted into 3-liter pots filled with sand. During the spring and summer seasons experiments were conducted with and without a 18% black shade netting placed 1.5 m above the plants. Nutritional supply was provided by nutrient solution recirculating in an automatically operated irrigation system. The evaluated traits were as follows: number of leaves, fresh and dry leaf matter, stem length, stem diameter, fresh and dry stem matter, fresh and dry shoot matter, root length and fresh and dry root matter. The cultivars Gloriosa (in autumn-winter), Grandes Lagos and Gloriosa (in the spring) and Crocantela and Vera (in the summer), presented greater matter yield and are deemed the most suitable for cultivation in these seasons. The use of a shade netting within the sheltered environment did not improve the performance of the cultivars and its use is not necessary in the spring and summer.

The objective of this study was to determine the optimal plot size to evaluate fresh matter in millet (Pennisetum glaucum L.) and slender leaf rattlebox (Crotalaria ochroleuca), in scenarios formed by combinations of numbers of treatments, numbers of replicates, and levels of precision. Fifteen uniformity trials with millet and slender leaf rattlebox, in single cropping or intercropping, were carried out. Fresh matter was evaluated in 540 basic experimental units (BEU) of 1 m × 1 m (15 trials × 36 BEU per trial). The soil heterogeneity index of Smith (1938) was estimated. Plot size was determined by the method of Hatheway (1961) in scenarios formed by combinations of i treatments (i = 5, 10, 15 and 20), r replicates (r = 3, 4, 5, 6, 7 and 8), and d precision levels (d = 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18% and 20%). To evaluate the fresh matter of millet and slender leaf rattlebox, in single or intercropping, in experiments in completely randomized or randomized block designs, with 5 to 20 treatments and with five replicates, plots with 10 m² of usable area are sufficient for differences between treatments of 10% of the overall mean of the experiment to be considered significant at 0.05 probability level. RESUMO - O objetivo deste trabalho foi determinar o tamanho ótimo de parcela para avaliar a massa de matéria fresca de milheto (Pennisetum glaucum L.) e de crotalária ochroleuca (Crotalaria ochroleuca) em cenários formados por combinações de números de tratamentos, números de repetições e níveis de precisão experimental. Foram conduzidos 15 ensaios de uniformidade com milheto e crotalária ochroleuca, em cultivo solteiro e em consórcio. Foi avaliada a massa de matéria fresca em 540 unidades experimentais básicas (UEB) de 1 m × 1 m (15 ensaios × 36 UEB por ensaio). Foi estimado o índice de heterogeneidade do solo de Smith (1938). Foi determinado o tamanho de parcela por meio do método de Hatheway (1961) em cenários formados pelas combinações de i tratamentos (i = 5, 10, 15 e 20), r repetições (r = 3, 4, 5, 6, 7 e 8) e d níveis de precisão (d = 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18% e 20%). Para avaliar a massa de matéria fresca de milheto e de crotalária ochroleuca, em cultivo solteiro ou em consórcio, nos delineamentos inteiramente casualizado ou de blocos completos ao acaso, com 5 a 20 tratamentos e com cinco repetições, parcelas de 10 m² de área útil são suficientes para que diferenças entre tratamentos de 10% da média geral do experimento sejam consideradas significativas a 0.05 de probabilidade.

The aim of this study was determining the optimum plot size to evaluate the fresh matter of aerial part in flax (Linum usitatissimum L.), in scenarios formed by combinations of numbers of treatments, number of repetitions, and precision levels. The fresh matter of aerial part was weighed on 144 basic experimental units of 1.00 m × 1.00 m in uniformity trial with size of 12 m × 12 m (144 m2). It was estimated the soil heterogeneity index of Smith (1938). Also, the optimum plot size was determined by the Hatheway’s method (1961) in scenarios formed by combinations of i treatments (i = 5, 10, 15, and 20), r repetitions (r = 3, 4, 5, 6, 7 8, 9, and 10), and d precision levels (d = 10%, 12%, 14%, 16%, 18%, 20%, 22%, 24%, 26%, 28%, 30%, 32%, 34%, 36%, 38%, and 40%). In experiments planned on randomized block design, with 5 to 20 treatments and four repetitions, plots with 7 m2 are sufficient to identify significant differences between treatments regarding fresh matter of aerial part in flax, at 5% probability, of 34% of the experiment overall mean.

