title: p-values in pvclust & results in hclust
body: <p>I'm running some cluster analysis and I'm trying to figure out two main things:</p>
  
  <p>1) How to best interpret the results of the p-values in pvclust (what is the null that they are establishing?)</p>
  
  <p>2) How to translate these results to hclust</p>
  
  <p>I'll use the <code>mtcars</code> data set as an example...</p>
  
  <p>In using the <code>pvclust</code> function first (using euclidean distance and complete linkage):</p>
  
  <pre><code>d.pv &lt;- pvclust(t(mtcars), method = "euclidean", 
              method.hclust = "complete", nboot = 10)
  </code></pre>
  
  <p>I then produce my dendrogram and as for red boxes to be placed around significant clusters (alpha = 0.95)</p>
  
  <pre><code>plot(d.pv)
  pvrect(d.pv, alpha = 0.95)
  </code></pre>
  
  <p>I get this figure:</p>
  
  <p><a href="https://i.stack.imgur.com/9KEhz.png" rel="noreferrer"><img src="https://i.stack.imgur.com/9KEhz.png" alt="enter image description here"></a></p>
  
  <p>I can also call up the observations that were significant:</p>
  
  <pre><code>pvpick(team.clus.pv, alpha = 0.95)
  </code></pre>
  
  <p>But what is the significance of these findings? We see two clusters in the dendrogram, so is this significant finding (p = 0.02) that these two clusters differ? Is it that simple?</p>
  
  <p>Since cluster analysis is a descriptive/exploratory technique, what if I built this using the <code>hclust</code> package and specified that I felt there were 3 clusters of interest?</p>
  
  <pre><code>d &lt;- dist(mtcars, method = "euclidean")
  hc &lt;- hclust(d, method = "complete")
  plot(hc)
  rect.hclust(hc, k = 3, border = "red")
  </code></pre>
  
  <p>Now my dendrogram looks like this:</p>
  
  <p><a href="https://i.stack.imgur.com/dOfJA.png" rel="noreferrer"><img src="https://i.stack.imgur.com/dOfJA.png" alt="enter image description here"></a></p>
  
  <p>Because I am interested in 3 clusters, is there a way to get <code>pvclust</code> to make the comparison between these 3 clusters? Or maybe that isn't what <code>pvclust</code> is comparing? What is the null hypothesis here? </p>
  
  <p>If I look at the dendrogram produced from <code>pvclust</code>, it seems that within the red box on the right the two other clusters I am interested in specifying (with <code>hclust</code>) also have significant p-values. How would I report this or explain it?</p>