Sampling sufficiency, correlation and path analysis in forage pea

Cargnelutti Filho, Alberto; Neu, Ismael Mario Márcio; Loro, Murilo Vieira; Bubans, Valéria Escaio; Ortiz, Vithória Morena

doi:10.1590/0103-8478cr20220579

Brasil

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Crop production • Cienc. Rural 54 (3) • 2024 • https://doi.org/10.1590/0103-8478cr20220579 linkcopy

Sampling sufficiency, correlation and path analysis in forage pea

Suficiência amostral, correlação e análise de trilha em ervilha forrageira

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT:

It is important to determine the number of plants to be evaluated to allow accurate inferences about the traits under evaluation. Investigating the linear relations among traits is important for identifying traits for indirect selection. So, the objectives of this study were to determine the sample size (number of plants) necessary to estimate the means of forage pea traits and to investigate the relations among the traits. Experiments were carried out in 2021 with three sowing dates (May 3, May 26 and July 13). Five hundred plants were randomly sampled, 100 plants in each of the five evaluation dates (June 25, August 30, July 24, September 17, September 16). In these 500 plants, the traits plant height, number of branches, number of nodes, number of leaves, number of pods, fresh matter of leaves, fresh matter of stems, fresh matter of pods, fresh matter of shoots, dry matter of leaves, dry matter of stems, dry matter of pods, and dry matter of shoots, were evaluated. The sample size was calculated to estimate the means of these traits, based on Student’s t-distribution, and the relations among traits were investigated through correlation and path analysis. In an experiment, to estimate the means of these 13 traits of forage pea, with an estimation error of approximately 10% of the mean, 99 plants per treatment should be sampled. The numbers of pods and leaves have a positive linear relations with fresh and dry matter of shoots.

Key words: Pisum sativum subsp. arvense (L.) Poir; linear relations; number of plants; sample sizing.

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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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[TFN1] ⁽¹⁾ PH - plant height, in cm; NB - number of branches; NN - number of nodes; NL - number of leaves; NP - number of pods; FML - fresh matter of leaves, in g plant^-1; FMS - fresh matter of stems, in g plant^-1; FMP - fresh matter of pods, in g plant^-1; FMSH - fresh matter of shoots (FMSH = FML + FMS + FMP), in g plant^-1; DML - dry matter of leaves, in g plant^-1; DMS - dry matter of stems, in g plant^-1; DMP - dry matter of pods, in g plant^-1; and DMSH - dry matter of shoots (DMSH = DML + DMS + DMP), in g plant^-1.

