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<!DOCTYPE html>
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<title>Load the functions</title>
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<h1>Load the functions</h1>
<pre><code class="r">source('Tw2.R')
ls()
</code></pre>
<pre><code>## [1] "dist.cohen.d" "dist.sigma2" "dist.ss2" "is.dist"
## [5] "Wstar" "Wstar.test" "WT" "WT.mean"
## [9] "WT.test"
</code></pre>
<h1>Univariate case test</h1>
<p>In the univariate case, distance W* is equivalent to the original Welch MANOVA implemented in R with <code>oneway.test</code>. The statistic for the test and distance W* should be the same modulo numerical issues.</p>
<pre><code class="r">set.seed(2.15)
test.one = function(z){
y=rnorm(100)
dm = as.matrix(dist(y))
f=factor(sample(3, 100, replace = T))
Wstar(dm, f) / oneway.test(y~f)$statistic
}
sapply(1:10, test.one)
</code></pre>
<pre><code>## F F F F F F F F F F
## 1 1 1 1 1 1 1 1 1 1
</code></pre>
<h2>Compare theoretical results to W* and PERMANOVA</h2>
<h3>Type I error</h3>
<pre><code class="r">library(vegan); packageVersion("vegan")
</code></pre>
<pre><code>## Loading required package: permute
</code></pre>
<pre><code>## Loading required package: lattice
</code></pre>
<pre><code>## This is vegan 2.4-2
</code></pre>
<pre><code>## [1] '2.4.2'
</code></pre>
<pre><code class="r">simulate.null = function(ns, ef){
y=rnorm(sum(ns), sd=rep(c(1,ef,ef^2), ns))
f = factor(rep(c(1,2,3), ns))
dm = as.matrix(dist(y))
c(Wstar = Wstar.test(dm, f)$p.value, Permanova = adonis(dm~f)$aov.tab[1,6], WelchF = oneway.test(y~f)$p.value)
}
simulate.null(ns=c(5,5,5), ef=1)
</code></pre>
<pre><code>## Wstar Permanova WelchF
## 0.9900000 0.9890000 0.9901083
</code></pre>
<pre><code class="r">n.set = c(5,10,20,40)
ef = c(1, sqrt(0.2), sqrt(0.8))
params = expand.grid(n1=n.set, n2=n.set, n3=n.set,ef=ef, replicates=1:1000)
head(params)
</code></pre>
<pre><code>## n1 n2 n3 ef replicates
## 1 5 5 5 1 1
## 2 10 5 5 1 1
## 3 20 5 5 1 1
## 4 40 5 5 1 1
## 5 5 10 5 1 1
## 6 10 10 5 1 1
</code></pre>
<pre><code class="r">dim(params)
</code></pre>
<pre><code>## [1] 192000 5
</code></pre>
<pre><code class="r">library(foreach); packageVersion("foreach")
</code></pre>
<pre><code>## [1] '1.4.3'
</code></pre>
<pre><code class="r">library(doParallel); packageVersion("doParallel")
</code></pre>
<pre><code>## Loading required package: iterators
</code></pre>
<pre><code>## Loading required package: parallel
</code></pre>
<pre><code>## [1] '1.0.10'
</code></pre>
<pre><code class="r">registerDoParallel(cores=8)
date()
</code></pre>
<pre><code>## [1] "Mon Feb 27 14:30:59 2017"
</code></pre>
<pre><code class="r">res = foreach(i=1:(dim(params)[1]), .combine=rbind) %dopar% {
c(params[i,], simulate.null(params[i,1:3], params[i,4]))
}
date()
</code></pre>
<pre><code>## [1] "Mon Feb 27 23:54:08 2017"
</code></pre>
<pre><code class="r">#colnames(res) = c("Replicate", "n1", "n2", "fracSd", "effect", "adonis.p", "welchT.p", "welchTS.p")
write.table(res, "WStar_null.txt", sep="\t")
</code></pre>
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