Research Article

# Sample sizes to estimate mean values for tassel traits in maize genotypes

Published: November 21, 2016
Genet. Mol. Res. 15(4): gmr15049151 DOI: https://doi.org/10.4238/gmr15049151
C.A. Wartha, C. Filho, A.D. Lúcio, D.N. Follmann, J.A. Kleinpaul, F.M. Simões, C.A. Wartha, C. Filho, A.D. Lúcio, D.N. Follmann, J.A. Kleinpaul, F.M. Simões (2016). Sample sizes to estimate mean values for tassel traits in maize genotypes. Genet. Mol. Res. 15(4): gmr15049151. https://doi.org/10.4238/gmr15049151
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### Abstract

Tassel traits are important in maize breeding programs aiming to reduce the size and number of branches and maintain satisfactory pollen production in order to increase grain yield. The objectives of this study were to determine the sample size (number of tassels) required to estimate the mean values for tassel traits in maize genotypes and to verify the variability of sample size among genotypes. Twenty maize genotypes were evaluated in an experiment carried out in a randomized block design with three replicates. Twenty tassels were randomly collected in each plot, for a total of 1200 tassels. In each tassel, the following traits were measured: peduncle dry matter, branching space dry matter, central spike dry matter, tassel dry matter, peduncle length, branching space length, central spike length, tassel length, tassel dry matter to tassel length ratio, number of primary branches, number of secondary branches, and tassel branch number. Measures of central tendency and variability were calculated, analysis of variance and mean comparison tests were performed, normality was verified, and the sample size was determined. In order to estimate the means with the same precision, the sample size for weight traits was greater than that for length traits. For tassel traits, 11, 20, and 43 tassels are sufficient to estimate the mean with a precision of 40, 30, and 20%, respectively, of the estimated mean at a 95% confidence level. These data show that there is sample size variability among maize genotypes.

### INTRODUCTION

Maize (Zea mays L.) is one of the most cultivated cereals in the world because of its use in a wide variety of industries, such as feed and foods industries. The estimated world maize production for the 2016/2017 agricultural year is 1013.87 million tons in an area of 178.62 million hectares (FAO, 2016). According to the Food and Agriculture Organization, the United States is the world’s largest maize grower, followed by China and Brazil, with an estimated production of 355, 224, and 83 million tons, respectively, in the 2016/2017 agricultural year. The increased grain yield of modern maize cultivars is the result of agronomic practices and genetic gains derived through maize breeding programs (Lauer et al., 2012).

The morphology of staminate and pistillate inflorescences in maize and their separation through the plant favor the study and development of inbred lines and hybrid seed, along with accentuated heterotic responses in the F1 generation (Allard, 1999). For heterosis to occur the genitors should be divergent (Hallauer et al., 2010). In this sense, most maize traits contribute to grain yield, with tassel weight contributing to heterosis in grain yield in diallel crosses (Ribeiro et al., 2014).

Morphological tassel traits are of importance in maize breeding programs, in which inbred lines are developed with the aim of reducing the size and number of branches and maintaining satisfactory pollen production (Duvick, 2005; Fischer and Edmeades, 2010). Larger tassels act as a drain for photoassimilates, which could be directed toward grain production, and restrict the passage of solar radiation through the canopy (Edwards, 2011). In addition, smaller tassels produce lower levels of auxins and decrease apical dominance, which has an inhibitory effect on ear development (Sangoi et al., 2006). In addition to the environment, it permits the production of one or more ear per plant.

Thus, studies evaluating tassel traits related to grain yield have been carried out in half-sib families of an ESALQ-PB1 population (Andrade and Miranda Filho, 2008), in parental lines of Pioneer-brand maize hybrids (Lauer et al., 2012), in recombinant inbred lines in temperate and tropical climates (Brewbaker, 2015), in inbred lines of two heterotic groups (Nardino et al., 2016a), and in F1 hybrids (Nardino et al., 2016b). In general, those studies have confirmed the relationship between tassel traits and grain yield.

In order to generate reliable results from breeding programs involving maize tassels or other agricultural crops, it is important to accurately determine the sample size (number of tassels and/or plants) to be used. As reported by Storck et al. (2016), sampling should be undertaken when it is not possible to evaluate the entire experimental unit. An appropriate sample size enables the population mean to be effectively estimated, reducing the sampling error within the plot and subsequently, the experimental error. Furthermore, Bussab and Morettin (2011) stated that the sample size is directly related to data variability and the desired reliability, and that it is inversely related to the level of error previously set by the researcher. Consistent with the above observations, larger sample sizes reduce the experimental error, but increase the demand on the size of the experimental area, manpower, financial resources, and time required for sampling. However, smaller sample sizes increase the experimental error (Cargnelutti Filho et al., 2012; Storck et al., 2016).

