Sample size for canonical correlation analysis in corn

Cargnelutti Filho, Alberto; Toebe, Marcos

doi:10.1590/1678-4499.20210335

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Article • Bragantia 81 • 2022 • https://doi.org/10.1590/1678-4499.20210335 copy

Sample size for canonical correlation analysis in corn

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The canonical correlation analysis has been successfully used in many areas aiming to extract important information from a pair of data sets. Thus, the objective of this work was to determine the sample size (number of plants) required to estimate the canonical correlations in corn characteristics. Six characteristics were measured in 361, 373, and 416 plants, respectively, of the single, three-way and double cross hybrids of the 2008/2009 crop year and in 1,777, 1,693, and 1,720 plants, respectively, of the single, three-way, and double cross hybrids (2009/2010 crop) (six cases). The canonical correlation analyses were carried out between characteristics group of the plant architecture (plant height at harvest and ear insertion height) versus grain production (hundred grains mass and grains mass per plant) (scenario 1), and dimensions of ear (ear length and ear diameter) versus grain production (hundred grains mass and grains mass per plant) (scenario 2). The sample size (number of plants) for the estimation of canonical correlations was determined by resampling with replacement and application of the model linear response with plateau. Measuring 270 plants is sufficient to estimate the canonical correlation between groups with two characteristics in each group for corn. This sample size can be used as reference for reliable canonical correlation analysis.

Key words
Zea mays ; multivariate analysis; resampling; model linear response with plateau

	1st canonical pair	2nd canonical pair		1st canonical pair	2nd canonical pair
Single cross hybrid P32R21 (n = 361 plants) in the 2008/2009 crop year
Correlation	0.3986^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.0330ns	Correlation	0.9153^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.2597^* * Significant by the χ2 test at 5% probability of error; ns: not significant.
Characteristics	Canonical coefficients		Characteristics	Canonical coefficients
PH	-0.9044	0.8841	EL	0.5100	-1.0979
EIH	-0.1453	-1.2564	ED	0.6195	1.0401
HGM	-0.3298	-1.1398	HGM	-0.0167	1.1864
GM	-0.7831	0.8914	GM	1.0089	-0.6245
Three-way cross hybrid DKB566 (n = 373 plants) in the 2008/2009 crop year
Correlation	0.3464^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.1228^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	Correlation	0.9158^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.0496ns
Characteristics	Canonical coefficients		Characteristics	Canonical coefficients
PH	-0.7144	1.3099	EL	0.5485	-1.2100
EIH	-0.3477	-1.4510	ED	0.5497	1.2095
HGM	-0.3731	1.0666	HGM	0.0810	1.1270
GM	-0.7702	-0.8268	GM	0.9597	-0.5964
Double cross hybrid DKB747 (n = 416 plants) in the 2008/2009 crop year
Correlation	0.4834^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.0077ns	Correlation	0.9198^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.0624ns
Characteristics	Canonical coefficients		Characteristics	Canonical coefficients
PH	-0.8600	1.1737	EL	-0.5945	1.1171
EIH	-0.1819	-1.4437	ED	-0.5185	-1.1543
HGM	-0.2449	-1.2014	HGM	-0.0077	-1.2261
GM	-0.8382	0.8949	GM	-0.9955	0.7157
Single cross hybrid 30F53 (n = 1,777 plants) in the 2009/2010 crop year
Correlation	0.6158^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.0853^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	Correlation	0.9487^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.1193^* * Significant by the χ2 test at 5% probability of error; ns: not significant.
Characteristics	Canonical coefficients		Characteristics	Canonical coefficients
PH	-1.2004	-0.2622	EL	-0.6398	1.4073
EIH	0.9109	-0.8246	ED	-0.4225	-1.4870
HGM	-0.0547	1.1413	HGM	0.0801	1.1398
GM	-0.9724	-0.6000	GM	-1.0363	-0.4813
Three-way cross hybrid DKB566 (n = 1,693 plants) in the 2009/2010 crop year
Correlation	0.3596^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.1025^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	Correlation	0.9111^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.0840^* * Significant by the χ2 test at 5% probability of error; ns: not significant.
Characteristics	Canonical coefficients		Characteristics	Canonical coefficients
PH	-1.3258	-0.2382	EL	0.4271	-1.1959
EIH	1.0650	-0.8247	ED	0.6785	1.0733
HGM	-0.5523	1.0469	HGM	-0.0243	-1.1834
GM	-0.5889	-1.0268	GM	1.0128	0.6127
Double cross hybrid DKB747 (n = 1,720 plants) in the 2009/2010 crop year
Correlation	0.3127^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.0229ns	Correlation	0.8875^* * Significant by the χ2 test at 5% probability of error; ns: not significant.	0.1838^* * Significant by the χ2 test at 5% probability of error; ns: not significant.
Characteristics	Canonical coefficients		Characteristics	Canonical coefficients
PH	-1.3433	0.7676	EL	0.4895	-1.1796
EIH	0.5288	-1.4539	ED	0.6192	1.1169
HGM	-0.4983	0.9939	HGM	0.0841	-1.1086
GM	-0.6761	-0.8826	GM	0.9604	0.5601

