r.dist {asbio} | R Documentation |
Visualize the sampling distribution of Pearson's product moment correlation
Description
Stumbling points for many methods of inference for the true correlation \rho
and for independence are: 1) asymmetry, 2) explicit bounds on \rho
, and 3) dependence on sample size, of the sampling distribution of r.
The functions here allow visualization of these characteristics. The algorithm used for the sampling distribution of r is based on the first two steps in an asymptotic series (see Kenney and Keeping 1951).
Usage
r.dist(rho, r, n)
see.r.dist.tck()
Arguments
rho |
Population correlation |
r |
A numeric vector containing possible estimates of |
n |
Sample size, an integer. |
Details
All distributions are standardized to have an area of one.
Author(s)
Ken Aho
References
Kenney, J. F. and E. S. Keeping (1951) Mathematics of Statistics, Pt. 2, 2nd ed. Van Nostrand, Princeton, NJ.
Weisstein, E. W. (2012) Correlation Coefficient–Bivariate Normal Distribution. From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/CorrelationCoefficientBivariateNormalDistribution.html
See Also
Examples
# dev.new(height=3.5)
op <- par(mfrow=c(1,2),mar=c (0,0,1.5,3), oma = c(5, 4.2, 0, 0))
vals <- r.dist(0.9, seq(-1, 1, .001), 5)
plot(seq(-1, 1, .001), vals, type = "l",ylab = "", xlab = "")
vals <- r.dist(0.5, seq(-1, 1, .001), 5)
lines(seq(-1, 1, .001), vals, lty = 2)
vals <- r.dist(0.0, seq(-1, 1, .001), 5)
lines(seq(-1, 1, .001), vals, lty = 3)
legend("topleft", lty = c(1, 2, 3), title = expression(paste(italic(n)," = 5")),
legend = c(expression(paste(rho, " = 0.9")),expression(paste(rho, " = 0.5")),
expression(paste(rho, " = 0"))),bty = "n")
vals <- r.dist(0.9, seq(-1, 1, .001), 30)
plot(seq(-1, 1, .001), vals, type = "l",xlab= "", ylab= "")
vals <- r.dist(0.5, seq(-1, 1, .001), 30)
lines(seq(-1, 1, .001), vals, lty = 2)
vals <- r.dist(0.0, seq(-1, 1, .001), 30)
lines(seq(-1, 1, .001), vals, lty = 3)
legend("topleft", lty = c(1, 2, 3), title = expression(paste(italic(n)," = 30")),
legend = c(expression(paste(rho, " = 0.9")),expression(paste(rho, " = 0.5")),
expression(paste(rho, " = 0"))), bty = "n")
mtext(side = 2, expression(paste(italic(f),"(",italic(r),")")), outer = TRUE, line = 3)
mtext(side = 1, expression(italic(r)), outer = TRUE, line = 3, at = .45)
par(op)