In maize, the sample size has been studied to estimate mean values for morphological and productive traits of ears (Martin et al., 2005; Storck et al., 2007), and morphological and productive traits of plants and ears in different soil tillage systems and straw (Modolo et al., 2013). Furthermore, Cargnelutti Filho et al. (2010) established the sample dimension to measure Pearson correlation coefficients among pairs of traits in maize hybrids. Also, the sample size was determined to estimate the coefficient of variation of the mean (Toebe et al., 2014) and Pearson correlation coefficients for different maize hybrids (Toebe et al., 2015).

The above studies presented significant results for the experimental design in maize crops. However, to our knowledge, no studies have investigated sample sizes for the estimation of mean values for tassel traits in maize genotypes, and it is assumed that the sample sizes differ among genotypes. The objectives of the present study were to determine the sample size (number of tassels) required to estimate mean values for tassel traits in maize genotypes and to verify sample size variability among genotypes.

### MATERIAL AND METHODS

An experiment was carried out on maize during the 2015/2016 agricultural year in an experimental area located at 29°42'S, 53°49'W, and 95 m in altitude. Based on the Köppen climate classification updated by Peel et al. (2007), the climate of the region is Cfa, humid subtropical, with hot summers and without a dry season (Heldwein et al., 2009). The soil is classified as sandy loam typic Paleudalf (Santos et al., 2013).

Sowing was performed on October 21, 2015. The experimental design was a randomized block with 20 genotypes and three replicates, for a total of 60 plots. The 20 genotypes included 18 single-cross hybrids (30A68, 30F53, AG 8780, AG 9025, AM 9724, AS 1666, AS 1677, BM 3066, Celeron, DKB 230, DKB 290, MS 2010, MS 2013, P1630, P2530, SHS 7915, Status VIP, and SX 7331) and two three-way cross hybrids (20A55 and MS 3022). These 20 genotypes were used because they belong to a network of maize cultivars used in evaluation trials to identify genotypes adapted for the State of Rio Grande do Sul, in southern Brazil.

Each plot consisted of two rows, each 5-m long, with spacing of 0.80 m between rows and 0.20 m between plants. The plant density was adjusted by manually thinning to five plants per meter of each row, and a final population of 62,500 plants per hectare. Thus, each plot consisted of 50 plants, totaling 3000 plants in the experiment (20 genotypes x three plots per genotype x 50 plants per plot). Basic fertilizer was applied on the day of sowing, using the commercial NPK formulation at a 5-20-20 proportion, for a total of 37.5 kg/ha N, 150 kg/ha P2O5, and 150 kg/ha K2O. Posteriorly, topdressing fertilization with 121.5 kg/ha N was divided between three applications, when the plants presented four, six, and eight expanded leaves (November 7 and 23, and December 10, 2015). Cultural practices regarding pest and weed control were followed to maintain competition-free conditions for the crop.

Twenty tassels were randomly collected from each plot and stored in paper packaging 104 days after sowing, when the plants were in the reproductive stage. The packages were identified and dried in an oven at 55°C until the samples reached constant weight. The following traits were measured in each tassel: peduncle dry matter (PDM, considering the region between the flag leaf collar and the first branch), in grams per tassel; branching space dry matter (BSDM), in grams per tassel; central spike dry matter (CSDM), in grams per tassel; tassel dry matter (TDM = PDM + BSDM + CSDM), in grams per tassel; peduncle length (PL, considering the distance between the collar of the flag leaf and the first branch), in centimeters; branching space length (BSL), in centimeters; central spike length (CSL), in centimeters; tassel length (TL = PL + BSL + CSL), in centimeters; number of primary branches (NPB); number of secondary branches (NSB); and tassel branch number (TBN = NPB + NSB) (Figure 1). Weight traits were measured using a digital scale with precision of 0.01 g. Furthermore, the TDM to tassel length ratio (TDMTL) was calculated in grams per centimeter.

Representation of traits evaluated in a maize tassel from the 30F53 genotype, composed of one central spike, four primary branches, one secondary branch, a branching space, and peduncle, based on the methods described by Upadyayula et al. (2006).

