# sample.ratio: Demonstrate the ratio estimation in sampling survey In animation: A Gallery of Animations in Statistics and Utilities to Create Animations

## Description

This function demonstrates the advantage of ratio estimation when further information (ratio) about x and y is available.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```sample.ratio( X = runif(50, 0, 5), R = 1, Y = R * X + rnorm(X), size = length(X)/2, p.col = c("blue", "red"), p.cex = c(1, 3), p.pch = c(20, 21), m.col = c("black", "gray"), legend.loc = "topleft", ... ) ```

## Arguments

 `X` the X variable (ancillary) `R` the population ratio Y/X `Y` the Y variable (whose mean we what to estimate) `size` sample size `p.col, p.cex, p.pch` point colors, magnification and symbols for the population and sample respectively `m.col` color for the horizontal line to denote the sample mean of Y `legend.loc` legend location: topleft, topright, bottomleft, bottomright, ... (see `legend`) `...` other arguments passed to `plot.default`

## Details

From this demonstration we can clearly see that the ratio estimation is generally better than the simple sample average when the ratio R really exists, otherwise ratio estimation may not help.

## Value

A list containing

 `X` X population `Y` Y population `R` population ratio `r` ratio calculated from samples `Ybar` population mean of Y `ybar.simple` simple sample mean of Y `ybar.ratio` sample mean of Y via ratio estimation

Yihui Xie

## References

`sample`, `sample.simple`, `sample.cluster`, `sample.strat`, `sample.system`