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

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

Author(s)

Yihui Xie

References

Examples at https://yihui.org/animation/example/sample-ratio/

See Also

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

animation documentation built on Oct. 7, 2021, 9:18 a.m.