The data set obtained from the 12 traits was subjected to analysis of variance and F test at 5% significance and mean values for genotypes were clustered by the Scott-Knott test (Scott and Knott, 1974) at a 5% significance level. For analysis of variance, a mathematical model of block design with sampling within plots was used, as defined by Storck et al. (2016). In order to evaluate experimental precision, selective accuracy (SA) (Resende and Duarte, 2007) was determined by the following: SA = (1 – 1 / Fc)0.5, where Fc is the value derived from the F test for the genotype. According to the class limits established by Resende and Duarte (2007), the experimental precision was ranked as very high (SA ≥ 0.90), high (0.70 ≤ SA < 0.90), moderate (0.50 ≤ SA < 0.70), and low (SA < 0.50).

Thereafter, normality of the data was verified by the Kolmogorov-Smirnov test (Siegel and Castellan Júnior, 2006) for the traits PDM, BSDM, CSDM, TDM, PL, BSL, CSL, TL, TDMTL, NPB, NSB, and TBN, of 20 tassels from each of the 60 plots, totaling 720 tests (20 genotypes x three plots per genotype x 12 traits). Normality was investigated in order to verify the suitability of the data set for the study of sample size based on the Student t distribution.

Based on data from 20 tassels sampled from each experimental unit (plot) of each genotype, the sample size (n) for the traits PDM, BSDM, CSDM, TDM, PL, BSL, CSL, TL, TDMTL, NPB, NSB, and TBN was determined using the following equation:

$n={t}_{\alpha /2}^{2}C{V}^{2}/{D}^{2}$

where CV is the coefficient of variation between 20 tassels (%); D is the semi-amplitude of the confidence interval for the mean (%) (established as D = 5, 10, 20, 30, and 40%); and t is the critical value of the Student’s t distribution at the 5% significance level. Thus, 60 variables (sample size) were obtained by the combination of 12 traits (PDM, BSDM, CSDM, TDM, PL, BSL, CSL, TL, TDMTL, NPB, NSB, and TBN) at precision levels of 5% (D5), 10% (D10), 20% (D20), 30% (D30), and 40% (D40) of the estimated mean in the experimental unit.

In order to investigate variability in sample size among genotypes, the data set from these 60 variables (sample size) was subjected to analysis of variance using the mathematical model of randomized block design, as described by Storck et al. (2016). Genotype means were clustered using the Scott-Knott test (Scott and Knott, 1974) at a 5% significance level. Statistical analyzes were performed using the GENES software (Cruz, 2013) and Microsoft Office Excel.

### RESULTS AND DISCUSSION

The mean TDM was 3.11 g/tassel, tassel length was 47.50 cm, and tassel branch number was 14.00 (Table 1). Similar results were obtained, respectively, by Upadyayula et al. (2006), Lauer et al. (2012), and Brewbaker (2015), proving that there was adequate plant development in the present experiment.

### Degrees of freedom (DF) and mean squares of the causes of variation (block, genotype, experimental error, and sampling error), mean, coefficient of experimental variation (CVe), coefficient of sampling variation (CVs), and selective accuracy for tassel traits of 20 maize genotypes.

Causes of variation d.f. Mean square
PDM BSDM CSDM TDM PL BSL
Block 2 0.0053ns 0.4019ns 0.0352ns 0.6155ns 5.3038ns 17.3976ns
Genotype 19 0.4382* 39.7248* 1.1918* 47.5530* 207.8687* 380.5366*
Experimental error 38 0.0195* 1.6080* 0.0500* 2.0325* 17.8210* 16.6530*
Sampling error 1140 0.0034 0.3885 0.0176 0.5360 2.9877 3.0543
Mean - 0.2592 2.1716 0.6746 3.1053 8.7803 12.1131
CVe (%) - 53.92 58.39 33.14 45.91 48.08 33.69
CVs (%) - 22.49 28.70 19.68 23.58 19.69 14.43
Selective accuracy - 0.977 0.980 0.979 0.978 0.956 0.978
CSL TL TDMTL NPB NSB TBN
Block 2 6.7342ns 68.9991ns 0.0001ns 72.7358ns 3.4358ns 106.6975ns
Genotype 19 819.5201* 488.5188* 0.0214* 1054.1886* 100.1796* 1700.2900*
Experimental error 38 12.5195* 29.6708* 0.0009* 28.2288* 6.3543* 52.5615*
Sampling error 1140 6.8588 11.5412 0.0002 4.4512 1.1279 6.3673
Mean - 26.6031 47.4964 0.0652 11.4092 2.5933 14.0025
CVe (%) - 13.30 11.47 44.85 46.57 97.20 51.78
CVs (%) - 9.84 7.15 20.52 18.49 40.95 18.02
Selective accuracy - 0.992 0.969 0.980 0.987 0.968 0.984

PDM = peduncle dry matter, in grams per tassel; BSDM = branching space dry matter, in grams per tassel; CSDM = central spike dry matter, in grams per tassel; TDM = tassel dry matter, in grams per tassel; PL = peduncle length, in centimeters; BSL = branching space length, in centimeters; CSL = central spike length, in centimeters; TL = tassel length, in centimeters; TDMTL = tassel dry matter:tassel length ratio, in grams per centimeter; NPB = number of primary branches, in units; NSB = number of secondary branches, in units; TBN = tassel branch number, in units. *Significant effect as determined by the F test at a 5% significance level. nsNot significant.

