Optimal plot size for cabbage experiments

Among the factors that influence the detection of minimum significant differences between treatments in conventional experiments is the size of the plot, whose correct determination allows the reduction of experimental error, consequently, increases the precision of the experiment and the reliability of the interpretations and conclusions obtained. There are different methods to estimate the optimal plot size, which relate plot size and residual variation, highlighting among these the methods of maximum curvature, maximum modified curvature, maximum curvature of the coefficient of variation and regression with plateau response. In addition to these, there is the Hatheway method that takes into account factors such as number of treatments, repetitions and levels of significance. Since there is little work to estimate the optimal plot size in experiments with species of the genus Brassica, the present study aimed to increase the experimental precision in experiments with cabbage in the Research, Society and Development, v. 9, n. 11, e2239119744, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i11.9744 4 municipality of Alegre ES by determining the optimal plot size with based on Hatheway's methods, maximum curvature, maximum curvature of the coefficient of variation and plateau regression. The work was carried out by means of a blank test carried out in the experimental area of the Center for Agricultural Sciences of the Federal University of Espírito Santo, Alegre ES, in which both productive and growth variables were evaluated. At the end of the project, propose the optimal plot size to be used in experiments with cabbage in order to increase the experimental precision and the reliability of the results obtained in future experiments.

different methods to estimate the optimal plot size, which relate plot size and residual variation, highlighting among these the methods of maximum curvature, maximum modified curvature, maximum curvature of the coefficient of variation and regression with plateau response. In addition to these, there is the Hatheway method that takes into account factors such as number of treatments, repetitions and levels of significance. Since there is little work to estimate the optimal plot size in experiments with species of the genus Brassica, the present study aimed to increase the experimental precision in experiments with cabbage in the Research, Society andDevelopment, v. 9, n. 11, e2239119744, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i11.9744 4 municipality of Alegre -ES by determining the optimal plot size with based on Hatheway's methods, maximum curvature, maximum curvature of the coefficient of variation and plateau regression. The work was carried out by means of a blank test carried out in the experimental area of the Center for Agricultural Sciences of the Federal University of Espírito Santo, Alegre -ES, in which both productive and growth variables were evaluated. At the end of the project, propose the optimal plot size to be used in experiments with cabbage in order to increase the experimental precision and the reliability of the results obtained in future experiments.
Keywords: Brassica oleracea L. var. capitata L.; Experimental planning; Hatheway; Maximum curvature; Maximum curvature of the coefficient of variation; Plateau regression.
Al final del proyecto, proponer el tamaño de parcela óptimo para ser utilizado en experimentos con repollo con el fin de aumentar la precisión experimental y la confiabilidad de los resultados obtenidos en experimentos futuros.

Introduction
Among the most consumed vegetables in Brazil, brassicas are one of the most consumed, only behind Solanaceae, such as potatoes and tomatoes. In Europe, Portugal and Spain have the highest per capita consumption. In Brazil, the preference for these vegetables is not different, with cabbage (Brassica oleracea L. var. Capitata L.) being the most consumed brassica. Obtaining new information in various areas of study, including agronomy, is often obtained by conducting scientific experiments. In planning and carrying out these, several factors such as the size and shape of the plot, the number of repetitions, the experimental design, among others, directly influence the variability inherent in the experiment. This Research, Society andDevelopment, v. 9, n. 11, e2239119744, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i11.9744 6 variability interferes with the results of the statistical analysis of the data, inflating the estimate of the experimental error, and consequently leading the researcher to interpretations and conclusions with low precision and experimental reliability.
Regarding the plot, there is no single size defined for all the experiments, but rather an optimal size, which is affected by several factors, such as soil characteristics and climatic conditions (Oliveira & Steffanel, 1995).
Different methods have been used to obtain the optimal plot size in different crops, such as tomatoes (Lúcio et al., 2012), sweet pepper (Lúcio et al., 2003), zucchini (Lúcio et al., 2008), radish (Silva et al., ., 2008). ., 2012) green beans (Haesbaert et al., 2011), wheat (Henriques Neto et al., 2009), cassava (Paranaíbaet al., 2009aParanaíba et al., 2009b). Guarçoni et al. (2017) studied the optimal plot size of experimental cabbage for characteristics of mass, diameter and compactness. The linear response regression method was 16, 7 and 5 plants per plot, respectively, for characteristics of mass, diameter and compactness. . Since the linear response regression method was adequate to determine the optimal size of experimental plots for the three characteristics studied.
The objective of this work is to determine the optimal plot size using the Hatheway method, modified maximum curvature, maximum curvature of the coefficient of variation and plateau regression and to compare the methods and recommend the optimal plot size in future experiments with cabbage.

