PLOT SIZE, NUMBER OF TREATMENTS AND REPLICATES AND EXPERIMENTAL PRECISION IN BUCKWHEAT

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 m of useful area are sufficient to identify significant differences between treatments, at 5% probability level, of 15% of the overall mean of the experiment.

Considering the importance of this crop, it is essential that inferences regarding treatments be accurate in field experiments. For this, it is necessary to define plot size and number of replicates, which can be performed through uniformity trials. In these trials the experimental area can be divided into basic experimental units (BEU) (STORCK et al., 2016). The data of these BEU can be used to calculate the coefficient of variation (CV) between the BEU and the soil heterogeneity index (b) of Smith (1938). The CV and b index estimates can be used in the methodology of Hatheway (1961) to calculate the optimal plot size according to the experimental design, number of treatments, number of replicates and experimental precision. With this methodological approach, after establishing the experimental design and the number of treatments, the researcher can choose the best combination of plot size, number of replicates and level of experimental precision.
Studies with buckwheat together with other soil cover species have been conducted in the randomized complete block design and with different plot sizes and number of replicates, such as: 25 m 2 and three replicates (ZIECH et al., 2015); 20 m 2 and three replicates (GÖRGEN et al., 2016); 4 m 2 and six replicates (PEREIRA et al., 2017); and 24 m 2 and four replicates (SKORA NETO;CAMPOS, 2017). These studies pointed out promising aspects of buckwheat and other soil cover species and no reference was mentioned regarding the definition of plot size and number of replicates for fresh weight evaluation. Also, no approach to the coefficient of variation of fresh weight was mentioned.
Applying the methodologies of Smith (1938) and Hatheway (1961) in a set of uniformity trials conducted in different sowing periods and with different cultivars makes it possible to generate useful information to be used as a reference in the planning of experiments with buckwheat crop, aiming at higher experimental precision. These methodologies have been used in beans (MAYOR -DURÁN; BLAIR; MUÑOZ, 2012), sunflower (SOUSA et al., 2015;SOUSA;SILVA;ASSIS, 2016), banana (DONATO et al., 2018, cactus pear (GUIMARÃES et al., 2019;GUIMARÃES et al., 2020) and in species with potential for soil cover, such as: velvet bean (CARGNELUTTI FILHO et al., 2014a); forage turnip (CARGNELUTTI FILHO et al., 2014b); and flax (CARGNELUTTI FILHO et al., 2018).
It is assumed that the application of these methodologies is promising for the definition of experimental planning in buckwheat crop. Thus, the objective of this study was to determine the optimal plot size to evaluate the fresh weight of buckwheat (Fagopyrum esculentum Moench) of the cultivars IPR91 -Baili and IPR92-Altar, in scenarios formed by combinations of numbers of treatments, numbers of replicates and levels of experimental precision.
In each uniformity trial with a dimension of 8 m × 8 m (64 m 2 ), the central area with size of 6 m × 6 m (36 m 2 ) was divided into 36 basic experimental units (BEU) of 1 m × 1 m (1 m 2 ), forming a matrix of six rows and six columns. In each BEU, the plants were cut close to the soil surface, and their FW was immediately weighed, in g m -2 , on a digital scale (accuracy: 1 g). Weighing was performed immediately after cutting, in order to minimize the possible variations in plant moisture. Fresh weight samples were collected in six randomly chosen BEUs of each uniformity trial. The samples were placed in paper bags identified by BEU and dried in an oven with forced air ventilation at 65 ± 3 °C, until reaching constant weight, to determine the dry weight (in % and in g m -2 ). This sampling was only performed to quantify the dry weight in each uniformity trial.
In each of the 16 trials, the parameters V1 (estimation of variance by BEU between the plots with size of one BEU) and b (estimation of the soil heterogeneity index) and the coefficient of determination (R 2 ) of the function VU (X) =V1/X b , of Smith (1938), were estimated. These parameters were estimated by logarithmic transformation and linearization of the function VU (X) =V1/X b (SMITH, 1938), i.e., logVU (X) = logV1 -b logX, whose estimation was weighted by the degrees of freedom (DF=n-1), associated with each plot size, according to the application of Sousa, Silva and Assis (2016). The observed values of the dependent [VU (X) ] and independent (X) variables and the function VU (X) =V1/X b (SMITH, 1938) were represented graphically.
