# E.SY: Estimation of the Population Total under Systematic Sampling... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the Horvitz-Thompson estimator of the population total according to an SY sampling design

## Usage

 `1` ```E.SY(N, a, y) ```

## Arguments

 `N` Population size `a` Number of groups dividing the population `y` Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample

## Details

Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation under an SY sampling design

## Value

The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest

## Author(s)

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com

## References

Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.

`S.SY`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# Uses the Lucy data to draw a Systematic sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population is divided in 6 groups # The selected sample sam <- S.SY(N,6) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.SY(N,6,estima) ```

### Example output

```Loading required package: dplyr

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

filter, lag

The following objects are masked from ‘package:base’:

intersect, setdiff, setequal, union

The following objects are masked from Lucy:

Employees, ID, Income, Level, SPAM, Taxes, Ubication, Zone

[1] "ID"        "Ubication" "Level"     "Zone"      "Income"    "Employees"
[7] "Taxes"     "SPAM"
N       Income    Employees        Taxes
Estimation     2394 1.030026e+06 1.502340e+05 27714.000000
Standard Error    0 2.831152e+04 3.303355e+03  1577.105663
CVE               0 2.748622e+00 2.198806e+00     5.690646
DEFF            NaN 1.000000e+00 1.000000e+00     1.000000
```

TeachingSampling documentation built on April 22, 2020, 1:05 a.m.