There was a significant effect of genotypes in relation to the 12 traits studied (PDM, BSDM, CSDM, TDM, PL, BSL, CSL, TL, TDMTL, NPB, NSB, and TBN), demonstrating the existence of genetic variability (Table 1). This variability permitted the separation of genotypes into groups by the Scott-Knott test (Table 2). The block effect was not significant, showing that the blocks were not heterogeneous. High SA values (SA ≥ 0.956) ensured very high experimental precision in the evaluation of these 12 traits, as stated by Resende and Duarte (2007).

### Mean values for tassel traits evaluated in 20 maize genotypes.

Genotype PDM BSDM CSDM TDM PL BSL
20A55 0.36a 3.33a 0.88a 4.56a 10.25a 14.83a
30A68 0.33b 2.08c 0.77b 3.19c 10.03a 13.2b
30F53 0.2d 1.46d 0.86a 2.53d 6.98c 9.39d
AG8780 0.36a 2.25c 0.48c 3.09c 11.34a 14.92a
AG9025 0.13e 1.73d 0.69b 2.56d 5.74c 10.74c
AM9724 0.17e 2.4c 0.72b 3.29c 6.79c 12.61b
AS1666 0.26c 1.36d 0.69b 2.32d 10.2a 9.09d
AS1677 0.12e 1.5d 0.57c 2.19d 5.55c 11.37c
BM3066 0.26c 3.15a 0.67b 4.07a 7.76b 13.47b
Celeron 0.31b 1.82d 0.56c 2.69d 11.09a 10.68c
DKB230 0.12e 1.19e 0.33d 1.65e 6.3c 12.7b
DKB290 0.4a 2.82b 0.54c 3.76b 11.4a 15.78a
MS2010 0.27c 2.66b 0.69b 3.62b 10.49a 12.42b
MS2013 0.24c 3.41a 0.86a 4.5a 8.25b 13.15b
MS3022 0.3b 2.78b 0.73b 3.8b 8.89b 10.8c
P1630 0.2d 0.72e 0.75b 1.67e 8.7b 8.32d
P2530 0.22d 0.85e 0.82a 1.88e 8.06b 7.12e
SHS7915 0.24c 2.23c 0.76b 3.23c 8.43b 10.71c
StatusVIP 0.32b 2.87b 0.55c 3.74b 8.75b 15.79a
SX7331 0.38a 2.82b 0.58c 3.78b 10.63a 15.19a
CSL TL TDMTL NPB NSB TBN
20A55 24.55e 49.63c 0.09a 13.47b 2.72b 16.18b
30A68 31.74a 54.96a 0.06c 9.88c 2.05c 11.93c
30F53 30.89b 47.26c 0.05c 6.77d 0.92d 7.68d
AG8780 22.94f 49.19c 0.06c 11.82c 3.75a 15.57b
AG9025 29.94b 46.42d 0.05c 8.95c 1.43c 10.38c
AM9724 27.34d 46.73d 0.07b 10.45c 3.83a 14.28b
AS1666 28.81c 48.11c 0.05c 6.73d 1.65c 8.38d
AS1677 28.16c 45.09e 0.05c 8.05d 1.8c 9.85c
BM3066 21.35g 42.58e 0.09a 18.63a 3.72a 22.35a
Celeron 26.97d 48.74c 0.05c 11.07c 2.05c 13.12c
DKB230 24.78e 43.78e 0.04d 10.1c 2.5b 12.6c
DKB290 21.48g 48.66c 0.08b 12.7b 3.9a 16.6b
MS2010 28.71c 51.62b 0.07b 14.93b 3.77a 18.7b
MS2013 26.6d 47.99c 0.09a 14.18b 4a 18.18b
MS3022 24.87e 44.57e 0.08a 13.4b 3.23b 16.63b
P1630 30.71b 47.73c 0.04d 6.4d 0.27d 6.67d
P2530 32.23a 47.41c 0.04d 4.55e 0d 4.55e
SHS7915 27.41d 46.54d 0.07b 8.85c 2.57b 11.42c
StatusVIP 19.31h 43.84e 0.08a 19.82a 4.35a 24.17a
SX7331 23.29f 49.11c 0.08b 17.43a 3.37a 20.8a