portuguesO objetivo deste trabalho foi determinar o tamanho otimo de parcela para avaliar a massa de materia fresca de aveia preta (Avena strigosa Schreb) e de ervilhaca (Vicia sativa L.), em cenarios formados por combinacoes de numeros de tratamentos, numeros de repeticoes e niveis de precisao. Foram conduzidos 15 ensaios de uniformidade com aveia preta e ervilhaca, em cultivo solteiro e em consorcio. Foi avaliada a massa de materia fresca em 540 unidades experimentais basicas (UEB) de 1 m × 1 m (36 UEB por ensaio). Foi estimado o indice de heterogeneidade do solo de SMITH (1938). Foi determinado o tamanho de parcela por meio do metodo de HATHEWAY (1961) em cenarios formados pelas combinacoes de i tratamentos (i = 5, 10, 15 e 20), r repeticoes (r = 3, 4, 5, 6, 7 e 8) e d niveis de precisao (d = 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18% e 20%). Para avaliar a massa de materia fresca de aveia preta e de ervilhaca, em cultivo solteiro ou em consorcio, nos delineamentos inteiramente casualizado e de blocos completos ao acaso, com 5 a 20 tratamentos e com cinco repeticoes, parcelas de 10 m2 sao suficientes para identificar diferencas significativas entre tratamentos, a 0,05 de probabilidade, de 10% da media geral do experimento EnglishThe aim of this study was to determine the optimal plot size for evaluating the fresh weight of black oats (Avena strigosa Schreb) and the common vetch (Vicia sativa L.) in scenarios comprising combinations of the number of treatments, number of replications and levels of precision. Fifteen uniformity trials were conducted with single-crop and intercropped black oats and vetch. Fresh weight was evaluated in 540 basic experimental units (BEU), each of 1 m × 1 m (36 BEU per trial). The Smith index of soil heterogeneity (1938) was estimated. Plot size was determined using the HATHEWAY method (1961), in scenarios comprising combinations of i treatments (i = 5, 10, 15 and 20), r replications (r = 3, 4, 5, 6, 7 and 8) and d levels of precision (d = 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18% and 20%). To evaluate the fresh weight of monocropped or intercropped black oats and vetch in a completely randomized or randomized complete block design, with from 5 to 20 treatments and five replications, plots of 10 m2 are sufficient to identify, at a probability of 0.05, significant differences between treatments of 10% of the overall mean value of the experiment

O objetivo deste trabalho foi determinar o tamanho de amostra (número de cápsulas) necessário para a estimação da média de caracteres produtivos de linho (Linum usitatissimum L.), cultivar CDC Normandy, em níveis de precisão. Em área experimental de 15m×15m (225 m2) aos 137 dias após a semeadura, foram selecionadas, aleatoriamente, 300 plantas e coletada uma cápsula por planta. Em cada cápsula foram avaliados os caracteres massa de cápsula, massa de grãos por cápsula, número de grãos por cápsula e massa de mil grãos. Para cada caractere, foram calculadas medidas de tendência central, variabilidade, assimetria e curtose. Foi determinado o tamanho de amostra por meio de reamostragem, com reposição, de 10.000 reamostras. Para a estimação da média desses caracteres de linho, cultivar CDC Normandy, com amplitude do intervalo de confiança de 95% igual a 10% da estimativa da média são necessárias 78 cápsulas.

The objective of this work was to evaluate the influence of the number of replicates on experimental precision in corn (Zea mays). Data on the grain yield of 15 corn cultivars, evaluated in a randomized complete block design, with nine replicates (r = 9), were used. From the experiment with nine replicates, further experiments were conducted with combinations of 2, 3, ..., r-1 replicates. The analysis of variance was carried out for each experiment. Experimental precision statistics and central tendency and variability measures were calculated, dispersion diagrams were prepared, and models of these statistics were adjusted as a function of the number of replicates. The number of replicates was determined by the visual analysis of the graphs with the experimental precision statistics. Increasing the number of replicates improves the estimates of experimental precision but decreases gains. Therefore, the increase in the number of replicates is important to improve corn cultivar discrimination. Six replicates are recommended as the benchmark for experiments with corn cultivars. Fasoulas’ differentiation index, based on the percentage of significant contrasts, is an appropriate statistic for evaluating experimental precision. Resumo: O objetivo deste trabalho foi avaliar a interferência do número de repetições na precisão experimental, em milho (Zea mays). Foram utilizados dados de produtividade de grãos de 15 cultivares de milho, avaliada em blocos ao acaso, com nove repetições (r = 9). A partir do experimento com nove repetições, formaram-se experimentos pelas combinações de 2, 3, ..., r-1 repetições. Para cada experimento, foi realizada a análise de variância. Foram calculadas estatísticas de precisão experimental e medidas de tendência central e de variabilidade, confeccionados diagramas de dispersão e ajustados modelos dessas estatísticas em função do número de repetições. O número de repetições foi determinado pela análise visual dos gráficos das estatísticas de precisão experimental. O aumento do número de repetições melhora a precisão experimental, mas diminui os ganhos. Portanto, o aumento do número de repetições é importante para aumentar a discriminação das cultivares de milho. Recomendam-se seis repetições como referência para experimentos com cultivares de milho. O índice de diferenciação de Fasoulas, baseado no percentual de contrastes significativos, é uma estatística apropriada para avaliar a precisão experimental.