Characteristics	Correlation	P_97.5%	Mean	P_2.5%	ACI	P_97.5%	Mean	P_2.5%	ACI
		---------- n = 10 plants ----------				---------- n = 1,000 plants ----------
Single cross hybrid P32R21 in the 2008/2009 crop year
Architecture vs. grains	CC1	0.9402	0.6742	0.2966	0.6436	0.4630	0.4006	0.3378	0.1252
Architecture vs. grains	CC2	0.5944	0.2280	0.0087	0.5857	0.0886	0.0365	0.0017	0.0869
Ear vs. grains	CC1	0.9914	0.9429	0.8227	0.1687	0.9251	0.9156	0.9051	0.0201
Ear vs. grains	CC2	0.7921	0.3664	0.0196	0.7725	0.3258	0.2597	0.1914	0.1344
Three-way cross hybrid DKB566 in the 2008/2009 crop year
Architecture vs. grains	CC1	0.9237	0.6596	0.2907	0.6331	0.4136	0.3498	0.2892	0.1244
Architecture vs. grains	CC2	0.6113	0.2286	0.0091	0.6023	0.1823	0.1222	0.0641	0.1182
Ear vs. grains	CC1	0.9938	0.9431	0.7844	0.2094	0.9275	0.9161	0.9038	0.0237
Ear vs. grains	CC2	0.7567	0.3181	0.0136	0.7430	0.1114	0.0516	0.0034	0.1080
Double cross hybrid DKB747 in the 2008/2009 crop year
Architecture vs. grains	CC1	0.9383	0.6890	0.3247	0.6135	0.5399	0.4855	0.4316	0.1083
Architecture vs. grains	CC2	0.6262	0.2442	0.0127	0.6135	0.0776	0.0272	0.0009	0.0767
Ear vs. grains	CC1	0.9917	0.9389	0.7812	0.2105	0.9291	0.9199	0.9099	0.0192
Ear vs. grains	CC2	0.7475	0.2940	0.0125	0.7350	0.1267	0.0638	0.0068	0.1199
Single cross hybrid 30F53 in the 2009/2010 crop year
Architecture vs. grains	CC1	0.9563	0.7577	0.4138	0.5424	0.6593	0.6178	0.5730	0.0863
Architecture vs. grains	CC2	0.6592	0.2558	0.0095	0.6497	0.1436	0.0852	0.0253	0.1183
Ear vs. grains	CC1	0.9951	0.9655	0.8715	0.1236	0.9567	0.9490	0.9396	0.0171
Ear vs. grains	CC2	0.7795	0.3179	0.0136	0.7658	0.1900	0.1192	0.0468	0.1432
Three-way cross hybrid DKB566 in the 2009/2010 crop year
Architecture vs. grains	CC1	0.9193	0.6658	0.3178	0.6014	0.4194	0.3632	0.3051	0.1143
Architecture vs. grains	CC2	0.6287	0.2358	0.0083	0.6204	0.1700	0.1013	0.0276	0.1425
Ear vs. grains	CC1	0.9908	0.9424	0.8242	0.1666	0.9212	0.9115	0.9003	0.0209
Ear vs. grains	CC2	0.7415	0.3102	0.0141	0.7274	0.1539	0.0842	0.0160	0.1379
Double cross hybrid DKB747 in the 2009/2010 crop year
Architecture vs. grains	CC1	0.9131	0.6371	0.2871	0.6260	0.3757	0.3157	0.2586	0.1171
Architecture vs. grains	CC2	0.5667	0.2089	0.0062	0.5605	0.0823	0.0309	0.0016	0.0807
Ear vs. grains	CC1	0.9892	0.9251	0.7428	0.2465	0.9023	0.8878	0.8714	0.0309
Ear vs. grains	CC2	0.7669	0.3299	0.0131	0.7538	0.2480	0.1836	0.1162	0.1318