Materials and Methods
A blank test was carried out with the cabbage crop in the experimental area of the Center for Agricultural Sciences of the Federal University of Espírito Santo (CCAUFES),

Alegre -ES.
The plants used in the experiment were obtained by seeds, being the transplant to the field, as well as the sowing time, the cultivation treatments and the control of pests and diseases carried out according to what is recommended for the crop.
On August 1, 2013, cabbage seeds were sown in the Green Valley cultivar. At 18 days, the seedlings were transplanted to the field in the experimental area. The spacing used was 0.3 m between each other and 0.6 between lines, totaling 10 lines each with 24 plants. On September 11, 2013, straw was placed on the cultivation line to control weeds and improve the soil moisture condition, and the next day fertilization with 20-00-20 fertilizer (10 g / plant) was carried out. On October 9, 2013, an insecticide was applied to control pests, and on Research, Society and Development, v. 9, n. 11, e2239119744, 2020 (CC BY 4 Method described by Hatheway (1961), cited by Oliveira et al. (2011), by the expression: Research, Society and Development, v. 9, n. 11, e2239119744, 2020 (CC BY 4. Where, is the optimal size of the plot; b is the soil heterogeneity index; d is the minimum significant difference to be detected between the means of treatments I (% of the mean); r is the number of repetitions to detect differences of d%; CV is the estimate of the coefficient of variation for the plots composed of a SU (%); 1 t is the tabulated value of the t distribution at the level of significance 1 and degree of freedom gl = (I -1) (r -1) for random block design; 2 t is the tabulated value of the t distribution at the significance level 2 = 2(1p) e gl = (I -1) (r -1), where p corresponds to the probability of obtaining significant results.
Modified maximum curvature method, described by Lessman and Atkins (1963) and adapted by Meier and Lessman (1971), cited by Silva et al. (2012), the point where the curvature is maximum in the curve that relates the coefficient of variation with the size of the plot with X basic units will be determined algebraically. This relationship will be estimated according to the model , where Y represents the variability index and X corresponds to the size of the plot in basic units.
The minimum plot size limit ( 0 X ), which consists of the abscissa value corresponding to the point of maximum curvature, will be estimated by the expression: The plateau regression method will be used, the linear model and the quadratic model (Silva et al., 2012). In the segmented linear response model method, the model consists of two segments; the first describes a decreasing line up to a certain constant P, which is the plateau, and the second refers to the plateau, which after a certain value of the coefficient of variation (CV) assumes a constant value. The model considered will be the one shown below: The method of the segmented quadratic response model will be defined by:
In Hatheway's method (1961), the reduction in the convenient size of the experimental plot (Xc) is given by an increase in the number of repetitions (r), an increase in the number of treatments (I), an increase in the difference to detect between treatments (d) and when reducing the coefficient of variation (CV), which shows a clear relationship between the size of the plot and the variables.
The Coefficient of Variation (CV), followed by Precision (b), Number of Blocks (d) and finally the Number of treatments, are the variables that have the greatest influence on the size of the plot. The method of Meier and Lessman (1971) does not present a consistent plot size, Research, Society and Development, v. 9, n. 11, e2239119744, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i11.9744 20 so Chaves (1985) stated that the values found by this method should be interpreted as the minimum limit of plot size and not as an optimal size.

Conclusions
We conclude that the optimal size of the cabbage plot by the method of Hatheway (1961) presents several possibilities for the variables under analysis, so that what should be considered for the choice of the experimental plot is the availability of space in the place where the experiment is installed, the desired precision, being sensible to use a DMS less than 15% so that the precision of the experiment is not sacrificed, and the field conditions. The size of the experimental plots, found by the method of Meier & Lessman (1971), of a plant tends to limit the optimal number, so the value must be higher than that found, with the need to try other methods to estimate this value.
The work has as a suggestion for readers to inform the ideal repetition number for each variable when working with an experiment for the cultivation of cabbage.