animation (version 2.4.1)

sample.ratio: Demonstrate the ratio estimation in sampling survey

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

Value

A list containing A list containing

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.

See Also

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

Examples

oopt = ani.options(interval = 2, nmax = ifelse(interactive(), 50, 2))

## 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
saveHTML({
    par(mar = c(4, 4, 1, 0.5), mgp = c(2, 1, 0))
    ani.options(interval = 2, nmax = ifelse(interactive(), 50, 2))
    sample.ratio()
}, img.name = "sample.ratio", htmlfile = "sample.ratio.html", ani.height = 400, 
    ani.width = 500, title = "Demonstration of the Ratio Estimation", 
    description = c("Estimate the mean of Y, making use of the ratio", 
        "Y/X which will generally improve the estimation."))

ani.options(oopt)