PDM = peduncle dry matter, in grams per tassel; BSDM = branching space dry matter, in grams per tassel; CSDM = central spike dry matter, in grams per tassel; TDM = tassel dry matter, in grams per tassel; PL = peduncle length, in centimeters; BSL = branching space length, in centimeters; CSL = central spike length, in centimeters; TL = tassel length, in centimeters; TDMTL = tassel dry matter:tassel length ratio, in grams per centimeter; NPB = number of primary branches, in units; NSB = number of secondary branches, in units; TBN = tassel branch number, in units. Means not followed by the same superscript letter differ by the Scott-Knott test at a 5% significance level.

The experimental error (variation among plots) was significant in relation to the traits PDM, BSDM, CSDM, TDM, PL, BSL, CSL, TL, TDMTL, NPB, NSB, and TBN (Table 1). Thus, it can be inferred that the coefficients of experimental variation (CVe) were superior to the coefficients of sampling variation (CVs) for all traits. Moreover, these coefficients presented high magnitude, i.e., 11.47% ≤ CVe ≤ 97.20%, and 7.15% ≤ CVs ≤ 40.95%. These results show there was greater variability of plants among experimental units than within experimental units. Therefore, increasing the number of replicates is appropriate to improve experimental precision (Barbin, 2003). As reported by Barbin (2003), this method is effective at reducing the estimate of variance of the estimated mean. The high values of CVe and CVs indicate that it is important to adjust the number of replicates and the sample size in order to improve the experimental precision. In this context, Storck et al. (2007) evaluated maize ears and suggested increasing the number of replicates and decreasing the number of ears in the plot, fixing the total number of ears assessed by genotype.

The mean P value (minimum level of significance) of the Kolmogorov-Smirnov test (Siegel and Castellan Júnior, 2006) relative to the data of 20 tassels in the 720 cases analyzed (20 genotypes x three plots per genotype x 12 traits) was 0.73. Data of the PDM, BSDM, CSDM, TDM, PL, BSL, CSL, TL, TDMTL, NPB, NSB, and TBN fully adhered to the normal distribution (P > 0.20) in 650 cases (90.3%). Considering a minor adjustment, i.e., P > 0.05, 695 cases (96.5%) had an adjusted normal distribution. Therefore, these results indicate that this database is suitable for the study of sample size determination based on the Student t distribution.

The results of analysis of variance of the sample size, and those of the Scott-Knott test, in relation to the 12 studied traits (PDM, BSDM, CSDM, TDM, PL, BSL, CSL, TL, TDMTL, NPB, NSB, and TBN) are shown in Tables 3, 4, 5, and 6Table 3). Consequently, as expected, no statistical differences were detected by the Scott-Knott test in terms of the sample sizes of those traits. Therefore, the average size for those traits is representative of all genotypes. Thus, 32 tassels per experimental unit for BSDM (Table 4) and 17 tassels per experimental unit for TDMTL (Table 6) are sufficient to obtain estimates of the genotype mean with a precision of 10% (D10).

### Causes of variation (block and genotype) and respective degrees of freedom (DF), F test value for genotype (Fc), and coefficient of variation (CV) of sample sizes (number of tassels) for tassel traits in 20 maize genotypes.

Causes of variation PDM BSDM CSDM TDM PL BSL
Block (d.f. = 2) ns ns ns ns ns ns
Genotype (d.f. = 19) * ns * * * *
Fc 7.13 1.67 3.41 2.69 6.21 4.29
CV(%) 35.19 41.47 30.54 41.41 48.39 39.83
CSL TL TDMTL NPB NSB TBN
Block (d.f. = 2) ns ns ns ns ns ns
Genotype (d.f. = 19) * * ns * * *
Fc 2.45 3.76 1.62 2.75 6.70 3.10
CV(%) 40.72 38.25 50.82 40.56 138.63 43.91

PDM = peduncle dry matter, in grams per tassel; BSDM = branching space dry matter, in grams per tassel; CSDM = central spike dry matter, in grams per tassel; TDM = tassel dry matter, in grams per tassel; PL = peduncle length, in centimeters; BSL = branching space length, in centimeters; CSL = central spike length, in centimeters; TL = tassel length, in centimeters; TDMTL = tassel dry matter:tassel length ratio, in grams per centimeter; NPB = number of primary branches, in units; NSB = number of secondary branches, in units; TBN = tassel branch number, in units. *Significant effect as determined by the F test at a 5% significance level. nsNot significant.