Statistic	PH	NB	NN	NL	NP	FML	FMS	FMP	FMSH	DML	DMS	DMP	DMSH
-----------------------------------------------------Sowing on May 03 and evaluation on June 25 - 53 days after sowing----------------------------------------------------------
Minimum	14.00	2.00	7.00	15.00	-	2.43	2.02	-	4.76	0.22	0.16	-	0.42
Median	22.00	4.00	11.00	38.50	-	5.47	5.52	-	11.20	0.57	0.49	-	1.06
Mean	21.77	3.59	10.71	38.46	-	5.79	5.94	-	11.73	0.59	0.52	-	1.11
Maximum	29.00	5.00	14.00	68.00	-	12.65	12.65	-	25.30	1.12	1.02	-	2.10
Standard deviation	2.98	0.84	1.34	10.53	-	2.11	2.22	-	4.28	0.21	0.18	-	0.37
CV(%)	13.71	23.45	12.54	27.37	-	36.40	37.34	-	36.51	35.59	35.73	-	33.70
Skewness	-0.10	-0.24	-0.14	0.15	-	0.76	0.76	-	0.75	0.43	0.63	-	0.41
P-value	0.359	0.000	0.008	0.825	-	0.615	0.454	-	0.611	0.709	0.167	-	0.674
----------------------------------------------------Sowing on May 03 and evaluation on August 30 - 119 days after sowing---------------------------------------------------
Minimum	95.00	1.00	15.00	27.00	1.00	3.45	8.96	0.15	19.39	0.58	2.01	0.02	3.65
Median	150.00	1.00	26.00	86.50	11.00	16.29	32.12	10.19	59.76	2.48	6.47	1.33	10.23
Mean	148.91	1.89	24.79	114.00	13.99	20.34	44.99	13.89	79.22	2.90	8.39	1.93	13.23
Maximum	191.00	6.00	31.00	430.00	47.00	65.69	167.84	61.96	252.74	8.98	26.36	10.19	39.70
Standard deviation	21.75	1.29	3.47	79.71	9.12	12.75	30.00	11.51	49.82	1.78	5.18	1.78	8.06
CV(%)	14.61	68.47	14.01	69.92	65.16	62.66	66.68	82.87	62.89	61.19	61.74	92.32	60.94
Skewness	-0.17	1.52	-0.73	1.77	1.44	1.28	1.50	1.86	1.35	1.31	1.29	2.11	1.34
P-value	0.630	0.000	0.014	0.002	0.006	0.004	0.001	0.002	0.008	0.048	0.002	0.003	0.016
---------------------------------------------------Sowing on May 26 and evaluation on July 24 - 59 days after sowing---------------------------------------------------------
Minimum	13.00	1.00	7.00	11.00	-	1.04	1.30	-	2.40	0.14	0.17	-	0.33
Median	19.00	2.00	12.00	23.50	-	2.38	2.93	-	5.19	0.38	0.38	-	0.76
Mean	18.87	2.01	11.30	24.73	-	2.70	3.08	-	5.78	0.39	0.40	-	0.79
Maximum	25.00	4.00	13.00	50.00	-	6.14	6.66	-	12.64	0.75	0.79	-	1.53
Standard deviation	2.56	0.97	1.03	7.63	-	1.14	1.27	-	2.37	0.14	0.14	-	0.27
CV(%)	13.57	48.22	9.11	30.84	-	42.18	41.32	-	41.06	34.68	34.88	-	34.05
Skewness	0.04	0.39	-1.37	0.76	-	1.20	1.06	-	1.16	0.65	0.65	-	0.67
P-value	0.273	0.000	0.000	0.272	-	0.056	0.284	-	0.054	0.253	0.332	-	0.521
-----------------------------------------------Sowing on May 26 and evaluation on September 17 - 114 days after sowing----------------------------------------------------
Minimum	106.00	2.00	17.00	20.00	0.00	3.31	15.79	0.00	20.95	0.60	3.05	0.00	3.84
Median	160.25	4.00	23.00	70.50	8.00	14.26	49.29	7.60	73.51	2.24	11.04	1.02	14.87
Mean	157.33	3.71	23.02	97.45	10.35	17.30	55.28	11.47	84.05	2.57	12.41	1.64	16.61
Maximum	210.00	7.00	30.00	369.00	45.00	56.85	145.06	46.03	230.06	8.39	32.34	6.52	43.09
Standard deviation	21.64	1.31	2.98	74.75	8.90	11.51	29.05	10.79	47.69	1.63	6.03	1.60	8.55
CV(%)	13.76	35.38	12.97	76.71	86.00	66.51	52.55	94.11	56.74	63.25	48.60	97.98	51.48
Skewness	-0.24	0.64	0.08	1.84	1.17	1.54	1.38	1.10	1.38	1.48	1.26	1.10	1.25
P-value	0.526	0.001	0.649	0.001	0.100	0.020	0.110	0.017	0.011	0.018	0.117	0.012	0.007
-------------------------------------------------Sowing on July 13 and evaluation on September 16 - 65 days after sowing----------------------------------------------------
Minimum	25.00	2.00	7.00	27.00	-	2.07	3.09	-	5.16	0.31	0.39	-	0.70
Median	43.00	3.00	13.00	66.50	-	8.12	12.36	-	20.51	1.23	1.95	-	3.16
Mean	42.31	3.25	12.78	72.99	-	8.47	13.49	-	21.97	1.27	2.04	-	3.31
Maximum	62.50	6.00	18.00	170.00	-	21.61	32.44	-	52.62	2.93	4.37	-	7.30
Standard deviation	8.01	1.05	1.99	28.02	-	3.25	5.61	-	8.77	0.46	0.85	-	1.27
CV(%)	18.92	32.25	15.55	38.39	-	38.33	41.58	-	39.94	36.05	41.51	-	38.43
Skewness	0.17	0.45	-0.04	1.26	-	1.05	0.91	-	0.95	0.62	0.66	-	0.63
P-value	0.974	0.000	0.034	0.213	-	0.391	0.455	-	0.421	0.188	0.683	-	0.649

