Sample size for principal component analysis in corn

Cargnelutti Filho, Alberto; Toebe, Marcos

doi:10.1590/S1678-3921.pab2021.v56.02510

Alberto Cargnelutti FilhoCorresponding author

Universidade Federal de Santa Maria, Departamento de Fitotecnia, Avenida Roraima, nº 1.000, Camobi, CEP 97105-900 Santa Maria, RS, Brazil. E-mail: alberto.cargnelutti.flho@gmail.com

http://orcid.org/0000-0002-8608-9960

Marcos Toebe

Universidade Federal de Santa Maria, Departamento de Ciências Agronômicas e Ambientais, Campus Frederico Westphalen, Linha 7 de Setembro, s/nº, BR-386, Km 40, CEP 98400-000 Frederico Westphalen, RS, Brazil. E-mail: m.toebe@gmail.com

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

Corresponding author

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Figure 1.
Percentile 97.5%, mean, percentile 2.5%, and amplitude of confidence interval of 95% (ACI) for 3,000 estimates of eigenvalues of the first four principal components (PC1, PC2, PC3, and PC4), based in resampling of the 361 plants of single-cross hybrid P32R21 in the 2008/2009 crop year (left column), and 1,777 plants of single-cross hybrid 30F53 in the 2009/2010 crop year (right column). On the X axis the number of plants ranges from 15 to 1,000.

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Figure 2.
Percentile 97.5%, mean, percentile 2.5%, and amplitude of confidence interval of 95% (ACI) for 3,000 estimates of eigenvalues of the first four principal components (PC1, PC2, PC3, and PC4), based in resampling of the 373 plants of three-way cross hybrid DKB566 in the 2008/2009 crop year (left column) and 1,693 plants of three-way cross hybrid DKB566 in the 2009/2010 crop year (right column). On the X axis the number of plants ranges from 15 to 1,000.

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Figure 3.
Percentile 97.5%, mean, percentile 2.5%, and amplitude of confidence interval of 95% (ACI) for 3,000 estimates of eigenvalues of the first four principal components (PC1, PC2, PC3, and PC4), based in resampling of the 416 plants of double-cross hybrid DKB747 in the 2008/2009 crop year (left column) and 1,720 plants of double-cross hybrid DKB747 in the 2009/2010 crop year (right column). On the X axis the number of plants ranges from 15 to 1,000.

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Table 1.
Estimates of the variance (eigenvalues) of twelve principal components (PC1, PC2, …, PC12), from twelve traits in corn hybrids (Zea mays) grown in two crop years.

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Table 2.
Maximum, percentile 97.5% (P_97.5%), mean, percentile 2.5% (P_2.5%), minimum, and amplitude of confidence interval of 95% (ACI = P_97.5% - P_2.5%) for 3,000 estimates of eigenvalues of the first four principal components (PC1, PC2, PC3, and PC4), and estimates obtained from 3,000 resamples with replacement for n = 15 and 1,000 plants of corn hybrids (Zea mays) grown in two crop years.

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Table 3.
Parameter estimates of the model linear response with plateau (a, b), determination coefficient (r²), required sample size (n_o, number of plants) to estimate the eigenvalues of the first four principal components (PC1, PC2, PC3, and PC4), and amplitude of confidence interval of 95% in sample size ACI(n_o) for corn hybrids (Zea mays) grown in two crop years.

