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#############################################################
# #
# Original Splus: Ulric Lund #
# E-mail: ulund@calpoly.edu #
# #
#############################################################
#############################################################
# #
# rao.test function #
# Author: Claudio Agostinelli #
# E-mail: claudio@unive.it #
# Date: May, 31, 2006 #
# Version: 0.3-1 #
# #
# Copyright (C) 2006 Claudio Agostinelli #
# #
#############################################################
rao.test <- function(..., alpha = 0) {
y <- list(...)
x <- list()
for (i in 1:length(y)) {
if (is.data.frame(y[[i]])) {
x <- c(x, as.list(y[[i]]))
} else if (is.matrix(y[[i]])) {
for (j in 1:ncol(y[[i]])) {
x <- c(x, list(y[[i]][,j]))
}
} else if (is.list(y[[i]])) {
x <- c(x, y[[i]])
} else {
x <- c(x, list(y[[i]]))
}
}
if (length(x)<2)
stop("There must be at least two samples")
for (i in 1:length(x)) {
x[[i]] <- conversion.circular(x[[i]], units="radians", zero=0, rotation="counter", modulo="2pi")
attr(x[[i]], "circularp") <- attr(x[[i]], "class") <- NULL
}
if (!any(c(0, 0.01, 0.025, 0.05, 0.1, 0.15)==alpha))
stop("'alpha' must be one of the following values: 0, 0.01, 0.025, 0.05, 0.1, 0.15")
# Handling missing values
x <- lapply(x, na.omit)
result <- RaoTestRad(x)
result$call <- match.call()
result$alpha <- alpha
class(result) <- "rao.test"
return(result)
}
RaoTestRad <- function(x) {
n <- unlist(lapply(x, length))
k <- length(x)
c.data <- lapply(x, cos)
s.data <- lapply(x, sin)
x <- unlist(lapply(c.data, mean.default))
y <- unlist(lapply(s.data, mean.default))
s.co <- unlist(lapply(c.data, var.default))
s.ss <- unlist(lapply(s.data, var.default))
s.cs <- c(1:k)
for(i in 1:k) {
s.cs[i] <- var.default(c.data[[i]], s.data[[i]])
}
s.polar <- 1/n * (s.ss/x^2 + (y^2 * s.co)/x^4 - (2 * y * s.cs)/x^3)
tan <- y/x
H.polar <- sum(tan^2/s.polar) - (sum(tan/s.polar))^2/sum(1/s.polar)
U <- x^2 + y^2
s.disp <- 4/n * (x^2 * s.co + y^2 * s.ss + 2 * x * y * s.cs)
H.disp <- sum(U^2/s.disp) - (sum(U/s.disp))^2/sum(1/s.disp)
result <- list()
result$statistic <- c(H.polar, H.disp)
result$df <- k-1
result$p.value <- c((1 - pchisq(H.polar, k - 1)), (1 - pchisq(H.disp, k - 1)))
return(result)
}
#############################################################
# #
# print.rao.test function #
# Author: Claudio Agostinelli #
# E-mail: claudio@unive.it #
# Date: November, 19, 2003 #
# Version: 0.1-1 #
# #
# Copyright (C) 2003 Claudio Agostinelli #
# #
#############################################################
print.rao.test <- function(x, digits=4, ...) {
statistic <- x$statistic
p.value <- x$p.value
alpha <- x$alpha
df <- x$df
cat("\n")
cat("Rao's Tests for Homogeneity", "\n")
if(alpha == 0) {
cat("\n")
cat(" Test for Equality of Polar Vectors:", "\n", "\n")
cat("Test Statistic =", round(statistic[1], digits=digits), "\n")
cat("Degrees of Freedom =", df, "\n")
cat("P-value of test =", round(p.value[1], digits=digits), "\n", "\n")
cat(" Test for Equality of Dispersions:", "\n", "\n")
cat("Test Statistic =", round(statistic[2], digits=digits), "\n")
cat("Degrees of Freedom =", df, "\n")
cat("P-value of test =", round(p.value[2], digits=digits), "\n", "\n")
} else {
cat("\n")
cat(" Test for Equality of Polar Vectors:", "\n", "\n")
cat("Test Statistic =", round(statistic[1], digits=digits), "\n")
cat("Degrees of Freedom =", df, "\n")
cat("Level", alpha, "critical value =", round(qchisq(1 - alpha, df), digits=digits), "\n")
if (statistic[1] > qchisq(1 - alpha, df)) {
cat("Reject null hypothesis of equal polar vectors", "\n", "\n")
} else {
cat("Do not reject null hypothesis of equal polar vectors", "\n", "\n")
}
cat(" Test for Equality of Dispersions:", "\n", "\n")
cat("Test Statistic =", round(statistic[2], digits=digits), "\n")
cat("Degrees of Freedom =", df, "\n")
cat("Level", alpha, "critical value =", round(qchisq(1 - alpha, df), digits=digits), "\n")
if (statistic[2] > qchisq(1 - alpha, df)) {
cat("Reject null hypothesis of equal dispersions", "\n", "\n")
} else {
cat("Do not reject null hypothesis of equal dispersions", "\n", "\n")
}
}
invisible(x)
}
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