Re: [R] Jonckheere-Terpstra test
Hello, Can anyone tell me how to write the R script to get the P-value
for the Jonckheere-Terpstra (JT) test? Following is the code I am using.
I cannot get the P-value to print out. Any help would be appreciated.
Thanks. Marie
jt - function(x, alpha=.05){
if(is.list(x) == 0) stop(Please enter a list of vectors.)
k - length(x)
us - matrix(0,k,k)
for(i in 1:(k-1)){
for(j in (i+1):k){
us[i,j] - wilcox.test(x[[j]],
x[[i]])$statistic
}
}
sum(us)
}
con - c(40,35,38,43,44,41)
gpb - c(38,40,47,44,40,42)
gpc - c(48,40,45,43,46,44)
jt(list(con,gpb,gpc))
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Re: [R] Jonckheere-Terpstra test
Hi Marie,
Here is a function that I wrote based on the JT.test function in package
SAGx, to account for missing values and to order based on the groups.
JT.fun - function(y, g) {
nas - is.na(y) | is.na(g)
ord - order(g[!nas])
d - y[!nas][ord]
g - g[!nas][ord]
return (JT.test(data=t(as.matrix(d)),class=g) )
}
Here is an example showing how to use it:
library(SAGx)
y - rnorm(30, mean=rep( c(0,1,2), ea=10) )
grp - rep(1:3, ea=10)
JT.fun( y , grp)
This will give you a two-sided p-value. If your alternative is one-sided then
you divide this p-value by 2.
Hope this helps,
Ravi.
- Original Message -
From: Marie Kraska [EMAIL PROTECTED]
Date: Saturday, March 25, 2006 12:35 pm
Subject: Re: [R] Jonckheere-Terpstra test
Hello, Can anyone tell me how to write the R script to get the P-value
for the Jonckheere-Terpstra (JT) test? Following is the code I am
using.I cannot get the P-value to print out. Any help would be
appreciated.Thanks. Marie
jt - function(x, alpha=.05){
if(is.list(x) == 0) stop(Please enter a list of vectors.)
k - length(x)
us - matrix(0,k,k)
for(i in 1:(k-1)){
for(j in (i+1):k){
us[i,j] - wilcox.test(x[[j]],
x[[i]])$statistic
}
}
sum(us)
}
con - c(40,35,38,43,44,41)
gpb - c(38,40,47,44,40,42)
gpc - c(48,40,45,43,46,44)
jt(list(con,gpb,gpc))
__
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https://stat.ethz.ch/mailman/listinfo/r-help
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guide.html
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RE: [R] Jonckheere-Terpstra test
The Jonckheere-Terpstra test is a distribution-free test for ordered alternatives in a one-way layout. More specifically, assume X_ij = m + t_j + e_ij, i=1,...,n_j and j=1,...,k, where the errors are idependent and identically distributed. Then you can use the Jonckheere-Terpstra to test H_0:t_1=t_2=...=t_k against H_A:t_1=t_2=...=t_k, where at least one of the inequalities is strict. To my knowledge there is no R code for this test but the test statistic is not too hard to calculate (you have to calculate some Mann-Whitney counts) and the p-value can be found in a table - or in case you have many observations you can use a large-sample approximation. The original article appeared in Biometrika, Vol. 41, No. 1/2. (Jun., 1954), pp. 133-145 But it is probably easier to read page 120-123 in Nonparametric statistical methods by Hollander and Wolfe (1973) Wiley Sons. A NOT-distribution-free alternative to this test is described in Biometrika, Vol. 72, No. 2. (Aug., 1985), pp. 476-480. Kim. -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of [EMAIL PROTECTED] Sent: 5. oktober 2003 14:51 To: [EMAIL PROTECTED] Subject: [R] Jonckheere-Terpstra test Hello, can anybody here explain what a Jonckheere-Terpstra test is and whether it is implemented in R? I just know it's a non-parametric test, otherwise I've no clue about it ;-( . Are there alternatives to this test? thanks for help, Arne __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
RE: [R] Jonckheere-Terpstra test
On 06-Oct-03 Kim Mouridsen wrote: The Jonckheere-Terpstra test is a distribution-free test for ordered alternatives in a one-way layout. More specifically, assume X_ij = m + t_j + e_ij,i=1,...,n_j and j=1,...,k, where the errors are idependent and identically distributed. Then you can use the Jonckheere-Terpstra to test H_0:t_1=t_2=...=t_k against H_A:t_1=t_2=...=t_k, where at least one of the inequalities is strict. To be more precise: the Jonkheere test applies where H_A is stochastically increasing in j (P[X_j = x] = P[X_j+1 = x], for all x, with inequality for at least one j). When k=2, the Jonkheere statistic is the same as the Mann-Whitney U. For k 2, it is the sum for j1 = 1:(k-1) of the sum for j2 = (j1+1):k of the Mann-Whitney Us for samples j1 and j2. To apply it cleanly, there is an assumption of no ties (as if variables were continuous). To my knowledge there is no R code for this test but the test statistic is not too hard to calculate (you have to calculate some Mann-Whitney counts) and the p-value can be found in a table - or in case you have many observations you can use a large-sample approximation. I once published an algorithm for the exact distribution in JRSS C (Applied Statistics), 1984, pp. 1-6. This was devised in the days of programmable calculators and 64K 4MHz micros when RAM and computation time were major issues. However, the code is easily implemented and may be as straightforward as any, even now. Let W denote the Jonkheere statistic. To compute the distribution of W over the range 0:M use the following algorithm (which applies as it stands to the M-W U statistic with sample sizes m, n). NOTE that indexing starts at 0. U[M,m,n]: [A] f(0) = 1 ; f(1) = ... = f(M) = 0 [B] If (n+1 M) go to [C] P = min(m+n,M) for( t = (n+1):P ) for( u = M:t ) ## Note reverse order: t = M,M-1,...,t f(u) = f(u) - f(u-t) [C] Q = min(m,M) for( s = 1:Q ) for( u = s:M ) f(u) = f(u) + f(u-s) For Jongkheere with sample sizes n-1, n_2, ... , n_k, let N_i = n_(i+1) + ... + n_k , i = 1, 2, ... , k-1 Run the above first from [A] with m = n_1, n = N_1 and then repeatedly from [B] with m = n_2, n = N_2; ... ; m = n_(k-1), n = N_(k-1) = n_k. At the end, f(0), f(1), ... , f(M) will contain the frequencies (counts) of the numbers of ways in which a value W = 0, 1, ... , M can arise (purely combinatorial). On H_0, all redistributions of sample values are equally likely, so to get the probability distribution divide by the number of all possible reallocations (the combinatorial number of choices of (n_1, n_2, ... , n_k) out of N = sum(n_i)). Or you can compute the complete frequency distribution and divide each term by the sum of all. The above 'algorithmicises' the algebra of the generating function for the counts. Have fun! Ted. E-Mail: (Ted Harding) [EMAIL PROTECTED] Fax-to-email: +44 (0)870 167 1972 Date: 06-Oct-03 Time: 13:10:25 -- XFMail -- __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
Re: [R] Jonckheere-Terpstra test
[EMAIL PROTECTED] writes:
can anybody here explain what a Jonckheere-Terpstra test is and whether it is
implemented in R? I just know it's a non-parametric test, otherwise I've no
clue about it ;-( . Are there alternatives to this test?
Search google.
The third one (at least on my hit) references a description I used
when teaching back in the dark ages. The others seem relevant, too.
best,
-tony
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