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Estimate	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	PC11	PC12
	Single-cross hybrid P32R21 (n=361 plants) in the 2008/2009 crop year
Variance (eigenvalues)	6.58	1.46	1.11	0.95	0.85	0.38	0.30	0.22	0.14	0.01	0.00	0.00
Percentage of variance	54.86	12.16	9.26	7.88	7.05	3.19	2.47	1.85	1.18	0.10	0.00	0.00
Cumulative percentage of variance	54.86	67.02	76.29	84.17	91.22	94.41	96.87	98.72	99.90	100.00	100.00	100.00
	Three-way cross hybrid DKB566 (n=373 plants) in the 2008/2009 crop year
Variance (eigenvalues)	6.63	1.59	1.41	0.90	0.66	0.25	0.21	0.19	0.16	0.01	0.00	0.00
Percentage of variance	55.23	13.24	11.73	7.46	5.50	2.07	1.72	1.59	1.35	0.10	0.00	0.00
Cumulative percentage of variance	55.23	68.47	80.20	87.66	93.16	95.23	96.95	98.55	99.90	100.00	100.00	100.00
	Double-cross hybrid DKB747 (n=416 plants) in the 2008/2009 crop year
Variance (eigenvalues)	6.73	1.48	1.22	1.06	0.69	0.29	0.22	0.16	0.14	0.01	0.00	0.00
Percentage of variance	56.11	12.33	10.20	8.84	5.74	2.38	1.84	1.33	1.17	0.07	0.00	0.00
Cumulative percentage of variance	56.11	68.44	78.64	87.47	93.21	95.59	97.43	98.76	99.93	100.00	100.00	100.00
	Single-cross hybrid 30F53 (n=1,777 plants) in the 2009/2010 crop year
Variance (eigenvalues)	7.30	1.59	1.17	0.70	0.50	0.33	0.20	0.11	0.09	0.01	0.00	0.00
Percentage of variance	60.86	13.26	9.78	5.80	4.16	2.75	1.65	0.91	0.75	0.08	0.00	0.00
Cumulative percentage of variance	60.86	74.12	83.90	89.70	93.86	96.61	98.26	99.17	99.92	100.00	100.00	100.00
	Three-way cross hybrid DKB566 (n=1,693 plants) in the 2009/2010 crop year
Variance (eigenvalues)	6.70	1.66	1.26	0.79	0.60	0.39	0.24	0.21	0.14	0.01	0.00	0.00
Percentage of variance	55.79	13.85	10.48	6.57	4.96	3.21	2.03	1.77	1.21	0.12	0.00	0.00
Cumulative percentage of variance	55.79	69.64	80.12	86.70	91.66	94.87	96.90	98.67	99.88	100.00	100.00	100.00
	Double-cross hybrid DKB747 (n=1,720 plants) in the 2009/2010 crop year
Variance (eigenvalues)	6.55	1.69	1.29	0.89	0.65	0.36	0.22	0.20	0.13	0.01	0.00	0.00
Percentage of variance	54.60	14.08	10.72	7.42	5.44	3.02	1.87	1.67	1.07	0.11	0.00	0.00
Cumulative percentage of variance	54.60	68.68	79.40	86.83	92.26	95.28	97.15	98.82	99.89	100.00	100.00	100.00
	Overall mean
Variance (eigenvalues)	6.75	1.58	1.24	0.88	0.66	0.33	0.23	0.18	0.13	0.01	0.00	0.00
Percentage of variance	56.24	13.15	10.36	7.33	5.47	2.77	1.93	1.52	1.12	0.10	0.00	0.00
Cumulative percentage of variance	56.24	69.40	79.76	87.09	92.56	95.33	97.26	98.78	99.90	100.00	100.00	100.00