### Sample size (number of tassels) of 20 maize genotypes for semi-amplitudes of the interval with 95% confidence equals to 5% (D5), 10% (D10), 20% (D20), 30% (D30), and 40% (D40) of the mean in relation to the traits peduncle dry matter, branching space dry matter, central spike dry matter, and tassel dry matter.

Genotype Peduncle dry matter Branching space dry matter
D5 D10 D20 D30 D40 D5 D10 D20 D30 D40
20A55 95c 24 6 3 2 142 36 9 4 3
30A68 85c 22 6 3 2 148 37 10 5 3
30F53 46d 12 3 2 1 85 22 6 3 2
AG8780 54d 14 4 2 1 98 25 7 3 2
AG9025 233a 59 15 7 4 150 38 10 5 3
AM9724 135b 34 9 4 3 169 43 11 5 3
AS1666 113c 29 8 4 2 76 19 5 3 2
AS1677 213a 54 14 6 4 112 28 7 4 2
BM3066 162b 41 11 5 3 143 36 9 4 3
Celeron 61d 16 4 2 1 108 27 7 3 2
DKB230 171b 43 11 5 3 106 27 7 3 2
DKB290 36d 9 3 1 1 103 26 7 3 2
MS2010 76c 19 5 3 2 201 51 13 6 4
MS2013 90c 23 6 3 2 105 27 7 3 2
MS3022 118c 30 8 4 2 126 32 8 4 2
P1630 144b 36 9 4 3 144 36 9 4 3
P2530 87c 22 6 3 2 87 22 6 3 2
SHS7915 138b 35 9 4 3 220 55 14 7 4
StatusVIP 39d 10 3 2 1 108 27 7 3 2
SX7331 37d 10 3 2 1 86 22 6 3 2
Mean 107 28 8 4 3 126 32 9 4 3
Central spike dry matter Tassel dry matter
D5 D10 D20 D30 D40 D5 D10 D20 D30 D40
20A55 72c 18 5 2 2 103a 26 7 3 2
30A68 50c 13 4 2 1 84b 21 6 3 2
30F53 43c 11 3 2 1 47b 12 3 2 1
AG8780 77b 20 5 3 2 76b 19 5 3 2
AG9025 47c 12 3 2 1 84b 21 6 3 2
AM9724 67c 17 5 2 2 122a 31 8 4 2
AS1666 39c 10 3 2 1 46b 12 3 2 1
AS1677 61c 16 4 2 1 73b 19 5 3 2
BM3066 77b 20 5 3 2 115a 29 8 4 2
Celeron 59c 15 4 2 1 70b 18 5 2 2
DKB230 56c 14 4 2 1 69b 18 5 2 2
DKB290 57c 15 4 2 1 73b 19 5 3 2
MS2010 130a 33 9 4 3 153a 39 10 5 3
MS2013 85b 22 6 3 2 83b 21 6 3 2
MS3022 67c 17 5 2 2 94b 24 6 3 2
P1630 81b 21 6 3 2 50b 13 4 2 1
P2530 37c 10 3 2 1 36b 9 3 1 1
SHS7915 92b 23 6 3 2 158a 40 10 5 3
StatusVIP 58c 15 4 2 1 82b 21 6 3 2
SX7331 60c 15 4 2 1 64b 16 4 2 1
Mean 66 17 5 3 2 85 22 6 3 2

Means not followed by the same letter differ by the Scott-Knott test at a 5% significance level. In columns referring to D10, D20, D30, and D40, the superscript letters are the same as in the column referring to D5, and therefore were not placed.

### Sample size (number of tassels) of 20 maize genotypes for semi-amplitudes of the interval with 95% confidence equals to 5% (D5), 10% (D10), 20% (D20), 30% (D30), and 40% (D40) of the mean in relation to the traits peduncle length, branching space length, central spike length, and tassel length.