The objectives of this work were to determine the optimum plot size (Xo) and number of repetitions to evaluate the fresh and dry matter of rye (Secale cereale L.), and to investigate the variation of Xo between two cultivars and five sowing times. Thirty uniformity trials were conducted. Each trial with dimensions of 6 × 4 m was divided into 24 basic experimental units (BEU) of 1 × 1 m. Fresh and dry matter of rye were evaluated in the 720 BEU. The Xo was determined by the method of maximum curvature of the coefficient of variation model. The number of repetitions was determined in scenarios formed by combinations of treatments, experimental designs, and levels of precision. The optimal plot sizes to evaluate fresh and dry matter of rye are, respectively, 3.43 and 3.82 m2. Six repetitions are sufficient to evaluate fresh and dry matter in completely randomized and randomized block design with up to 50 treatments and make it possible to obtain a least significant difference less than or equal to 20% of the experiment mean.

The number of replications is assumed to interfere in the estimates of the path analysis coefficients. Thus, the objective of this work was to determine the sufficient number of replications for the path analysis of traits in maize cultivars. An experiment was conducted with 15 maize cultivars in a complete randomized block design with nine replications, and seven variables were measured. Then, 511 data files (matrices) formed by all combinations of the nine replications were organized, in groups of 1, 2, 3, 4, 5, 6, 7, 8 and 9 replications. In each matrix, containing the averages of 15 cultivars for the seven variables, Pearson's linear correlation coefficients were estimated, the multicollinearity diagnostics and path analysis were performed and dispersion diagrams were constructed. The sufficient number of replications for the path analysis was determined from the parameter estimates of the quadratic response plateau model. With the replications number increases, the accuracy of the path analysis coefficient estimates improves, but the gains in accuracy gradually decrease. Six replications are sufficient to perform the path analysis of agronomic traits of maize cultivars and can be used as a reference for designing future experiments.

The objectives of this work were to determine the sample size (number of plants) necessary to estimate the indicators of the of multicollinearity degree - condition number (CN), determinant of the correlation matrix (DET), and variance inflation factor (VIF) - in productive traits of rye and to verify the variability of the sample size between the indicators. Five and three uniformity trials were conducted with the cultivars BRS Progresso and Temprano, respectively, and seven productive traits were evaluated in 780 plants. Twenty-one cases were obtained from seven traits, combined five to five. In each case, 197 sample sizes were planned (20, 25, 30, ..., 1,000 plants) and in each size 2,000 resampling were performed, with replacement. For each resample the CN, DET and FIV were determined and the average among 2,000 estimates of each indicator of the multicollinearity degree was calculated. Then, for each case and indicator, the sample size was determined through three models: models of maximum modified curvature, segmented linear with plateau response, and segmented quadratic with plateau response. There was superiority the quadratic model segmented with plateau in adjusting the degree of multicollinearity according to the sample size for all indicators. There is a need greater sample size to detect multicollinearity when diagnosed by DET and for sizes larger than 101, 258 and 102 plants when diagnosing for the number of conditions, determinant and inflation factor performed, respectively.

RESUMO Os objetivos deste trabalho foram avaliar as relações lineares entre caracteres de linho (Linum usitatissimum L.) e identificar caracteres para a seleção indireta. Em área experimental de 15 × 15 m (225 m2), aos 134 dias após a semeadura, foram selecionadas, aleatoriamente, 300 plantas. Em cada planta, foram mensurados os caracteres altura de planta, número de ramos, número de cápsulas, massa verde de cápsulas, massa verde de parte aérea sem cápsulas, massa verde de parte aérea, massa seca de cápsulas, massa seca de parte aérea sem cápsulas e massa seca de parte aérea. Para cada caractere, foi calculada a média e o coeficiente de variação. Foi investigada a relação linear entre os caracteres por meio de análises de correlação e de trilha. Na cultura de linho, o número de cápsulas tem relação linear positiva com as massas verde e seca de cápsulas e de parte aérea e pode ser utilizado para seleção indireta. ABSTRACT The objectives of this study were to evaluate the linear relations among traits of flax (Linum usitatissimum L.) and identify traits for indirect selection. In experimental area of 15 × 15 m (225 m2) 300 plants were randomly collected at 134 days after seeding. The traits plant height, number of branches, number of capsules, fresh matter of capsules, fresh matter of aerial part without capsules, fresh matter of aerial part, dry matter of capsules, dry matter of aerial part without capsules, and dry matter of aerial part were measured in each plant. The mean and coefficient of variation were calculated for each trait. It was studied the linear relation among the traits through correlation and path analysis. In flax, the number of capsules has positive linear relation with fresh and dry matter of capsules and aerial part and it can be used for indirect selection.

