animation (version 1.1-4)

sample.ratio: Demonstrate the Ratio Estimation in Sampling Survey...

Description

Demonstrate the Ratio Estimation in Sampling Survey Demonstrate the advantage of ratio estimation when further information (ratio) about x and y is available.

Usage

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

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

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.

References

http://animation.yihui.name/samp:ratio_estimation

See Also

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

Examples

oopt = ani.options(interval = 2, nmax = 50)
## observe the location of the red line (closer to the population mean)
res = sample.ratio()
## absolute difference with the true mean
matplot(abs(cbind(res$ybar.ratio, res$ybar.simple) -
res$Ybar), type = "l")
legend("topleft", c("Ratio Estimation", "Sample Average"),
lty = 1:2, col = 1:2)

## if the ratio does not actually exist:
sample.ratio(X = rnorm(50), Y = rnorm(50))
## ratio estimation may not be better than the simple average

## HTML animation page
ani.options(ani.height = 400, ani.width = 500, nmax = 50,
interval = 2, title = "Demonstration of the Ratio Estimation",
description = "Estimate the mean of Y, making use of the ratio
Y/X which will generally improve the estimation.")
ani.start()
par(mar = c(4, 4, 1, 0.5), mgp = c(2, 1, 0))
sample.ratio()
ani.stop()
ani.options(oopt)