For each experimental plan, the optimal plot size (Xo), in number of BEU (approximated to the upper integer), was calculated using the expression (HATHEWAY, 1961). In this expression, b is the estimate of the soil heterogeneity index (in this study, for each cultivar, the mean b of the eight uniformity trials was used); t 1 is the critical value of the Student's t-distribution for the significance level of the test (type I error) of α=5% (bilateral test at 5%), with DF degrees of freedom; t 2 is the critical value of the Student's t-distribution, corresponding to 2(1-P) (bilateral test), where P is the probability of obtaining a significant result, i.e., the power of the test (P=0.80, in this study), with DF degrees of freedom; CV is the estimate of the coefficient of variation between the plots with size of one BEU (in this study, for each cultivar, the mean CV of the eight uniformity trials was used), as a percentage; r is the = 2 1 + 2 2 2 2 number of replicates; and d is the difference between means of treatments to be detected as significant at 5% probability level, expressed as a percentage of the overall mean of the experiment (precision). The degrees of freedom (DF) to obtain the critical values (tabulated) of Student's t-distribution were obtained by the expressions DF=(i)(r-1), for the CRD, and DF=(i-1)(r-1), for the RCBD, where i is the number of treatments and r is the number of replicates. The values of t 1 and t 2 were obtained with the Microsoft Office Excel ® application, using the functions t 1 =INVT(5%;DF) and t 2 =INVT (40%;DF), respectively. Statistical analyses were performed using the Microsoft Office Excel ® application and R software (R Development Core Team, 2020).

RESULTS AND DISCUSSION
Among the 16 uniformity trials of buckwheat, the average fresh weight (FW) was 1852 g m -2 and there was no difference between the cultivars IPR91-Baili (1870 g m -2 ) and IPR92-Altar (1833 g m -2 ). At the time of evaluation, i.e., between 45 and 70 days after sowing, the mean dry weight content was 18.39%, and the contents of the cultivars IPR91-Baili (18.99%) and IPR92-Altar (17.80%) did not differ from each other. Consequently, the average dry weight of the cultivars IPR91-Baili (353 g m -2 ) and IPR92-Altar (324 g m -2 ) also did not differ and had an overall mean of 338 g m -2 (Table 1). Thus, it can be inferred that the fresh and dry weights were similar between the cultivars IPR91-Baili and IPR92-Altar.
In buckwheat, at 93 days after sowing, that is, at the full flowering stage, Ziech et al. (2015) obtained dry weight of 2.8 Mg ha -1 . In cuts performed at 47, 57 and 67 days after buckwheat sowing, Görgen et al. (2016) obtained dry weight of 2.301, 3.144 and 4.471 Mg ha -1 , respectively. At 71 days after sowing, in the reproductive period between flowering and milky grain stage, Pereira et al. (2017) obtained fresh weight and dry weight of 26.97 and 6.78 Mg ha -1 , respectively. Dry weights below 3.00 Mg ha -1 were obtained by Skora Neto and Campos (2017). The different environmental conditions, managements, cultivars and moments of evaluation make comparisons difficult. Nevertheless, it can be noted that the values obtained here were similar to those reported in these studies.
The mean coefficients of variation (CV) of fresh weight among the basic experimental units of 1 m 2 were 23.62% and 25.51%, respectively, for the cultivars IPR91 -Baili and IPR92-Altar, and the difference between the means was not significant (Table 1). No classification ranges of coefficients of variation specific to buckwheat were found in the literature. Thus, taking as reference the classification ranges of the coefficients of variation established by Pimentel-Gomes (2009) for field agricultural trials, these means are within the class of low experimental precision (CV between 20% and 30%), which demonstrates the need for using a plot size larger than 1 m 2 to improve experimental precision. Table 1. Sowing and evaluation dates, number of days after sowing (DAS), fresh weight (FW), in g m -2 , coefficient of variation (CV) of fresh weight among the basic experimental units of 1 m 2 (CV, in %), dry weight (DW) content, in % and dry weight, in g m -2 of buckwheat, of the cultivars IPR91-Baili and IPR92-Altar, in eight uniformity trials.
Means of FW, CV, DW content and DW not followed by the same lowercase letter in the column (comparison of cultivars; n = 8 uniformity trials) differ by Student's t-test (bilateral), for independent samples, at 5% probability level.
The wide oscillation of fresh weight (FW) and coefficients of variation between uniformity trials is possibly associated with the different environmental conditions between years and sowing times. This scenario of wide variability lends credibility to the study of plot size determination, as it contemplates real situations that occur in field experiments. The nonsignificant difference between cultivars in relation to FW and CV suggests that the plot size for experiments with these two buckwheat cultivars may be similar.
In the uniformity trials with the cultivars IPR91-Baili ( Figure 1) and IPR92-Altar (Figure 2), there was a reduction in variance by BEU between the plots [VU (X) ], with the increase in the planned plot size (X), which confirms the possibility of improving the experimental precision using plots larger than 1 m 2 . Visually, there are marked reductions in VU (X) with plots of up to eight BEU in size (8 m 2 ). After that, the reductions in VU (X) tend to stabilize, that is, the gains in precision with the increase in plot size become insignificant. In other species, such as velvet bean (CARGNELUTTI FILHO et al., 2014a); forage turnip (CARGNELUTTI FILHO et al., 2014b); and flax (CARGNELUTTI FILHO et al., 2018), the ratio of VU (X) and X was similar. Thus, plot of 8 m 2 should be used to evaluate the fresh weight of buckwheat. However, the optimal plot size (Xo) should be investigated using appropriate methodologies, such as the method of Hatheway (1961).   Smith (1938). Fresh weight data of buckwheat, cultivar IPR92-Altar, obtained in eight uniformity trial.
