Geschrieben von MoMO am 15.02.2013 um 20:17:
Siegel Tukey test
Hallo Leute,
Ich soll im Rahmen einer Seminararbeit einen Code mit der Programmiersprache R schreiben, welcher den Rangsummentest von Siegel Tukey durchführt. Nun bin ich leider Anfänger auf diesem gebiet. ich hab einwenig gegoogelt um mir Inspirationen zu holen und stoße immer wieder auf diesen Code der wohl Allgegenwärtig zu sein scheint:
siegel.tukey <- function(x, y, id.col = FALSE, adjust.median = F,
rnd = -1, alternative = "two.sided", mu = 0, paired = FALSE,
exact = FALSE, correct = TRUE, conf.int = FALSE, conf.level = 0.95) {
###### published on:
# http://www.r-statistics.com/2010/02/siegel-tukey-a-non-parametric-test-for-equality-in-variability-r-code/
## Main author of the function: Daniel Malter
# x: a vector of data
# y: Group indicator (if id.col=TRUE); data of the second
# group (if
# id.col=FALSE). If y is the group indicator it MUST take 0
# or 1 to indicate
# the groups, and x must contain the data for both groups.
# id.col: If TRUE (default), then x is the data column and y
# is the ID column,
# indicating the groups. If FALSE, x and y are both data
# columns. id.col must
# be FALSE only if both data columns are of the same length.
# adjust.median: Should between-group differences in medians
# be leveled before
# performing the test? In certain cases, the Siegel-Tukey
# test is susceptible
# to median differences and may indicate significant
# differences in
# variability that, in reality, stem from differences in
# medians.
# rnd: Should the data be rounded and, if so, to which
# decimal? The default
# (-1) uses the data as is. Otherwise, rnd must be a
# non-negative integer.
# Typically, this option is not needed. However,
# occasionally, differences in
# the precision with which certain functions return values
# cause the merging
# of two data frames to fail within the siegel.tukey
# function. Only then
# rounding is necessary. This operation should not be
# performed if it affects
# the ranks of observations.
# … arguments passed on to the Wilcoxon test. See
# ?wilcox.test
# Value: Among other output, the function returns the data,
# the Siegel-Tukey
# ranks, the associated Wilcoxon’s W and the p-value for a
# Wilcoxon test on
# tie-adjusted Siegel-Tukey ranks (i.e., it performs and
# returns a
# Siegel-Tukey test). If significant, the group with the
# smaller rank sum has
# greater variability.
# References: Sidney Siegel and John Wilder Tukey (1960) “A
# nonparametric sum
# of ranks procedure for relative spread in unpaired
# samples.” Journal of the
# American Statistical Association. See also, David J.
# Sheskin (2004)
# ”Handbook of parametric and nonparametric statistical
# procedures.” 3rd
# edition. Chapman and Hall/CRC. Boca Raton, FL.
# Notes: The Siegel-Tukey test has relatively low power and
# may, under certain
# conditions, indicate significance due to differences in
# medians rather than
# differences in variabilities (consider using the argument
# adjust.median).
# Output (in this order)
# 1. Group medians (after median adjustment if specified)
# 2. Wilcoxon-test for between-group differences in medians
# (after the median
# adjustment if specified)
# 3. Data, group membership, and the Siegel-Tukey ranks
# 4. Mean Siegel-Tukey rank by group (smaller values indicate
# greater
# variability)
# 5. Siegel-Tukey test (Wilcoxon test on tie-adjusted
# Siegel-Tukey ranks)
is.formula <- function(x) class(x) == "formula"
if (is.formula(x)) {
y <- do.call(c, list(as.name(all.vars(x)[2])), envir = parent.frame(2))
x <- do.call(c, list(as.name(all.vars(x)[1])), envir = parent.frame(2)) # I am using parent.frame(2) since if the name of the variable in the equation is 'x', then we will mistakenly get the function in here instead of the vector.