RESUMO: Os objetivos deste trabalho foram determinar o tamanho ótimo de parcela e o número de repetições para avaliar a massa verde de feijão guandu ( Cajanus cajan (L.) Millsp.), em épocas e anos de avaliação. Foram realizados 80 ensaios de uniformidade de 6m×6m (36m2). Cada ensaio foi dividido em 36 unidades experimentais básicas (UEB) de 1m×1m, totalizando 2.880UEB. Foi pesada a massa verde das plantas de cada UEB. No ano agrícola 2011/2012, foram avaliados 16 ensaios aos 127 dias após a semeadura (DAS) e 24 aos 139DAS. Em 2012/2013, foram avaliados quatro ensaios em cada uma das épocas (163, 167, 170, 174, 177, 181, 184, 188, 191 e 195DAS). O tamanho ótimo de parcela foi determinado por meio do método da curvatura máxima do modelo do coeficiente de variação e as comparações de médias, entre épocas e os anos de avaliação, foram feitas pelo teste de Scott-Knott. O número de repetições, em cenários formados pelas combinações de i tratamentos (i=3, 4, ..., 50) e d diferenças mínimas entre médias de tratamentos a serem detectadas como significativas a 5% de probabilidade, pelo teste de Tukey, expressas em percentagem da média do experimento (d=10%, 15%, ..., 50%), foi determinado por processo iterativo até a convergência. O tamanho ótimo de parcela para avaliar a massa verde de feijão guandu é 8,39m2. Quatro repetições, para avaliar até 50 tratamentos, são suficientes para identificar, como significativas a 5% de probabilidade, pelo teste de Tukey, diferenças entre médias de tratamentos de 54,1% da média do experimento. ABSTRACT: The objectives of this research were to determine the optimum plot size and number of repetitions, to evaluate the fresh weight of pigeonpea ( Cajanus cajan (L.) Millsp.), in times and years. Eighty uniformity trials of 6m×6m (36m2) were conducted. Each trial was divided in 36 basic experimental units (BEU) of 1m×1m, totaling 2,880BEU. The fresh weight of plants, in each BEU was weighed. The agricultural year 2011/2012, were evaluated 16 trials at 127 days after sowing (DAS) and 24 to 139DAS. In 2012/2013, four trials at each of times (163, 167, 170, 174, 177, 181, 184, 188, 191 and 195DAS) were evaluated. The optimum plot size was determined by the method of maximum curvature of the coefficient of variation model and the means compared, among evaluation times and years, by Scott-Knott test. The number of repetitions, in scenarios of combinations of i treatments (i=3, 4, ..., 50) and d minimal differences between treatments means, to be detected as significant, 5% probability by Tukey's test, expressed in percentage of experiment avarage (d=10%, 15%, ..., 50%), was determined by iterative process until convergence. The optimum plot size to evaluate the fresh weight of pigeonpea is was 8.39m2. Four replications, to evaluate up to 50 treatments, are sufficient to identify, as significant at 5% probability by Tukey's test, differences between treatment means of 54.1% of the average experiment.

The aim of this study was to determine the optimal plot size and the number of replications to evaluate fresh weight in Sudan grass [Sorghum sudanense (Piper) Stapf.]. Twenty-six uniformity trials were carried out in two cultivars (BRS Estribo and CG Farrapo), in four sowing seasons (20 Dec, 20 Jan, 7 Feb and 24 Feb) and two methods for evaluating fresh weight (cutting and at flowering). The fresh weight was evaluated in 936 basic experimental units (BEU) (26 trials × 36 BEU per trial). One BEU comprised three rows of plants, 1 m in length (1.2 m2). The optimal plot size was determined using the maximum curvature method of the model of the coefficient of variation. For experiments in a completely randomised or randomised block design, in combinations of number of treatments and levels of experimental precision, the number of replications was determined by an iterative process. The optimal plot size to evaluate fresh weight in Sudan grass is 7.95 m2. Eight replications, to evaluate up to 50 treatments in a completely randomised or randomised block design, are sufficient to identify as significant at 0.05% probability by Tukey’s test, differences between the mean value of each treatment of 30.2% of the mean value of the experiment.