Error	PH	NB	NN	NL	NP	FML	FMS	FMP	FMSH	DML	DMS	DMP	DMSH
-----------------------------------------------------------Sowing on May 03 and evaluation on June 25 - 53 days after sowing---------------------------------------------------------
2%	185	542	155	738	-	1304	1373	-	1313	1247	1257	-	1118
4%	47	136	39	185	-	326	344	-	329	312	315	-	280
6%	21	61	18	82	-	145	153	-	146	139	140	-	125
8%	12	34	10	47	-	82	86	-	83	78	79	-	70
10%	8	22	7	30	-	53	55	-	53	50	51	-	45
15%	4	10	3	14	-	24	25	-	24	23	23	-	20
20%	2	6	2	8	-	14	14	-	14	13	13	-	12
Error (%)⁽²⁾	2.72	4.65	2.49	5.43	-	7.22	7.41	-	7.25	7.06	7.09	-	6.69
---------------------------------------------------------Sowing on May 03 and evaluation on August 30 - 119 days after sowing-----------------------------------------------------
2%	211	4615	194	4813	4180	3865	4377	6760	3894	3686	3753	8390	3656
4%	53	1154	49	1204	1045	967	1095	1690	974	922	939	2098	914
6%	24	513	22	535	465	430	487	752	433	410	417	933	407
8%	14	289	13	301	262	242	274	423	244	231	235	525	229
10%	9	185	8	193	168	155	176	271	156	148	151	336	147
15%	4	83	4	86	75	69	78	121	70	66	67	150	65
20%	3	47	2	49	42	39	44	68	39	37	38	84	37
Error (%)	2.90	13.59	2.78	13.87	12.93	12.43	13.23	16.44	12.48	12.14	12.25	18.32	12.09
-------------------------------------------------------------Sowing on May 26 and evaluation on July 24 - 59 days after sowing-------------------------------------------------------
2%	182	2289	82	937	-	1751	1681	-	1660	1185	1198	-	1142
4%	46	573	21	235	-	438	421	-	415	297	300	-	286
6%	21	255	10	105	-	195	187	-	185	132	134	-	127
8%	12	144	6	59	-	110	106	-	104	75	75	-	72
10%	8	92	4	38	-	71	68	-	67	48	48	-	46
15%	4	41	2	17	-	32	30	-	30	22	22	-	21
20%	2	23	1	10	-	18	17	-	17	12	12	-	12
Error (%)	2.69	9.57	1.81	6.12	-	8.37	8.20	-	8.15	6.88	6.92	-	6.76
------------------------------------------------------Sowing on May 26 and evaluation on September 17 - 114 days after sowing-------------------------------------------------
2%	187	1233	166	5792	7279	4354	2718	8718	3169	3938	2326	9450	2609
4%	47	309	42	1448	1820	1089	680	2180	793	985	582	2363	653
6%	21	137	19	644	809	484	302	969	353	438	259	1050	290
8%	12	78	11	362	455	273	170	545	199	247	146	591	164
10%	8	50	7	232	292	175	109	349	127	158	94	378	105
15%	4	22	3	103	130	78	49	155	57	71	42	168	47
20%	2	13	2	58	73	44	28	88	32	40	24	95	27
Error (%)	2.73	7.02	2.57	15.22	17.06	13.20	10.43	18.67	11.26	12.55	9.64	19.44	10.22
--------------------------------------------------------Sowing on July 13 and evaluation on September 16 - 65 days after sowing--------------------------------------------------
2%	353	1024	239	1451	-	1447	1702	-	1571	1280	1697	-	1454
4%	89	256	60	363	-	362	426	-	393	320	425	-	364
6%	40	114	27	162	-	161	190	-	175	143	189	-	162
8%	23	64	15	91	-	91	107	-	99	80	107	-	91
10%	15	41	10	59	-	58	69	-	63	52	68	-	59
15%	7	19	5	26	-	26	31	-	28	23	31	-	26
20%	4	11	3	15	-	15	18	-	16	13	17	-	15
Error (%)	3.75	6.40	3.09	7.62	-	7.61	8.25	-	7.93	7.15	8.24	-	7.63

