Calculates sample size for a simple random sampling (SRS)

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

Usage

silv_sample_size_simple(
  x,
  plot_size,
  total_area,
  max_error = 0.05,
  conf_level = 0.95,
  max_iter = 1000,
  quiet = FALSE
)

Arguments

x

vector of the variable measured in the pilot inventory (e.g. basal area, volume)

plot_size

a numeric vector of length one with plot size in squared meters

total_area

total area of the study area in squared meters

max_error

maximum allowed relative error

conf_level

confidence level

max_iter

maximum number of iteration to find the plot size

quiet

if TRUE, messages will be supressed

Value

SimpleSampleSize object

Details

Sample size is very important to be optimized, since a small sample size will entail a higher error, while a huge sample size will entail higher costs. The SRS is typically used for random sampling, although it might be used also for regular sampling. The number of samples is calculated using the expression:

\(n \ge \frac{t^2 \cdot CV^2}{\epsilon^2 + \frac{t^2 \cdot CV^2}{N}}\)

Where:

• t: the value of student's t for given sample size of the pilot inventory

• CV: the coefficient of variation of x

• \(\epsilon\): the relative error (max_error)

• N: the size of the pilot inventory

x is a variable measured in a pilot inventory. Let's say we measure forest variables in 10 pilot plots, aiming at basal area measurement so we have to measure only the DBH. After some calculations, we will have the basal area per hectare in each of the 10 plots. The sample size is then calculated from the variation of these values and the error that we will allow.

Examples

## pilot inventory measuring 4 plots of 25x25 meters
## total forest area 15 ha
## measured variable (x): basal area per hectare
silv_sample_size_simple(
  x          = c(33, 37.5, 42, 35.2),
  plot_size  = 25 * 25,  # squared plot of 25x25
  total_area = 15 * 1e4, # 15 ha
  max_error  = 0.05,
  conf_level = 0.95,
  max_iter   = 100
)
#> 
#> ── Simple Random Sampling ──────────────────────────────────────────────────────
#> Estimating minimum sample size using Simple Random Sampling.
#> 
#> ── Pilot inventory ──
#> 
#> • Plots measured: 4
#> • Plot size: 625 m²
#> • Total area: 15 ha
#> • Coefficient of variation: 10.43%
#> 
#> ── Results ──
#> 
#> • Minimum sampling plots: 18
#> • Maximum allowed error: 5%
#> • Confidence interval: 95% CI [35.08, 38.77]
#> • Sampling effort: 1.2 plots/ha
#> 
#> ℹ Calculations assume simple random sampling across the entire area.
#> <silviculture::SampleSize>
#>  @ sampling_res :List of 4
#>  .. $ min_plots      : num 18
#>  .. $ ci_lo          : num 35.1
#>  .. $ ci_up          : num 38.8
#>  .. $ sampling_effort: num 1.2
#>  @ sampling_opts:List of 5
#>  .. $ pilot_plots: num [1:4] 33 37.5 42 35.2
#>  .. $ plot_size  : num 625
#>  .. $ total_area : num 150000
#>  .. $ max_error  : num 0.05
#>  .. $ conf_level : num 0.95