In the methodology of Hatheway (1961), based on the fixed value of the soil heterogeneity index (b) of Smith (1938) and CV, the Xo is dependent on i, r and d. Thus, based on the number of treatments and the desired precision, it is possible to use the information of this study to define the plot size and the number of replicates. For example, if the researcher wants to evaluate the FW of five treatments of buckwheat, IPR91-Baili cultivar, in the CRD, and wants precision (d) of 10%, among the various options, he/she can use plots of 79 BEU (79 m 2 ) and three replicates, 51 BEU (51 m 2 ) and four replicates, 38 BEU (38 m 2 ) and five replicates, 29 BEU (29 m 2 ) and six replicates, 24 BEU (24 m 2 ) and seven replicates or 20 BEU (20 m 2 ) and eight replicates (Table 2). In these six options, the area of the experiment would be, respectively, 1185, 1020, 950, 870, 840, and 800 m 2 .
Therefore, for the same precision (d=10%, in this case), smaller plots and a greater number of replicates are more efficient in the use of the experimental area, as discussed in Cargnelutti Filho et al. (2014a, b), Storck et al. (2016) and Cargnelutti Filho et al. (2018). It is important to consider that the increase in the number of replicates requires a greater number of evaluations and, if the trait is difficult to be measured and/or costly to be evaluated, the use of larger plot size and smaller number of replicates can be advantageous, as long as there is sufficient experimental area. In addition, smaller plot sizes may not represent plant development, while larger plots would make it possible to evaluate the plants in the central area (useful area) and disregard the borders, reducing the interference from plants of the adjacent plots, that is, the inter-plot competition (STORCK et al., 2016). Therefore, the researcher should investigate within its availability of experimental area, number of treatments to be evaluated and the desired precision, which combination of plot size and number of replicates is most appropriate.
The information in this study allows investigations in 264 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 differences between means of treatments to be detected as significant at 5% probability level (d = 10%, 11%, 12%, 13%, 14%, 15%, 16%, 17%, 18%, 19%, and 20%), for each cultivar and each design (Table 2). Other scenarios can be simulated by means of the expression (HATHEWAY, 1961), based on the mean soil heterogeneity index (b) of the function of Smith (1938) and on the mean coefficient of variation (CV) of the FW, from the eight trials of each cultivar. In this context, as an example, to evaluate the FW of eight treatments of buckwheat, IPR91-Baili cultivar, with four replicates and with d=10%, in the RCBD, the parameters are: b=0.8207; DF=(8-1)(4-1)=21; t 1 =INVT(5%;21) =2.07961383; t 2 =INVT(40%;21)=0.85907403; CV=23.62%; r=4; d=10%. Therefore, the optimal plot size (Xo) will be: The Xo of 49 BEU was assumed because, according to the criterion established in this study, the Xo is approximated to the immediately higher integer. For the simulation of scenarios in the completely randomized design (CRD), only the expression to calculate the number of degrees of freedom is changed, that is, for this design, DF=i(r-1), where i is the number of treatments and r is the number of replicates. Thus, for this example the parameters are: b=0.8207; DF=(8)(4-1)=24; t 1 =INVT (5%;24)=2.06389854; t 2 =INVT(40%;24)=0.85685545; CV=23.62%; r=4; d=10%. Therefore, For the same experimental dimensions, the smaller plot size in the CRD (48 BEU) in comparison to the RCBD (49 BEU) confirms the higher efficiency of the CRD when the experimental area is homogeneous (STORCK et al., 2016). The results of this study serve to define the plot size and the number of replicates in experiments to evaluate the fresh weight of the buckwheat cultivars IPR91-Baili and IPR92-Altar, in experiments conducted in the completely randomized design (CRD) and randomized complete block design (RCBD). It is indicated, as reference, for the planning of experiments with buckwheat, the use of plots of 8 m 2 . This indication is supported by the practical viability in the field and stabilization of precision from this size. This plot size is slightly larger than that used by Pereira et al. (2017) and smaller than those used by Ziech et al. (2015), Görgen et al. (2016) and Skora Neto and Campos (2017) in studies with buckwheat along with other soil cover species.

CONCLUSIONS
In experiments to evaluate the fresh weight of the buckwheat cultivars IPR91-Baili and IPR92-Altar, in the completely randomized design and randomized complete block design, with 5 to 20 treatments and with eight replicates, plots with useful area of 8 m 2 are sufficient to identify significant differences between treatments, at 5% probability level, of 15% of the overall mean of the experiment.