Para modelos fidedignos de estimação de área foliar, é importante que as estimativas de seus parâmetros sejam precisas, e, para isso, devem ser geradas com número adequado de folhas. O objetivo deste trabalho foi determinar o número de folhas necessário para modelar a área foliar de mucuna cinza (Stizolobium cinereum) determinada por fotos digitais (Y), em função da largura do limbo do folíolo central da folha (x), por meio do modelo potência (Y=axb), gerado por processo iterativo. Em seis períodos de desenvolvimento da cultura (29, 43, 57, 73, 87 e 101 dias após a emergência) foram coletadas, aleatoriamente, total de 790 folhas. Cada folha é composta pelos folíolos esquerdo, central e direito. Foi mensurada a largura do limbo do folíolo central (x) e determinada a área foliar (soma da área dos folíolos esquerdo, central e direito) por meio do método de fotos digitais (Y). O número de folhas, necessário para a estimação dos parâmetros a e b do modelo potência e do coeficiente de determinação do modelo (R2), foi determinado por reamostragem, com reposição. Em mucuna cinza, o modelo potência (Ŷ=4,4019x1,8697, R2=0,9821) da largura do limbo do folíolo central (x) é adequado para estimar a área foliar obtida por fotos digitais (Y). Mensurar 240 folhas é suficiente para construção de modelos precisos do tipo potência, da área foliar de mucuna cinza determinada por fotos digitais (Y) em função da largura do limbo do folíolo central da folha (x).

The aim of this study was to determine the optimum plot size to evaluate the fresh matter of aerial part of dwarf pigeon pea (Cajanus cajan (L.) Millsp), cultivar IAPAR 43 (Arata), in scenarios formed by combinations of numbers of treatments, number of replications, and precision levels. The fresh matter of aerial part was weighed on basic experimental units of 1 m × 1 m in three uniformity trials with size of 24 m × 12 m (288 m2 in each trial). The soil heterogeneity index of Smith was estimated. Also, the optimum plot size was determined by Hatheway’s method in scenarios formed by combinations of i treatments (i = 5, 10, 15, and 20), r replications (r = 3, 4, 5, 6, 7 8, 9, and 10), and d precision levels (d = 5%, 10%, 15%, 20%, 25%, and 30%). In experiments designed on randomized block design with 5 to 20 treatments and four replications, plots with 9 m2 were enough to identify significant differences among treatments regarding the fresh matter of aerial part in dwarf pigeon pea at 5% probability of 30% of the experiment overall mean.

Os objetivos deste trabalho foram determinar o tamanho ótimo de parcela (Xo) e o número de repetições para avaliar a massa verde de parte aérea de milheto em épocas de avaliação. Foram conduzidos 42 ensaios de uniformidade de 6 m×4 m (24 m2), sendo cada ensaio dividido em 24 unidades experimentais básicas (UEB) de 1 m×1 m (1 m2). Aos 52, 69 e 82 dias após a semeadura, foram avaliados, respectivamente 18, 6 e 18 ensaios, nos quais se pesou a massa verde das plantas de cada UEB. O Xo foi determinado pelo método da curvatura máxima do modelo do coeficiente de variação, e as comparações de médias entre as épocas de avaliação foram realizadas pelo teste t de Student. O número de repetições, para experimentos nos delineamentos inteiramente casualizados e blocos ao acaso, em cenários formados pelas combinações de i tratamentos (i=3, 4, ..., 50) e d diferenças mínimas entre médias de tratamentos a serem detectadas como significativas a 5% de probabilidade, pelo teste de Tukey, expressas em percentagem da média do experimento (d=10%, 12%, ..., 30%), foi realizado por processo iterativo até a convergência. O tamanho ótimo de parcela para avaliar a massa verde de parte aérea de milheto é de 4,46 m2, para as três épocas de avaliação. Para avaliar até 50 tratamentos, nos delineamentos inteiramente casualizados e blocos ao acaso, quatro repetições são suficientes para que diferenças entre médias de tratamentos de 28,75% da média do experimento sejam significativas, pelo teste de Tukey, a 5% de probabilidade. The objectives of this work were to determine the optimum plot size (Xo) and number of repetitions, to evaluate the fresh weight of aerial part of millet, in evaluation times. Forty-two uniformity trials with 6 m×4 m (24 m2) were conducted. Each trial was divided in 24 experimental units basic (UEB) with 1 m×1 m (1 m2). At 52, 69 and 82 days after sowing were evaluated, respectively, 18, 6 and 18 trials, where the fresh weight of plants was weighed in each UEB. The Xo was determined by the method of maximum curvature of the model coefficient of variation and the means compared, among evaluation times, by Student’s t test. The number of repetitions for experiments on completely randomized and randomized block designs, in scenarios of combinations of i treatments (i=3, 4, ..., 50) and d minimal differences between treatments means, to be detected as significant, 5% probability by Tukey test, expressed in percentage of the average of the experiment (d=10%, 12%, ..., 30%), was determined by iterative process until convergence. The optimum plot size to evaluate the fresh weight of aerial part of millet is 4.46 m2, to the three evaluation times. To evaluate up to 50 treatments, in completely randomized and randomized block designs, four replications are sufficient for differences between treatment means of 28.75% of the average experiment are significant at 5% probability, by Tukey’s test.