Genotype Peduncle length Branching space length
D5 D10 D20 D30 D40 D5 D10 D20 D30 D40
20A55 85c 22 6 3 2 42b 11 3 2 1
30A68 52c 13 4 2 1 40b 10 3 2 1
30F53 54c 14 4 2 1 40b 10 3 2 1
AG8780 22c 6 2 1 1 24b 6 2 1 1
AG9025 172a 43 11 5 3 66a 17 5 2 2
AM9724 89c 23 6 3 2 36b 9 3 1 1
AS1666 53c 14 4 2 1 32b 8 2 1 1
AS1677 188a 47 12 6 3 53b 14 4 2 1
BM3066 114b 29 8 4 2 20b 5 2 1 1
Celeron 26c 7 2 1 1 32b 8 2 1 1
DKB230 208a 52 13 6 4 33b 9 3 1 1
DKB290 29c 8 2 1 1 25b 7 2 1 1
MS2010 31c 8 2 1 1 53b 14 4 2 1
MS2013 111b 28 7 4 2 44b 11 3 2 1
MS3022 85c 22 6 3 2 48b 12 3 2 1
P1630 152a 38 10 5 3 80a 20 5 3 2
P2530 64c 16 4 2 1 89a 23 6 3 2
SHS7915 72c 18 5 2 2 42b 11 3 2 1
StatusVIP 31c 8 2 1 1 16b 4 1 1 1
SX7331 25c 7 2 1 1 16b 4 1 1 1
Mean 84 22 6 3 2 42 11 3 2 2
Central spike length Tassel length
D5 D10 D20 D30 D40 D5 D10 D20 D30 D40
20A55 20a 5 2 1 1 12a 3 1 1 1
30A68 11b 3 1 1 1 4b 1 1 1 1
30F53 12b 3 1 1 1 5b 2 1 1 1
AG8780 25a 7 2 1 1 9b 3 1 1 1
AG9025 7b 2 1 1 1 7b 2 1 1 1
AM9724 18b 5 2 1 1 9b 3 1 1 1
AS1666 8b 2 1 1 1 7b 2 1 1 1
AS1677 17b 5 2 1 1 7b 2 1 1 1
BM3066 18b 5 2 1 1 10b 3 1 1 1
Celeron 14b 4 1 1 1 6b 2 1 1 1
DKB230 14b 4 1 1 1 13a 4 1 1 1
DKB290 21a 6 2 1 1 10b 3 1 1 1
MS2010 29a 8 2 1 1 17a 5 2 1 1
MS2013 19a 5 2 1 1 9b 3 1 1 1
MS3022 27a 7 2 1 1 16a 4 1 1 1
P1630 22a 6 2 1 1 11b 3 1 1 1
P2530 11b 3 1 1 1 10b 3 1 1 1
SHS7915 28a 7 2 1 1 17a 5 2 1 1
StatusVIP 20a 5 2 1 1 7b 2 1 1 1
SX7331 16b 4 1 1 1 5b 2 1 1 1
Mean 18 5 2 1 1 10 3 2 1 1

Means not followed by the same superscript letter differ by the Scott-Knott test at 5% significance level. In columns referring to D10, D20, D30, and D40, the letters are the same as in the column referring to D5, and therefore, are not shown.

### Sample size (number of tassels) of 20 maize genotypes for semi-amplitudes of the interval with 95% confidence equals to 5% (D5), 10% (D10), 20% (D20), 30% (D30), and 40% (D40) of the mean in relation to the traits tassel dry matter by tassel length ratio, number of primary branches, number of secondary branches, and tassel branch number.

Genotype Tassel dry matter: tassel length ratio Number of primary branches
D5 D10 D20 D30 D40 D5 D10 D20 D30 D40
20A55 82 21 6 3 2 102a 26 7 3 2
30A68 70 18 5 2 2 77a 20 5 3 2
30F53 39 10 3 2 1 91a 23 6 3 2
AG8780 51 13 4 2 1 38b 10 3 2 1
AG9025 70 18 5 2 2 97a 25 7 3 2
AM9724 113 29 8 4 2 56b 14 4 2 1
AS1666 36 9 3 1 1 47b 12 3 2 1
AS1677 65 17 5 2 2 77a 20 5 3 2
BM3066 84 21 6 3 2 50b 13 4 2 1
Celeron 57 15 4 2 1 37b 10 3 2 1
DKB230 44 11 3 2 1 55b 14 4 2 1
DKB290 61 16 4 2 1 18b 5 2 1 1
MS2010 110 28 7 4 2 65a 17 5 2 2
MS2013 62 16 4 2 1 45b 12 3 2 1
MS3022 59 15 4 2 1 69a 18 5 2 2
P1630 43 11 3 2 1 95a 24 6 3 2
P2530 33 9 3 1 1 76a 19 5 3 2
SHS7915 108 27 7 3 2 57b 15 4 2 1
StatusVIP 58 15 4 2 1 37b 10 3 2 1
SX7331 48 12 3 2 1 37b 10 3 2 1
Mean 65 17 5 3 2 62 16 5 3 2
Number of secondary branches Tassel branch number
D5 D10 D20 D30 D40 D5 D10 D20 D30 D40
20A55 234b 59 15 7 4 89a 23 6 3 1
30A68 368b 92 23 11 6 68a 17 5 2 1
30F53 860b 215 54 24 14 89a 23 6 3 1
AG8780 168b 42 11 5 3 28b 7 2 1 1
AG9025 1547b 387 97 43 25 115a 29 8 4 1
AM9724 246b 62 16 7 4 61b 16 4 2 1
AS1666 314b 79 20 9 5 46b 12 3 2 1
AS1677 478b 120 30 14 8 79a 20 5 3 1
BM3066 226b 57 15 7 4 46b 12 3 2 1
Celeron 214b 54 14 6 4 39b 10 3 2 1
DKB230 253b 64 16 8 4 40b 10 3 2 1
DKB290 167b 42 11 5 3 23b 6 2 1 2
MS2010 380b 95 24 11 6 74a 19 5 3 2
MS2013 254b 64 16 8 4 44b 11 3 2 2
MS3022 230b 58 15 7 4 67a 17 5 2 2
P1630 6251a 1563 391 174 98 107a 27 7 3 2
P2530 - - - - - 76a 19 5 3 2
SHS7915 236b 59 15 7 4 45b 12 3 2 2
StatusVIP 161b 41 11 5 3 36b 9 3 1 2
SX7331 172b 43 11 5 3 31b 8 2 1 2
Mean 672 169 43 20 11 61 16 5 3 2

