Does soybean sample size impact Tukey’s test for non-additivity?

Souza, Rafael Rodrigues de; Toebe, Marcos; Mello, Anderson Chuquel; Bittencourt, Karina Chertok; Toebe, Iris Cristina Datsch

doi:10.1590/0103-8478cr20220181

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Crop production • Cienc. Rural 53 (5) • 2023 • https://doi.org/10.1590/0103-8478cr20220181 copy

Does soybean sample size impact Tukey’s test for non-additivity?

O tamanho de amostra em soja impacta o teste de não aditividade de Tukey?

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT:

This study analyzed the interference of sample size on Tukey’s test for non-additivity and found the sample size to optimize the test for soybean grain yield. Six experiments were conducted in a completely randomized block design with either 20 or 30 cultivars and three repetitions of each treatment. Grain yield was determined per plant, totaling 9,000 sampled plants. Next, sample scenarios up to 100 plants were simulated, estimating F statistic for a degree of freedom of the error in each scenario. After that, the optimal sample size was defined via power models and maximum curvature point. Results showed the number of sampled plants per experimental unit influences the estimates of Tukey’s test for non-additivity. Also, the sampling of 14 to 19 plants per experimental unit allows for maintaining the accuracy of the test.

Key words:
analysis of variance; experimental planning; Glycine max; mathematical assumptions

Authorship

Rafael Rodrigues de Souza

Departamento de Fitotecnia, Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil. Universidade Federal de Santa Maria (UFSM)BrazilSanta Maria, RS, BrazilDepartamento de Fitotecnia, Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil.

Marcos Toebe ^*E-mail: m.toebe@gmail.com. *Corresponding author

Departamento de Ciências Agronômicas e Ambientais, Universidade Federal de Santa Maria (UFSM), 98400-000, Frederico Westphalen, RS, Brasil..Universidade Federal de Santa Maria (UFSM)BrazilFrederico, RS, BrazilDepartamento de Ciências Agronômicas e Ambientais, Universidade Federal de Santa Maria (UFSM), 98400-000, Frederico Westphalen, RS, Brasil..

https://orcid.org/0000-0003-2033-1467

Anderson Chuquel Mello

https://orcid.org/0000-0003-4509-957X

Karina Chertok Bittencourt

https://orcid.org/0000-0002-4127-0715

Iris Cristina Datsch Toebe

Programa de Pós-graduação em Informática na Educação, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brasil. Universidade Federal do Rio Grande do Sul (UFRGS)BrazilPorto Alegre, RS, BrazilPrograma de Pós-graduação em Informática na Educação, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brasil.

https://orcid.org/0000-0001-6831-6624

E-mail: m.toebe@gmail.com. ^*Corresponding author

Editors: Leandro Souza da Silva(0000-0002-1636-6643) Alessandro Dal’Col Lúcio(0000-0003-0761-4200)

DECLARATION OF CONFLICT OF INTERESTS

We have no conflict of interest to declare.

AUTHORS’ CONTRIBUTIONS

Conceptualization: RRS. Data acquisition: RRS and ACM Design of methodology and data analysis: RRS and MT. Supervision and coordination: MT and ICDT. RRS and KCB prepared the draft of the manuscript. All authors critically revised the manuscript and approved of the final version.

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (2)
Tables (1)

Thumbnail

Figure 1
Minimum, 2.5 percentiles, mean, 97.5 percentiles, and maximum values for the first sowing date (E1 - a), second sowing date (E2 - b), and third sowing date (E3 - c) in Erval Seco, and first sowing date (E4 - d), second sowing date (E5 - e), and third sowing date (E6 - f) in Itaqui for F statistic of a degree of freedom of the experimental error, according to the methodology described by Tukey (1949TUKEY, J.W. One degree of freedom for non-additivity. Biometrics, v.5, p.232-242, 1949. Available from: <Available from: https://doi.org/10.2307/3001938 >. Accessed: Jan. 22, 2022. doi: 10.2307/3001938.
https://doi.org/10.2307/3001938... ) in soybean.