----------------Sowing on May 03 and evaluation on June 25 - above the diagonal. Sowing on May 03 and evaluation on August 30 - below the diagonal-------------
	PH	NB	NN	NL	NP	FML	FMS	FMP	FMSH	DML	DMS	DMP	DMSH
PH	1	0.07	0.06	0.17	-	0.29	0.29	-	0.29	0.33	0.26	-	0.32
NB	0.10	1	-0.02	0.55	-	0.52	0.52	-	0.52	0.42	0.45	-	0.46
NN	0.62	-0.10	1	0.24	-	0.19	0.25	-	0.22	0.03	0.16	-	0.10
NL	0.07	0.63	0.10	1		0.60	0.57	-	0.59	0.44	0.54	-	0.51
NP	0.02	0.62	0.08	0.80	1	-	-	-	-	-	-	-	-
FML	0.15	0.74	0.09	0.87	0.80	1	0.96	-	0.99	0.81	0.90	-	0.90
FMS	0.23	0.83	0.04	0.75	0.69	0.93	1	-	0.99	0.75	0.93	-	0.89
FMP	-0.14	0.41	0.05	0.71	0.85	0.72	0.53	1	-	-	-	-	-
FMSH	0.15	0.78	0.06	0.84	0.81	0.98	0.96	0.74	1	0.79	0.93	-	0.90
DML	0.11	0.70	0.09	0.89	0.82	0.98	0.87	0.79	0.96	1	0.79	-	0.95
DMS	0.21	0.81	0.07	0.78	0.76	0.95	0.99	0.64	0.98	0.91	1	-	0.94
DMP	-0.18	0.34	0.04	0.68	0.79	0.65	0.45	0.99	0.66	0.74	0.56	1	-
DMSH	0.12	0.75	0.07	0.85	0.84	0.97	0.93	0.80	0.99	0.97	0.97	0.74	1
-------------Sowing on May 26 and evaluation on July 24 - above the diagonal. Sowing on May 26 and evaluation on September 17 - below the diagonal-------------
	PH	NB	NN	NL	NP	FML	FMS	FMP	FMSH	DML	DMS	DMP	DMSH
PH	1	-0.02	0.52	0.19	-	0.40	0.43	-	0.42	0.42	0.44	-	0.44
NB	0.09	1	-0.12	0.68	-	0.68	0.71	-	0.71	0.67	0.70	-	0.70
NN	0.33	0.08	1	0.10	-	0.14	0.14	-	0.14	0.16	0.14	-	0.15
NL	0.08	0.40	-0.09	1		0.79	0.78	-	0.79	0.75	0.77	-	0.78
NP	-0.16	0.25	-0.11	0.63	1	-	-	-	-	-	-	-	-
FML	0.12	0.56	-0.16	0.87	0.70	1	0.94	-	0.98	0.94	0.89	-	0.93
FMS	0.16	0.61	-0.13	0.79	0.66	0.94	1	-	0.99	0.91	0.96	-	0.96
FMP	-0.20	0.21	-0.12	0.64	0.95	0.67	0.61	1	-	-	-	-	-
FMSH	0.08	0.55	-0.15	0.83	0.79	0.97	0.98	0.76	1	0.94	0.94	-	0.96
DML	0.12	0.55	-0.15	0.84	0.71	0.99	0.93	0.68	0.96	1	0.92	-	0.98
DMS	0.13	0.57	-0.15	0.78	0.67	0.90	0.97	0.63	0.95	0.89	1	-	0.98
DMP	-0.25	0.18	-0.08	0.60	0.90	0.60	0.54	0.97	0.69	0.60	0.57	1	-
DMSH	0.07	0.54	-0.15	0.82	0.78	0.94	0.96	0.75	0.98	0.93	0.98	0.70	1
--------------------------------------------------Sowing on July 13 and evaluation on September 16 - above the diagonal----------------------------------------------------
	PH	NB	NN	NL	NP	FML	FMS	FMP	FMSH	DML	DMS	DMP	DMSH
PH	1	0.01	0.29	0.33	-	0.54	0.57	-	0.57	0.49	0.58	-	0.56
NB		1	-0.14	0.73	-	0.57	0.53	-	0.55	0.52	0.48	-	0.51
NN			1	-0.01	-	-0.01	-0.01	-	-0.01	0.12	0.06	-	0.08
NL				1	-	0.82	0.76	-	0.79	0.77	0.74	-	0.77
NP					1	-	-	-	-	-	-	-	-
FML						1	0.96	-	0.98	0.92	0.92	-	0.95
FMS							1	-	0.99	0.88	0.97	-	0.96
FMP								1	-	-	-	-	-
FMSH									1	0.90	0.96	-	0.96
DML										1	0.89	-	0.95
DMS											1	-	0.99
DMP												1	-
DMSH													1