Means not followed by the same superscript letter differ by the Scott-Knott test at a 5% significance level. In columns referring to D10, D20, D30, and D40, the superscript letters are the same as in the column referring to D5, and therefore, are not shown.

For the other 10 traits, the effect of genotypes was significant, which demonstrates distinct sample sizes among genotypes (Table 3). Thus, four sample size groups were formed for PDM, three groups for CSDM and PL, and two for TDM, BSL, CSL, TL, NPB, NSB, and TBN by the Scott-Knott test, confirming that different sample sizes among genotypes are required to estimate the mean of these traits with the same precision (Tables 4, 5, and 6). Therefore, it can be inferred that there is sample size variability among genotypes, as verified in maize (Martin et al., 2005; Storck et al., 2007; Toebe et al., 2015). In this context, Martin et al. (2005) suggested sampling each genotype with its respective sample size or using the largest sample size determined in order to cover all genotypes.

The sample size used to estimate the mean of each trait, with semi-amplitude of the confidence interval equal to 5% of the mean estimate (greater precision, in this study), and a 95% confidence level, ranged from four tassels for TL of the 30A68 genotype to 6251 tassels for NSB of the P1630 genotype (Tables 4, 5, and 6). These results confirm the presence of sample size variability among traits of maize genotypes, as verified among traits (Storck et al., 2007; Toebe et al., 2014) and between pairs of traits in maize (Cargnelutti Filho et al., 2010; Toebe et al., 2015). In line with this, Storck et al. (2007) suggested using the sample size determined for the most important trait for the experiment. Another possibility proposed by those authors is to take an average sample size per group of traits, which includes the largest number of traits.

If a researcher utilizes the same sample size to evaluate these traits in an experiment, greater precision in estimates will be obtained in relation to TL, decreasing gradually in the following order: CSL, BSL, TBN, NPB, TDMTL, CSDM, PL, TDM, PDM, BSDM, and NSB. Under the general conditions of the present experiment, the data set demonstrated that to estimate the mean with the same precision, the sample size for weight traits is greater than that for length traits. Cargnelutti Filho et al. (2012) also observed the necessity of a larger sample size to evaluate weight traits in relation to other traits (length and diameter) in jack bean and velvet bean seeds.

If the researcher selects the largest average number of sample size (NSB trait), 11, 20, and 43 tassels are sufficient to estimate the mean values for tassel traits with a precision of 40% (D40), 30% (D30), and 20% (D20), respectively, of the mean estimate and a 95% confidence level. Taking the average sample size for genotypes in groups of traits for a precision of 10% (D10) of the estimated mean, weight traits (PDM, BSDM, CSDM, and TDM) can be sampled with 32 tassels (Table 3), length traits (PL, BSL, CSL, and TL) with 22 tassels (Table 4), and branching traits (NPB, NSB, and TBN) with 169 tassels. Furthermore, assuming that the sample size is set at 43 tassels (20% precision) to estimate the mean values of treatments in an experiment with three replicates, 15 tassels can be sampled by repetition.

In conclusion, for tassel traits, 11, 20, and 43 tassels are sufficient to estimate the mean with a precision of 40, 30, and 20%, respectively, of the estimated mean at a 95% confidence level.

There is sample size variability among maize genotypes for peduncle dry matter, central spike dry matter, tassel dry matter, peduncle length, branching space length, central spike length, tassel length, number of primary branches, number of secondary branches, and tassel branch number.