SAMPLING METHODS AND NUMBER OF ROUNDWOODS FOR DETERMINING THE MOISTURE CONTENT

Donato, Danilo Barros; Castro, Renato Vinícius Oliveira; Carneiro, Angélica de Cássia Oliveira; Carvalho, Ana Márcia Macedo Ladeira; Vital, Benedito Rocha; Santos, Rosimeire Cavalcante dos

doi:10.1590/1806-90882018000400001

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Articles • Rev. Árvore 42 (4) • 2018 • https://doi.org/10.1590/1806-90882018000400001 copy

SAMPLING METHODS AND NUMBER OF ROUNDWOODS FOR DETERMINING THE MOISTURE CONTENT

MÉTODOGS DE AMOSTRAGEM E NÚMERO DE TORAS DE MADEIRA PARA DETERMINAÇÃO DO TEOR DE UMIDADE

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This study had the objective of comparing two methodologies of sampling, Simple Random Sampling (ACS) and Stratified Random Sampling (ACE) to determine the optimum number of roundwood samples to obtain the moisture content of the population. In order to achieve this goal, different percentages of allowable error (5,10,15 and 20%) were considered for each sampling methodology. In the conduction of this study, the samples were randomly taken from a lot of 250 steres of wood, 144 roundwood of three meters of length and distributed in four classes of diameter. Later, the moisture content of these samples was determined. And, from these values, the population estimates (average, standard deviation, variance, coefficient of variation, and standard error) by ACS and ACE methods, helped to determine the optimum number of roundwood (n) to be sampled from different percentages of allowable error adopted in this study at 95% probability. According to the results, the amount of roundwood to be sampled from ACS for each allowable error 5, 10, 15 and 20% was respectively 214, 55, 25 and 14. For the ACE (proportional allocation) the amount of roundwood was 141, 35, 16 and 9 for ACE (optimal allocation) this number was 136, 34, 15 and 8. It was concluded that the most indicated sampling method for this study, considering the allowable error, was the ACE method.

Keywords:
Simple casual sampling; Stratified casual sampling; Diameter class

Table 2 Results of the estimates of simple random sampling and stratified random sampling.

STATISTICS	ACS	ACE
Total number of roundwoods (N)	4639	4639
Total number of sampling units (n)	144	144
Number of roundwoods per stratum	-	36
Average moisture content (%)	61,84	56,88
t calculated	1,98	1,98
Standard Error	1,95	1,95
Sampling Error	3,86	2,76
Sampling Error (%)	6,24	4,85
Coefficient of Variation (%)	37,88	29,47
Confidence interval of the mean	61,84 ± 3,86	56,88 ± 2,76

Table 3 Number of roundwoods to be sampled per stratum for ACE using the optimal allocation and proportional allocation.

Allowable	Stratum	Diameter	Optimal	Proportional
Error		Class (cm)	Allocation	Allocation
	1	8 - 11	28	38
5%	2	11 - 14	67	69
	3	14 - 17	33	26
	4	17 - 20	8	8
	1	8 - 11	7	10
10%	2	11 - 14	17	17
	3	14 - 17	8	6
	4	17 - 20	2	2
	1	8 - 11	3	4
15%	2	11 - 14	7	8
	3	14 - 17	4	3
	4	17 - 20	1	1
	1	8 - 11	2	2
20%	2	11 - 14	4	4
	3	14 - 17	2	2
	4	17 - 20	0	1

Sociedade de Investigações Florestais Universidade Federal de Viçosa, CEP: 36570-900 - Viçosa - Minas Gerais - Brazil, Tel: (55 31) 3612-3959 - Viçosa - MG - Brazil
E-mail: rarvore@sif.org.br

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[1] *Corresponding author.

Simple Random Sampling Average	Stratified Random Sampling Mean by stratum
$\overset{─}{Y} = \frac{\sum_{i = 1}^{n} Y_{i}}{n}$	$\overset{─}{Y} = \frac{\sum_{j = 1}^{M} N_{j} {\overset{─}{Y}}_{j}}{N}$
Variance	Variance by stratum
$s^{2} = \frac{\sum_{i = 1}^{n} Y_{i}^{2} - \frac{{(\sum_{i = 1}^{n} Y_{i})}^{2}}{n}}{n - 1}$	$S_{j}^{2} = \frac{\sum_{i = 1}^{n_{j}} Y_{ij}^{2} - \frac{{(\sum_{i = 1}^{n_{j}} Y_{ij})}^{2}}{n_{j}}}{n_{j} - 1}$
Standard Deviation	Standard Deviation by stratum
$s = \pm \sqrt{s^{2}}$	$S_{j} = \pm \sqrt{S_{j}^{2}}$
Coefficient of Variation	Coefficient of Variation by stratum
$CV = \pm \frac{s}{\overset{─}{Y}} * 100$	${CV}_{j} = \frac{\sum_{j = 1}^{M} P_{j} S_{j}}{\overset{─}{Y} j} * 100$
Standard Error	Standard Error
$S_{\overset{─}{Y}} = \pm \sqrt{\frac{S^{2}}{n}}$	$S_{\overset{─}{Y}} = \pm \sqrt{S \frac{2}{\overset{─}{Y}}}$
Sampling Error	Sampling Error
$E = S_{\overset{─}{Y}} * t$	$E = s_{\overset{─}{Y}} * t$
Sampling Error (%)	Sampling Error (%)
$E (%) = \frac{E}{\overset{─}{Y}} * 100$	$E (%) = \frac{E}{\overset{─}{Y}} * 100$
Sampling Size	Sampling Size: proportional allocation
$n = \frac{t^{2} * {(CV)}^{2}}{{(E %)}^{2} + \frac{t^{2} * {(CV)}^{2}}{N}}$	$n = \frac{t^{2} * \sum_{j = 1}^{M} P_{j} S_{j}^{2}}{{(E)}^{2} + \frac{t^{2} * \sum_{j = 1}^{M} P_{j} S_{j}^{2}}{N}}$
	Sampling Size: optimal allocation
-	$n = \frac{t^{2} * {(\sum_{j = 1}^{M} P_{j} S_{j})}^{2}}{{(E)}^{2} + \frac{t^{2} * \sum_{j = 1}^{M} P_{j} S_{j}^{2}}{N}}$