Calculates sample size for a stratified sampling — silv_sample_size

Calculates the sample size needed for a stratified inventory, estimated from pilot inventory data.

Usage

silv_sample_size_stratified(
  data,
  x,
  strata,
  total_area,
  plot_size,
  method = "optimal",
  cost = NA,
  max_error = 0.05,
  conf_level = 0.95,
  max_iter = 1000,
  currency = "EUR",
  quiet = FALSE
)

Arguments

data: a data.frame of pilot inventory data
x: name of the variable in data that was measured (e.g. basal area, volume)
strata: name of the variable in data with the name of the stratum
total_area: name of the variable in data with the area of the stratum
plot_size: a numeric vector of length one with plot size in squared meters
method: a charater vector of length one with the id of the method. Available options are optimal, cost, and prop. See details
cost: name of the variable in data with the average cost of measuring one plot of the stratum. Used with method = 'cost' for sample size, and for message output in other methods
max_error: maximum allowed relative error
conf_level: confidence level
max_iter: maximum number of iteration to find the plot size
currency: currency to be shown in console output when using method = 'cost'
quiet: if TRUE, messages will be supressed

Value

S7 StratifiedSampleSize object with:

results: data.frame with the main results by stratum
strata_error: data.frame with maximum absolute error \(\mp\) C.I (max_abs_error, x_min, x_max), and the esimator of the typical error \(\mp\) C.I (sampling error, x_ci_lo, x_ci_hi)
sampling_error: data.frame with the maximum absolute error \(\mp\) C.I (max_abs_error, x_min, x_max), and the typical sampling error of the weighted mean \(\mp\) C.I (sampling error, x_ci_lo, x_ci_hi)
sampling_opts: list with function options

Details

Stratified Sampling calculates the number of plots to be inventored in different strata. For instance, you might have Pinus sylvestris and Pinus pinaster plots in the same forest, and you might want to get the optimal number of plots for field inventory of each stratum, for a given maximum relative error (e.g. 5%), and with a certain level of confidence (e.g 95%). Of course, the area of P. sylvestris will be different than the area occupied by P. pinaster. For instance, the total area of P. sylvestris could be 100 ha, while the area of P. pinaster could be 200 ha. Therefore, you need to create a pilot inventory and measure a variable such as basal area maybe in 5 pilot plots of P. sylvestris and 7 pilot plots of P. pinaster. With that data collected, you can use three stratified sample size methods:

Optimal Allocation with Constant Cost: using method = 'optimal'. The sampling units are distributed within the different strata taking into account the size (e.g. 100 ha vs 200 ha) and the heterogeinity (e.g. differences in basal area). It minimizes the number of sampling units.

\(n = \frac{t^2_{n - m} \cdot (\sum^{j = m}_{j = 1} P_j \cdot s_j)^2 }{\epsilon^2 + \frac{t^2_{n - m} \cdot \sum^{j = m}_{j = 1} P_j \cdot s_j^2}{N}}\)

Optimal Allocation with Variable Cost: using method = 'cost'. This method needs to know the cost of a sampling unit in each strata. It will minimize the cost of the inventory, taking into account the size, the heterogeinity, and the cost of the sampling unit of the strata.

\(n = \frac{t^2_{n-m} \cdot (\sum^{j = m}_{j = 1} \cdot P_j \cdot s_j \cdot \sqrt{c_j}) \cdot (\sum^{j = m}_{j = 1} \cdot \frac{P_j \cdot s_j}{\sqrt{c_j}})}{\epsilon^2 + \frac{t^2_{n - m} \cdot \sum^{j = m}_{j = 1} P_j \cdot s_j^2}{N}}\)

Proportional Allocation: using method = 'prop'. The sampling units are distributed proportional to the size of the strata. In the example, 33% of the estimated sampling units will be allocated to P. sylvestris and 66% to P. pinaster.

\(n = \frac{t^2_{n - m} \cdot \sum^{j = m}_{j = 1} P_j \cdot s_j^2 }{\epsilon^2 + \frac{t^2_{n - m} \cdot \sum^{j = m}_{j = 1} P_j \cdot s_j^2}{N}}\)

Where:

n: estimated sample size
t: the value of student's t
\(P_j\): proportion of pilot plots of \(j^{th}\) strata
\(s_j\): standard deviation of x
\(s_j^2\): variance of x
N: population size (number of plots of plot_size that fit in total_area)
\(\epsilon\): maximum allowed absolute error. Calculated from x and max_error
N: the size of the pilot inventory

Examples

## read pilot inventory ficticious data
data_path <- system.file("extdata/pilot_inventory.csv", package = "silviculture")
inventory_tbl <- read.csv(data_path)

## calculate sample size
sample_size_list <- silv_sample_size_stratified(
  data  = inventory_tbl,
  x     = basal_area,
  strata = stratum,
  total_area = area,
  method = "optimal",
  cost = cost,
  plot_size = 100,
  conf_level = .95,
  max_error = .05
)
#> 
#> ── Pilot inventory ─────────────────────────────────────────────────────────────
#> You are estimating the sample size using a Stratified Sampling using the
#> Optimal Allocation with Constant Cost method.
#> • Pilot inventory: 30 plots
#> • Maximum allowed error: 5%
#> • Total sampling plots: 164
#> • Actual error: 4.97%
#> • Total cost of the inventory: 5725 EUR
#> 
#> ── Operational inventory ───────────────────────────────────────────────────────
#> 
#> ── Stratum - Pinus pinaster ──
#> 
#> • Pilot inventory with 11 plots, in 9 ha
#> • Minimum sampling plots: 46 with a relative error of 3.74% (95% CI [62.56,
#>   67.42])
#> • Sampling effort: 5.1 plots/ha
#> • Cost per hectare: 255 EUR/ha
#> • Total cost: 2300 EUR
#> 
#> 
#> ── Stratum - Pinus radiata ──
#> 
#> • Pilot inventory with 8 plots, in 12 ha
#> • Minimum sampling plots: 71 with a relative error of 4.12% (95% CI [52.85,
#>   57.39])
#> • Sampling effort: 5.9 plots/ha
#> • Cost per hectare: 206.5 EUR/ha
#> • Total cost: 2485 EUR
#> 
#> 
#> ── Stratum - Pinus sylvestris ──
#> 
#> • Pilot inventory with 11 plots, in 7 ha
#> • Minimum sampling plots: 47 with a relative error of 5.6% (95% CI [52.85,
#>   59.13])
#> • Sampling effort: 6.7 plots/ha
#> • Cost per hectare: 134 EUR/ha
#> • Total cost: 940 EUR
#>