Sample size affects the precision of the analysis of variance in experiments with cauliflower seedlings

Bittencourt, Karina Chertok; Toebe, Marcos; Souza, Rafael Rodrigues de; Pazetto, Stella Bonorino; Toebe, Iris Cristina Datsch

doi:10.1590/0103-8478cr20220180

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Crop production • Cienc. Rural 53 (5) • 2023 • https://doi.org/10.1590/0103-8478cr20220180 copy

Sample size affects the precision of the analysis of variance in experiments with cauliflower seedlings

O tamanho de amostra afeta a precisão da análise de variância em experimentos com mudas de couve-flor

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT:

This study verified whether sample size would affect the precision of the analysis of variance in experiments with cauliflower seedlings. An experiment was carried out where the number of leaves and shoot, root and total length were measured. For each variable, resamplings with repositions were performed in sample scenarios of 1, 2, …, 100 seedlings per experimental unit, and the sample size was defined for the variance components through Schumacher models and maximum curvature points. The mean squares of the analysis of variance suffer direct interference from the number of sampled seedlings. The sampling of 16 seedlings per experimental unit is enough to estimate the analysis of variance reliably, promoting satisfactory precision gains compared to the sampling of only one seedling per experimental unit.

Key words:
Brassica oleracea; horticulture; experimental planning; precision gain

Universidade Federal de Santa Maria Universidade Federal de Santa Maria, Centro de Ciências Rurais , 97105-900 Santa Maria RS Brazil , Tel.: +55 55 3220-8698 , Fax: +55 55 3220-8695 - Santa Maria - RS - Brazil
E-mail: cienciarural@mail.ufsm.br

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

Trait	Statistic^*	Schumacher model	R²	RMSE	d	Precision gain (%)	Sample size
NL	EMS	PG_i = 92.7268 × exp(-2.0653 × n ^-1)	0.98	1.70	0.99	80.34	15
NL	TMS	PG_i = 90.8951 × exp(-2.6275 × n ^-1)	0.99	1.59	0.99	76.82	16
NL	SMS	PG_i = 90.9115 × exp(-2.7168 × n ^-1)	0.99	1.43	0.99	76.55	16
NL	IMS	PG_i = 92.1433 × exp(-2.2303 × n ^-1)	0.98	1.65	0.99	79.22	15
TL	EMS	PG_i = 101.0929 × exp(-0.9950 × n ^-1)	0.79	4.69	0.93	93.11	13
TL	TMS	PG_i = 95.2857 × exp(-1.4891 × n ^-1)	0.94	2.61	0.98	85.09	14
TL	SMS	PG_i = 97.0627 × exp(-1.3535 × n ^-1)	0.93	2.96	0.98	87.37	13
TL	IMS	PG_i = 98.4280 × exp(-1.2088 × n ^-1)	0.89	3.52	0.97	89.40	13
SL	EMS	PG_i = 101.2845 × exp(-0.9737 × n ^-1)	0.78	4.83	0.93	93.42	13
SL	TMS	PG_i = 97.7196 × exp(-1.1904 × n ^-1)	0.88	3.64	0.96	88.85	13
SL	SMS	PG_i = 98.8328 × exp(-1.1430 × n ^-1)	0.87	3.86	0.96	90.14	13
SL	IMS	PG_i = 100.1760 × exp(-1.0428 × n ^-1)	0.82	4.39	0.94	91.96	13
RL	EMS	PG_i = 94.5164 × exp(-1.9269 × n ^-1)	0.98	1.66	0.99	82.45	15
RL	TMS	PG_i = 90.8445 × exp(-2.6214 × n ^-1)	0.99	1.54	0.99	76.79	16
RL	SMS	PG_i = 90.6974 × exp(-2.6674 × n ^-1)	0.99	1.55	0.99	76.52	16
RL	IMS	PG_i = 91.0810 × exp(-2.5692 × n ^-1)	0.99	1.52	0.99	77.17	16