Os objetivos deste trabalho foram determinar o tamanho ótimo de parcela e o número de repetições, para avaliar a massa verde de ervilha forrageira (Pisum sativum subsp. arvense (L.) Poir). Foram realizados 27 ensaios de uniformidade de 5m×5m (25m2). Cada ensaio foi dividido em 25 unidades experimentais básicas (UEB) de 1m×1m, totalizando 675UEB. Foi pesada a massa verde das plantas de cada UEB. Nove ensaios (225UEB) foram avaliados aos 92 dias após a semeadura (DAS), nove ensaios (225UEB) foram avaliados aos 98 DAS e os outros nove ensaios (225UEB) aos 106 DAS. O tamanho ótimo de parcela (Xo) foi determinado por meio do método da curvatura máxima do modelo do coeficiente de variação e as comparações de médias, entre as épocas de avaliação, foram feitas pelo teste t de Student. O número de repetições, para experimentos nos delineamentos inteiramente casualizado e blocos ao acaso, em cenários formados pelas combinações de i tratamentos (i=3, 4, ..., 50) e d diferenças mínimas entre médias de tratamentos a serem detectadas como significativas a 5% de probabilidade, pelo teste de Tukey, expressas em percentagem da média do experimento (d=10%, 12%, ..., 30%), foi determinado por processo iterativo até a convergência. O tamanho ótimo de parcela para avaliar a massa verde de ervilha forrageira é de 5,03UEB de 1m2 (5,03m2). Quatro repetições, para avaliar até 50 tratamentos, nos delineamentos inteiramente casualizado e blocos ao acaso, são suficientes para identificar, como significativas a 5% de probabilidade, pelo teste de Tukey, diferenças entre médias de tratamentos de 32,4% da média do experimento. The objectives of this research were to determine the optimum plot size and number of repetitions and to evaluate the fresh weight of forage pea (Pisum sativum subsp. arvense (L.) Poir). Twenty-seven uniformity trials of 5m×5m (25m2) were conducted. Each trial was divided in 25 basic experimental units (UEB) of 1m×1m, totaling 675UEB. The fresh weight of plants, in each UEB was weighed. Nine trials (225UEB) were evaluated at 92 days after sowing, nine trials (225UEB) at 98 days after sowing and the other nine trials (225UEB) at 106 days after sowing. The optimum plot size (Xo) was determined by the method of maximum curvature of the model coefficient of variation and the means compared, among evaluation times, by Student's t test. The number of repetitions for experiments on completely randomized and randomized block designs, in scenarios of combinations of i treatments (i=3, 4, ..., 50) and d minimal differences between treatments means, to be detected as significant, 5% probability by Tukey test, expressed in percentage of the average of the experiment (d=10%, 12%, ..., 30%), was determined by interative process until convergence. The optimum plot size to evaluate the fresh weight of forage pea is 5.03UEB was of 1m2 (5.03m2). Four replications, to evaluate up to 50 treatments, in completely randomized and randomized block designs, are sufficient to identify, as significant at the 5% probability by Tukey test, differences between treatment means 32.4% of the average experiment.

Os objetivos deste trabalho foram determinar o tamanho de amostra (número de plantas) para a estimação da média de caracteres morfológicos e produtivos de aveia preta (Avena strigosa Schreb) e verificar a variabilidade do tamanho de amostra entre caracteres e entre épocas de avaliação. Num experimento a campo, em dez épocas de avaliação (22, 28, 34, 42, 48, 55, 76, 83, 90 e 105 dias após a semeadura), foram selecionadas, aleatoriamente, 52 plantas, totalizando 520 plantas. Em cada planta, foram mensurados os caracteres morfológicos (altura de planta, números de folhas e de perfilhos) e os produtivos (massas verde e seca). Foram calculadas medidas de tendência central e de variabilidade, verificada a normalidade e calculado o tamanho de amostra. Na cultura de aveia preta, há variabilidade do tamanho de amostra entre caracteres e entre épocas de avaliação. Para estimar a média com mesma precisão, o tamanho de amostra dos caracteres produtivos é maior que o dos morfológicos. O tamanho de amostra na fase intermediária de desenvolvimento da cultura é maior que nas fases inicial (primeiras épocas de avaliação) e final (últimas épocas de avaliação). Para a estimação da média dos caracteres morfológicos e produtivos, para um erro de estimação máximo de 20% da média, com grau de confiança de 95%, 47 plantas são suficientes. The objectives of this research were to determine the sample size (number of plants) to estimate the average of the morphological and productive characters of black oat (Avena strigosa Schreb) and check the variability of the sample size among characters and evaluation times. A field experiment was conducted and in ten evaluation times (22, 28, 34, 42, 48, 55, 76, 83, 90 and 105 days after sowing) were randomly selected 52 plants, totaling 520 plants. In each plant, were measured morphological (plant height, number of leaves and number of tillers) and productive characters (fresh and dry matters). Measures of central tendency and variability were calculated, normality was checked and the sample size was calculated. In the culture of black oat, there is variability in the sample size among characters and evaluation times. To estimate average with the same precision, the sample size of productive characters is greater than morphological. The sample size at the intermediate stage of crop development is greater than the final (last evaluation times) and initial stages (first evaluation times). For the morphological and productive characters, 47 plants are enough to predict the average, with an estimation error maximum of 20% of estimated average, with a degree confidence of 95%.