Effect	D1E1	D1E2	D2E1	D2E2	D3E1	D1E1	D1E2	D2E1	D2E2	D3E1
	FMSH	FMSH	FMSH	FMSH	FMSH	DMSH	DMSH	DMSH	DMSH	DMSH
Direct of PH on	0.198	0.103	0.368	0.137	0.410	0.241	0.067	0.387	0.125	0.365
Indirect of PH via NB	0.023	0.035	-0.010	0.024	0.002	0.019	0.027	-0.010	0.023	0.001
Indirect of PH via NN	0.008	-0.021	-0.024	-0.041	-0.030	0.000	-0.007	-0.021	-0.039	-0.003
Indirect of PH via NL	0.061	0.025	0.087	0.034	0.185	0.057	0.024	0.081	0.035	0.202
Indirect of PH via NP	-	0.006	-	-0.075	-	-	0.007	-	-0.072	-
Pearson’s Correlation (r)	0.290^*	0.146ns	0.422^*	0.080ns	0.567^*	0.317^*	0.119ns	0.437^*	0.071ns	0.564^*
Direct of NB on	0.321	0.342	0.402	0.271	0.118	0.265	0.272	0.414	0.264	0.051
Indirect of NB via PH	0.014	0.010	-0.009	0.012	0.006	0.017	0.007	-0.009	0.011	0.005
Indirect of NB via NN	-0.002	0.003	0.006	-0.010	0.015	0.000	0.001	0.005	-0.010	0.001
Indirect of NB via NL	0.192	0.238	0.310	0.160	0.411	0.179	0.233	0.288	0.162	0.447
Indirect of NB via NP	-	0.188	-	0.119	-	-	0.238	-	0.115	-
Pearson’s Correlation (r)	0.525^*	0.782^*	0.708^*	0.552^*	0.550^*	0.461^*	0.751^*	0.699^*	0.543^*	0.505^*
Direct of NN on	0.131	-0.034	-0.046	-0.124	-0.104	0.007	-0.011	-0.040	-0.121	-0.010
Indirect of NN via PH	0.012	0.064	0.193	0.045	0.119	0.015	0.042	0.203	0.041	0.106
Indirect of NN via NB	-0.005	-0.033	-0.050	0.021	-0.017	-0.004	-0.027	-0.052	0.021	-0.007
Indirect of NN via NL	0.085	0.038	0.046	-0.038	-0.006	0.079	0.037	0.043	-0.038	-0.006
Indirect of NN via NP	-	0.024	-	-0.052	-	-	0.030	-	-0.050	-
Pearson’s Correlation (r)	0.224^*	0.058ns	0.143ns	-0.147ns	-0.008ns	0.097ns	0.071ns	0.154ns	-0.147ns	0.082ns
Direct of NL on	0.350	0.375	0.456	0.405	0.564	0.326	0.367	0.425	0.410	0.614
Indirect of NL via PH	0.035	0.007	0.071	0.012	0.135	0.042	0.004	0.074	0.011	0.120
Indirect of NL via NB	0.176	0.217	0.273	0.107	0.086	0.145	0.173	0.281	0.104	0.037
Indirect of NL via NN	0.032	-0.003	-0.005	0.012	0.001	0.002	-0.001	-0.004	0.011	0.000
Indirect of NL via NP	-	0.240	-	0.296	-	-	0.305	-	0.288	-
Pearson’s Correlation (r)	0.593^*	0.835^*	0.795^*	0.832^*	0.786^*	0.515^*	0.848^*	0.776^*	0.824^*	0.772^*
Direct of NP on	-	0.302	-	0.473	-	-	0.383	-	0.459	-
Indirect of NP via PH	-	0.002	-	-0.022	-	-	0.001	-	-0.020	-
Indirect of NP via NB	-	0.213	-	0.068	-	-	0.170	-	0.066	-
Indirect of NP via NN	-	-0.003	-	0.014	-	-	-0.001	-	0.013	-
Indirect of NP via NL	-	0.298	-	0.254	-	-	0.292	-	0.257	-
Pearson’s Correlation (r)	-	0.812^*	-	0.787^*	-	-	0.845^*	-	0.776^*	-
Coefficient of determination	0.462	0.839	0.796	0.888	0.742	0.367	0.847	0.783	0.864	0.705
Residual variable	0.538	0.161	0.204	0.112	0.258	0.633	0.153	0.217	0.136	0.295
Condition number	4.26	11.77	6.08	6.12	8.70	4.26	11.77	6.08	6.12	8.70