Characteristics	Correlation	a	b	r²	n_o	ACI(n_o)
Single cross hybrid P32R21 (n = 361 plants) in the 2008/2009 crop year
Architecture vs. grains	CC1	0.51070	-0.00109	0.910	325	0.156
Architecture vs. grains	CC2	0.38041	-0.00131	0.853	205	0.111
Ear vs. grains	CC1	0.11653	-0.00042	0.860	211	0.027
Ear vs. grains	CC2	0.56364	-0.00112	0.915	348	0.173
Three-way cross hybrid DKB566 (n = 373 plants) in the 2008/2009 crop year
Architecture vs. grains	CC1	0.48426	-0.00099	0.901	332	0.154
Architecture vs. grains	CC2	0.34106	-0.00042	0.864	486	0.138
Ear vs. grains	CC1	0.13183	-0.00047	0.857	215	0.032
Ear vs. grains	CC2	0.51376	-0.00229	0.849	164	0.139
Double cross hybrid DKB747 (n = 416 plants) in the 2008/2009 crop year
Architecture vs. grains	CC1	0.49703	-0.00121	0.904	295	0.141
Architecture vs. grains	CC2	0.39674	-0.00129	0.864	230	0.100
Ear vs. grains	CC1	0.13154	-0.00060	0.844	174	0.027
Ear vs. grains	CC2	0.48876	-0.00194	0.843	176	0.148
Single cross hybrid 30F53 (n=1,777 plants) in the 2009/2010 crop year
Architecture vs. grains	CC1	0.42172	-0.00116	0.891	266	0.114
Architecture vs. grains	CC2	0.41754	-0.00117	0.824	229	0.150
Ear vs. grains	CC1	0.09173	-0.00030	0.877	231	0.023
Ear vs. grains	CC2	0.47266	-0.00094	0.823	309	0.181
Three-way cross hybrid DKB566 (n = 1,693 plants) in the 2009/2010 crop year
Architecture vs. grains	CC1	0.46799	-0.00100	0.899	321	0.146
Architecture vs. grains	CC2	0.36754	-0.00054	0.818	371	0.167
Ear vs. grains	CC1	0.11281	-0.00038	0.861	226	0.028
Ear vs. grains	CC2	0.49731	-0.00161	0.841	203	0.169
Double cross hybrid DKB747 (n = 1,720 plants) in the 2009/2010 crop year
Architecture vs. grains	CC1	0.47434	-0.00099	0.900	329	0.147
Architecture vs. grains	CC2	0.34475	-0.00108	0.845	226	0.101
Ear vs. grains	CC1	0.17481	-0.00062	0.862	216	0.042
Ear vs. grains	CC2	0.48840	-0.00087	0.891	378	0.161
Overall mean
Architecture vs. grains	CC1	-^* * Overall mean not calculated.	-	0.901	311	0.143
Architecture vs. grains	CC2	-	-	0.845	291	0.128
Ear vs. grains	CC1	-	-	0.860	212	0.030
Ear vs. grains	CC2	-	-	0.860	263	0.162

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