id.col <- TRUE
# print(x)
# print(ls.str())
# data=data.frame(c(x,y),rep(c(0,1),c(length(x),length(y))))
# print(data)
}
if (id.col == FALSE) {
data = data.frame(c(x, y), rep(c(0, 1), c(length(x), length(y))))
} else {
data = data.frame(x, y)
}
names(data) = c("x", "y")
data = data[order(data$x), ]
if (rnd > -1) {
data$x = round(data$x, rnd)
}
if (adjust.median == T) {
cat("\n", "Adjusting medians...", "\n", sep = "")
data$x[data$y == 0] = data$x[data$y == 0] - (median(data$x[data$y ==
0]))
data$x[data$y == 1] = data$x[data$y == 1] - (median(data$x[data$y ==
1]))
}
cat("\n", "Median of group 1 = ", median(data$x[data$y == 0]),
"\n", sep = "")
cat("Median of group 2 = ", median(data$x[data$y == 1]), "\n",
"\n", sep = "")
cat("Testing median differences...", "\n")
print(wilcox.test(data$x[data$y == 0], data$x[data$y == 1]))
# The following must be done for the case when id.col==F
x <- data$x
y <- data$y
cat("Performing Siegel-Tukey rank transformation...", "\n",
"\n")
sort.x <- sort(data$x)
sort.id <- data$y[order(data$x)]
data.matrix <- data.frame(sort.x, sort.id)
base1 <- c(1, 4)
iterator1 <- matrix(seq(from = 1, to = length(x), by = 4)) -
1
rank1 <- apply(iterator1, 1, function(x) x + base1)
iterator2 <- matrix(seq(from = 2, to = length(x), by = 4))
base2 <- c(0, 1)
rank2 <- apply(iterator2, 1, function(x) x + base2)
#print(rank1)
#print(rank2)
if (length(rank1) == length(rank2)) {
rank <- c(rank1[1:floor(length(x)/2)], rev(rank2[1:ceiling(length(x)/2)]))
} else {
rank <- c(rank1[1:ceiling(length(x)/2)], rev(rank2[1:floor(length(x)/2)]))
}
unique.ranks <- tapply(rank, sort.x, mean)
unique.x <- as.numeric(as.character(names(unique.ranks)))
rank.matrix <- data.frame(unique.x, unique.ranks)
ST.matrix <- merge(data.matrix, rank.matrix, by.x = "sort.x",
by.y = "unique.x")
print(ST.matrix)
cat("\n", "Performing Siegel-Tukey test...", "\n", sep = "")
ranks0 <- ST.matrix$unique.ranks[ST.matrix$sort.id == 0]
ranks1 <- ST.matrix$unique.ranks[ST.matrix$sort.id == 1]
cat("\n", "Mean rank of group 0: ", mean(ranks0), "\n", sep = "")
cat("Mean rank of group 1: ", mean(ranks1), "\n", sep = "")
print(wilcox.test(ranks0, ranks1, alternative = alternative,
mu = mu, paired = paired, exact = exact, correct = correct,
conf.int = conf.int, conf.level = conf.level))
}
einiges ist ja oben schon erklärt ich verstehe viele sachen aber überhaupt nicht ein beispiel für eine Ausgabe sieht wie folgt aus:
sort.x sort.id unique.ranks
1. 0 1 2.5
2 . 0 1 2.5
3. 1 1 5.0
4. 4 0 8.5
5. 4 0 8.5
6. 5 0 11.5
7. 5 0 11.5
8. 6 0 8.5
9. 6 0 8.5
10. 9 1 6.0
11. 10 1 2.5
12. 10 1 2.5
Durführung des Siegel-Tukey Tests
Durchschnittsrang Gruppe 0: 9.5
Durchschnittsrang Gruppe 1: 3.5
W = 36, p-value = 0.003601
Den Siegel Tukey Test an sich versteh ich natürlich und das Programm erfüllt seinen Zweck vielleicht könntet ihr mir weiterhelfen in dem ihr einige Befehle kommentiert z.b wie er denn Die Tabbele erstellt usw.
vielen Dank im Voraus und einen schönen Freitag abend wünsch ich noch