Phyllochron and leaf appearance rate are both important parameters in the production efficiency of agricultural crops. The objectives of this study were to determine the phyllochron and leaf appearance rate in 4 oat cultivars (Avena sativa L.) in 3 sowing dates and verify the variability of phyllochron and leaf appearance rate among cultivars and sowing dates. The experimental design was the completely randomized with 12 treatments and 20 repetitions. Treatments were formed by the combination of 4 cultivars (URS Charrua, URS Taura, URS Estampa, and URS Corona) and 3 sowing dates in 2014 (April 28, May 28, and July 14). In each plant (repetition) of each treatment, the number of expanded leaves (NEL) was counted 3 times per week from the first leaf emission until flowering. For each plant, cultivar, and sowing date, linear regression was adjusted between NEL and accumulated thermal time (ATT) and between NEL and number of days after emergence (DAE). Phyllochron was determined by the inverse of the angular coefficient of the linear regression between the NEL and ATT. The leaf appearance rate was determined by the inverse of the angular coefficient of the linear regression between NEL and DAE. In oat, there is variability of phyllochron and leaf appearance rate among cultivars and sowing dates. Phyllochron oscillates between 95.88 and 117.70 °C day∙leaf−1 and leaf appearance rate, between 6.41 and 9.65 days∙leaf−1. The oat cropping management in function of phyllochron and leaf appearance rate is dependent on cultivars and sowing dates.

O objetivo deste trabalho foi determinar a precisão experimental na avaliação da massa de matéria verde de nabo forrageiro, em cenários formados por combinações de tamanhos de parcela e número de tratamentos e de repetições. Utilizaram-se os dados de massa de matéria verde de 3.456 unidades experimentais básicas de 0,5×0,5 m (0,25 m2). Os cenários (1.728) foram planejados e formados pela combinação de seis tamanhos de parcela (0,25, 0,50, 1,00, 1,50, 2,00 e 2,25 m2), i tratamentos (i = 5, 6,..., 20) e r repetições (r = 3, 4,..., 20). Em cada cenário, foram realizadas 2.000 reamostragens, com reposição. Calculou-se a média das 2.000 estimativas, em cada cenário, quanto à diferença mínima significativa pelo teste de Tukey, ao índice de variação e ao coeficiente de variação experimental. Essas estatísticas, nesta ordem, são adequadas para avaliar a precisão experimental. Para avaliar a massa de matéria verde de nabo forrageiro, em experimentos em delineamento inteiramente casualizado, com 5 a 20 tratamentos e cinco repetições, parcelas com o tamanho de seis unidades experimentais básicas (1,50 m2) são suficientes para identificar diferenças significativas entre tratamentos - menores ou iguais a 36,88% da média geral do experimento -, pelo teste de Tukey, a 5% de probabilidade, em experimentos em delineamento inteiramente casualizado, com 5 a 20 tratamentos e cinco repetições.

The use of mathematical models in the study plant growth allows the identification of phases important to the cultivars and comparison between cultivars of the same species. The objectives of this work were to fit the Gompertz and Logistic growth models for the traits of plant height and stem length as a function of the accumulated thermal sum and accumulated solar radiation, to compare the fittings and the behavior of the sudangrass cultivars and indicate the model that best describes the growth of the cultivars during four sowing seasons. Were conducted eight uniformity trials with sudangrass. At 15 days after emergence, were began the collect and evaluation of five plants from each trial. Were measured plant height and stem length. The models were fitted using the values obtained for the traits of the five plants in each evaluation as a function of the accumulated thermal sum and accumulated solar radiation. Were estimated the parameters, determined their interval of confidence, critical points in the growth curves and quality indicators of the fit. The intrinsic nonlinearities and the parameter effect were also quantified. The accumulated thermal sum and accumulated solar radiation are adequate for the use as an independent variable in the model fitted. Both models were adequate to describe the growth of the traits plant height and stem length of cultivars BRS Estribo and CG Farrapo. However, the Logistic model is more accurate.