Thumbnail

Figure 2
Sample size determination via power model and maximum curvature points for Tukey’s test for non-additivity for the first sowing date (E1 - a), second sowing date (E2 - b), and third sowing date (E3 - c) in Erval Seco, and first sowing date (E4 - d), second sowing date (E5 - e), and third sowing date (E6 - f) in Itaqui.

Thumbnail

Table 1
Coefficient of determination (R²), root mean square error (RMSE), and d index of the power models, and maximum curvature points and sample sizes for Tukey’s test for non-additivity.

Figure 1 Minimum, 2.5 percentiles, mean, 97.5 percentiles, and maximum values for the first sowing date (E1 - a), second sowing date (E2 - b), and third sowing date (E3 - c) in Erval Seco, and first sowing date (E4 - d), second sowing date (E5 - e), and third sowing date (E6 - f) in Itaqui for F statistic of a degree of freedom of the experimental error, according to the methodology described by Tukey (1949TUKEY, J.W. One degree of freedom for non-additivity. Biometrics, v.5, p.232-242, 1949. Available from: <Available from: https://doi.org/10.2307/3001938 >. Accessed: Jan. 22, 2022. doi: 10.2307/3001938.
https://doi.org/10.2307/3001938... ) in soybean.

Figure 2 Sample size determination via power model and maximum curvature points for Tukey’s test for non-additivity for the first sowing date (E1 - a), second sowing date (E2 - b), and third sowing date (E3 - c) in Erval Seco, and first sowing date (E4 - d), second sowing date (E5 - e), and third sowing date (E6 - f) in Itaqui.

Table 1 Coefficient of determination (R²), root mean square error (RMSE), and d index of the power models, and maximum curvature points and sample sizes for Tukey’s test for non-additivity.

Trial^†	Power model	R²	RMSE	d index
E1	CI_95% = 12.0224×n^-0.3433	0.98	0.33	0.99
E2	CI_95% = 8.5780×n^-0.3392	0.96	0.31	0.99
E3	CI_95% = 11.2604×n^-0.2088	0.95	0.35	0.99
E4	CI_95% = 73.6162×n^-0.4034	0.99	0.92	0.99
E5	CI_95% = 22.1560×n^-0.3540	0.99	0.51	0.99
E6	CI_95% = 11.5640×n^-0.5749	0.99	0.12	0.99
Trial	Maximum curvature method	Maximum Curvature	Maximum CI_95%	Sample size
E1	Geral method	2.55	8.72	3
E1	Spline method	12.17	5.10	13
E1	Perpendicular distance method	16.39	4.60	17
E1	Linear plateau response method	26.84	3.89	27
E2	Geral method	1.97	6.82	2
E2	Spline method	12.23	3.67	13
E2	Perpendicular distance method	16.45	3.32	17
E2	Linear plateau response method	27.07	2.80	28
E3	Geral method	1.69	10.09	2
E3	Spline method	14.33	6.46	15
E3	Perpendicular distance method	18.25	6.14	19
E3	Linear plateau response method	35.04	5.36	36
E4	Geral method	10.13	28.93	11
E4	Spline method	11.28	27.70	12
E4	Perpendicular distance method	15.62	24.29	16
E4	Linear plateau response method	23.56	20.58	24
E5	Geral method	4.10	13.48	5
E5	Spline method	11.99	9.19	12
E5	Perpendicular distance method	16.25	8.26	17
E5	Linear plateau response method	26.23	6.97	27
E6	Geral method	3.14	5.99	4
E6	Spline method	9.06	3.26	10
E6	Perpendicular distance method	13.64	2.58	14
E6	Linear plateau response method	15.97	2.35	16

^(†) E1: first sowing date (October 24, 2017), E2: second sowing date (November 15, 2017), and E3: third sowing date (December 05, 2017) in Erval Seco-RS; E4: first sowing date (November 02, 2017), E5: second sowing date (November 30, 2017), and E6: third sowing date (December 21, 2017) in Itaqui-RS.

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