---
title: "Sampling"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Sampling}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---
  
```{r, echo = FALSE, message = FALSE, warning=FALSE}
knitr::opts_chunk$set(collapse = T, comment = "#>")
knitr::opts_chunk$set(fig.width=7, fig.height=5)
options(tibble.print_min = 6L, tibble.print_max = 6L)
library(forestmangr)
```


First we'll load up the package and some data:
```{r}
library(forestmangr)
data(exfm1)
data(exfm2)
data(exfm3)
data(exfm4)
data(exfm5)

data_acs_pilot <- as.data.frame(exfm3)
data_acs_def <- as.data.frame(exfm4)
data_ace_pilot <- as.data.frame(exfm1)
data_ace_def <- as.data.frame(exfm2)
data_as <- as.data.frame(exfm5)

```

## Simple Random Sampling

The objective of this example is to survey an area of 46.8 ha using the simple random sampling method. The aimed error is 20%. 10 plots of 3000 m² each were measured for a pilot inventory. The data collected is shown below:
```{r}
data_acs_pilot
```

Now we'll calculate the inventory variables for a 20% error, considering a finite population with the `sprs` function. Area values must be inserted in square meters, and total area values must be in hectares:
```{r}
sprs(data_acs_pilot, "VWB", 3000, 46.8,error = 20, pop = "fin")
```

With these results, we can see that in order to meet the desired error, we'll need 15 more samples. After a new survey was done, this are the new data:
```{r}
data_acs_def
```

Now the definitive inventory can be done:
```{r}
sprs(data_acs_def, "VWB", 3000, 46.8, error = 20, pop = "fin")
```

The desired error was met.

The area values can also be inserted as variables:
```{r}
sprs(data_acs_def, "VWB", "PLOT_AREA", "TOTAL_AREA", 
     error = 20, pop = "fin")
```


It's also possible to run multiple simple random sampling inventories. To demonstrate this, we'll use the example dataset for stratified sampling, but running simple random statistics. We'll still use the `sprs` function, but use the `.groups` argument to run a simple random sampling inventory for each stratum:
```{r}
sprs(data_ace_def, "VWB", "PLOT_AREA", "STRATA_AREA",
     .groups = "STRATA" ,error = 20, pop = "fin")

```


## Stratified Random Sampling

The objective of this example is to survey an area using the stratified random sampling method. The area was divided into 3 strata: one with 14.4 ha and 7 plots, another with 16.4 ha and 8 plots, and another with 14.2 ha and 7 plots. The plots have an area of 1000 square meters. In total, 22 plots were sampled for the pilot inventory. The data is shown below:
```{r}
data_ace_pilot
```

We'll calculate the statistics with an aimed error of 5%, considering a finite population using the `strs` function. Area values can be inserted as a numeric vector, or as a variable. The plot area must be inserted in square meters, and strata area must be in hectares:
```{r}
strs(data_ace_pilot, "VWB", 3000, c(14.4, 16.4, 14.2), 
     strata = "STRATA", error = 5, pop = "fin")
```

Analyzing the first table, we can see that in order to achieve the desired error, we must sample 24 additional plots. 4 in stratum 1, 8 in stratum 2 and 12 in stratum 3.

After a new survey, the new data is shown below:
```{r}
data_ace_def
```

Now we'll run the inventory again, this time with the definitive data:
```{r}
strs(data_ace_def, "VWB", "PLOT_AREA", "STRATA_AREA", 
     strata = "STRATA", error = 5, pop = "fin")
```

The desired error was met.

## Systematic Sampling

Now we'll survey an area of 18 hectares in which 18 plots of 200 m² each were systematically sampled:
```{r}
data_as
```

First, let's see what error we would get, if we used the simple random sampling method:
```{r}
sprs(data_as, "VWB", 200, 18)
```

We got a 22.2% error. Now, let's calculate the sampling error using the method of successive differences, with the `ss_diffs` function. To use this function, the data must be set in the measured order, the plot area must be in square meters, and the total area value must be in hectares.
```{r}
ss_diffs(data_as, "VWB", 200, 18)
```
We got a 4.2% error, which is significantly lower than before.