The objectives of this study were to adjust the Gompertz and logistic models to fit the fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars and indicate the model that best describes the growth in spring. Cultivars Ceres, Gloriosa, Grandes Lagos, and Rubinela were grown in protected environment and in soilless system, in the spring of 2016 and 2017. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters were weighed every four days until beginning of flowering. The Gompertz and logistic models were adjusted as a function of accumulated thermal sum. The parameters of the Gompertz and logistic models and their confidence intervals were estimated, the assumptions of the models were verified, the goodness-of-fit measures and critical points were calculated, and the parametric and intrinsic nonlinearities quantified. The logistic and Gompertz growth models fitted well to fresh and dry leaf and shoot matters of cultivars Ceres, Gloriosa, Grandes Lagos, and Rubinela, under spring conditions. The logistic model is the most suitable to describe the growth of lettuce cultivars.

The objectives of this study were to determine the sample size, in terms of number of plants, needed to estimate the average values of productive traits of the pigeon pea and to determine whether the sample size needed varies between traits and between crop years. Separate uniformity trials were conducted in 2011/2012 and 2012/2013. In each trial, 360 plants were demarcated, and the fresh and dry masses of roots, stems, and leaves and of shoots and the total plant were evaluated during blossoming for 10 productive traits. Descriptive statistics were calculated, normality and randomness were checked, and the sample size was calculated. There was variability in the sample size between the productive traits and crop years of the pigeon pea culture. To estimate the averages of the productive traits with a 20% maximum estimation error and 95% confidence level, 70 plants are sufficient. RESUMO: Os objetivos deste trabalho foram determinar o tamanho de amostra, em número de plantas, para a estimação da média de caracteres produtivos de feijão guandu e verificar se há variabilidade do tamanho de amostra entre caracteres e anos agrícolas. Foram conduzidos dois ensaios de uniformidade, um em 2011/2012 e o outro em 2012/2013. Em cada ensaio, foram demarcadas 360 plantas e, no florescimento, foram avaliadas as massas verde e seca de raiz, caule, folha, parte aérea e total, totalizando dez caracteres produtivos. Foram calculadas estatísticas descritivas, verificada a normalidade e a aleatoriedade e calculado o tamanho de amostra. Na cultura de feijão guandu, há variabilidade do tamanho de amostra entre os caracteres produtivos e entre os anos agrícolas. Para a estimação da média dos caracteres produtivos, com erro de estimação máximo de 20% da média e com grau de confiança de 95%, 70 plantas são suficientes.

O objetivo deste trabalho foi modelar a área foliar de feijão de porco determinada por fotos digitais em função do comprimento ou da largura e/ou do produto comprimento vezes largura do limbo do folíolo central da folha. Em seis períodos de desenvolvimento da cultura (29, 43, 57, 73, 87 e 101 dias após a emergência) foram coletadas, aleatoriamente, 745 folhas. Cada folha é composta pelos folíolos esquerdo, central e direito. Nas 745 folhas foi mensurado o comprimento (CFC) e a largura (LFC) e calculado o produto do comprimento pela largura (CFC×LFC) do limbo do folíolo central. A seguir, determinou-se a área foliar (soma da área dos folíolos esquerdo, central e direito) por meio do método de fotos digitais (Y). Do total de folhas, foram separadas, aleatoriamente, 605 folhas para a construção de modelos do tipo quadrático, potência e linear de Y em função do CFC, da LFC, e/ou do CFC×LFC e 140 folhas para a validação dos modelos. Em feijão de porco, o modelo tipo potência (Ŷ=3,7046x1,8747, R²=0,9757) da largura do limbo do folíolo central é adequado para estimar a área foliar obtida por fotos digitais. The objective of this work was to model the leaf area of jack bean determined by digital photos with the length or width and/or the product length × width of the central leaflet limb of the leaf. At six periods of crop development (29, 43, 57, 73, 87 and 101 days after emergence) 745 leaves were randomly collected. Each leaf is composed by left, center and right leaflets. The length (CFC) and width (LFC) were measured and the product length by the width (CFC×LFC) of the central leaflet calculated. The leaf area (sum of the leaf area of the left, center and right leaflets) was calculated by the method of digital photos (Y). An amount of 605 leaves were used to build models of the type quadratic, potency and linear, considering Y as function of the CFC, LFC and/or CFC×LFC. For validation, 140 leaves were used. The potency model of the leaf area obtained by method of digital photos (Ŷ=3.7046x1.8747, R²=0.9757) based on the width central leaflet, is adequate to estimate the leaf area in jack bean.