PC	Maximum	P_97.5%	Mean	P_2.5%	Minimum	ACI	Maximum	P_97.5%	Mean	P_2.5%	Minimum	ACI
	------------------------------------ n = 15 plants ------------------------------------						------------------------------------ n = 1000 plants ------------------------------------
	Single-cross hybrid P32R21 (n=361 plants) in the 2008/2009 crop year
PC1	9.53	8.50	6.81	5.05	3.87	3.45	6.96	6.82	6.59	6.37	6.15	0.45
PC2	3.57	2.87	1.98	1.27	0.79	1.61	1.65	1.58	1.47	1.36	1.29	0.22
PC3	2.36	1.87	1.28	0.76	0.52	1.11	1.29	1.21	1.12	1.03	0.95	0.18
PC4	1.63	1.30	0.84	0.45	0.24	0.85	1.08	1.02	0.95	0.87	0.80	0.15
	Three-way cross hybrid DKB566 (n=373 plants) in the 2008/2009 crop year
PC1	9.73	8.47	6.88	5.22	4.10	3.25	7.02	6.83	6.63	6.43	6.26	0.41
PC2	3.93	2.92	2.07	1.38	0.95	1.54	1.81	1.71	1.60	1.50	1.42	0.21
PC3	2.61	1.90	1.33	0.78	0.47	1.12	1.55	1.50	1.40	1.30	1.18	0.20
PC4	1.82	1.31	0.81	0.41	0.21	0.89	1.02	0.97	0.90	0.82	0.78	0.14
	Double-cross hybrid DKB747 (n=416 plants) in the 2008/2009 crop year
PC1	10.07	8.69	6.81	4.98	3.76	3.72	7.19	6.98	6.74	6.48	6.24	0.50
PC2	3.92	2.92	2.03	1.26	0.63	1.65	1.71	1.61	1.49	1.38	1.29	0.23
PC3	2.42	1.97	1.34	0.77	0.51	1.20	1.41	1.33	1.23	1.13	1.08	0.21
PC4	1.80	1.36	0.85	0.43	0.25	0.92	1.23	1.14	1.05	0.97	0.87	0.17
	Single-cross hybrid 30F53 (n=1,777 plants) in the 2009/2010 crop year
PC1	9.49	8.69	7.51	6.06	4.49	2.63	7.57	7.48	7.31	7.14	7.00	0.34
PC2	3.36	2.59	1.88	1.36	0.93	1.23	1.77	1.67	1.60	1.53	1.48	0.14
PC3	2.76	1.69	1.17	0.68	0.39	1.00	1.32	1.25	1.17	1.09	1.02	0.16
PC4	1.37	1.10	0.68	0.34	0.18	0.76	0.88	0.78	0.70	0.62	0.57	0.16
	Three-way cross hybrid DKB566 (n=1,693 plants) in the 2009/2010 crop year
PC1	9.30	8.37	6.93	5.35	4.25	3.03	7.03	6.89	6.70	6.52	6.41	0.38
PC2	4.03	2.85	2.03	1.40	1.01	1.45	1.78	1.72	1.67	1.61	1.56	0.12
PC3	2.29	1.86	1.27	0.73	0.39	1.12	1.42	1.35	1.26	1.16	1.09	0.19
PC4	1.58	1.26	0.78	0.41	0.23	0.85	0.94	0.87	0.79	0.72	0.66	0.15
	Double-cross hybrid DKB747 (n=1,720 plants) in the 2009/2010 crop year
PC1	9.20	8.29	6.78	5.13	3.64	3.17	7.03	6.75	6.55	6.35	6.18	0.41
PC2	4.17	2.94	2.08	1.39	1.05	1.55	1.87	1.80	1.70	1.60	1.54	0.20
PC3	2.38	1.92	1.33	0.79	0.56	1.13	1.50	1.39	1.29	1.19	1.13	0.20
PC4	1.71	1.30	0.83	0.44	0.28	0.86	1.05	0.98	0.89	0.81	0.75	0.17

PC	a	b	r²	n_o	ACI(n_o)
	Single-cross hybrid P32R21 (n=361 plants) in the 2008/2009 crop year
PC1	2.41629	-0.00770	0.870	236	0.598
PC2	1.05305	-0.00324	0.848	238	0.282
PC3	0.73308	-0.00179	0.849	274	0.241
PC4	0.59689	-0.00150	0.876	278	0.181
	Three-way cross hybrid DKB566 (n=373 plants) in the 2008/2009 crop year
PC1	2.28036	-0.00751	0.867	230	0.552
PC2	1.03608	-0.00376	0.851	204	0.269
PC3	0.78876	-0.00198	0.872	272	0.250
PC4	0.64283	-0.00156	0.887	294	0.185
	Double-cross hybrid DKB747 (n=416 plants) in the 2008/2009 crop year
PC1	2.57669	-0.00792	0.872	243	0.652
PC2	1.10661	-0.00352	0.851	229	0.300
PC3	0.80294	-0.00226	0.851	241	0.258
PC4	0.65355	-0.00139	0.875	3 11	0.221
	Single-cross hybrid 30F53 (n=1,777 plants) in the 2009/2010 crop year
PC1	1.80228	-0.00590	0.862	231	0.439
PC2	0.81845	-0.00309	0.852	205	0.185
PC3	0.69493	-0.00158	0.882	308	0.208
PC4	0.57522	-0.00104	0.915	372	0.190
	Three-way cross hybrid DKB566 (n=1,693 plants) in the 2009/2010 crop year
PC1	2.09806	-0.00683	0.867	232	0.513
PC2	0.98483	-0.00472	0.860	172	0.172
PC3	0.76152	-0.00150	0.894	344	0.245
PC4	0.60129	-0.00127	0.890	324	0.190
	Double-cross hybrid DKB747 (n=1,720 plants) in the 2009/2010 crop year
PC1	2.25906	-0.00728	0.870	234	0.555
PC2	1.00986	-0.00337	0.855	226	0.248
PC3	0.75625	-0.00148	0.884	344	0.248
PC4	0.60836	-0.00111	0.890	360	0.208
	Overall mean
PC1	-⁽¹⁾	-	0.868	234	0.552
PC2	-	-	0.853	212	0.243
PC3	-	-	0.872	297	0.242
PC4	-	-	0.889	323	0.196

[1] Corresponding author

Brasil

Brasil

Sample size for principal component analysis in corn

Tamanho de amostra para análise de componentes principais em milho

Abstract