title: split plot model anova with R
body: <p>I am trying to solve an exercise with R, that I found in the book <strong>Design of Experiments for Agriculture and the Natural Sciences</strong>(pag. 164)
  <a href="https://i.stack.imgur.com/xOmrl.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/xOmrl.png" alt="table" /></a></p>
  <p>I have passed the table to the R software</p>
  <pre class="lang-r prettyprint-override"><code>library(tibble)
  tb = tibble(&quot;replica&quot; = factor(x = rep(1:4,12), labels = c(&quot;I&quot;,&quot;II&quot;,&quot;III&quot;,&quot;IV&quot;)),
              &quot;row&quot; = factor(x = rep(1:4,c(12,12,12,12)), labels = c(&quot;12P&quot;,&quot;25P&quot;,&quot;12B&quot;,&quot;25B&quot;)),
              &quot;hybrid&quot; = factor(x = rep(1:2,c(24,24)), labels = c(&quot;P3730&quot;,&quot;B70XH55&quot;)),
              &quot;density&quot; = factor(x = c(rep(1:3,c(4,4,4)),rep(1:3,c(4,4,4)), rep(1:3,c(4,4,4)), rep(1:3,c(4,4,4))  ),
                           labels = c(&quot;12000&quot;,&quot;16000&quot;,&quot;20000&quot;)),
              &quot;valor&quot; = c(140,138,130,142,
                          145,146,150,147,
                          150,149,146,150,
                          136,132,134,138,
                          140,134,136,140,
                          145,138,138,142,
                          142,132,128,140,
                          146,136,140,141,
                          148,140,142,140,
                          132,130,136,134,
                          138,132,130,132,
                          140,134,130,136))
  </code></pre>
  <p><strong>but i have difficulty creating aov model</strong></p>
  <pre class="lang-r prettyprint-override"><code>model = aov(valor ~ replica + hybrid + replica/hybrid + row + replica/row + density + replica/density + row:density ,data = tb)
  </code></pre>
  <p>when applying <code>anova(model)</code>, it gives me discordant result with the table below</p>
  <p><a href="https://i.stack.imgur.com/gHeFN.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/gHeFN.png" alt="enter image description here" /></a></p>
  <p>If there is any other way to apply the model, please I am all ear to your answers. I apply <code>anova()</code> for the reason that <strong>I can extract the msres</strong> <code>anova(model)['Residuals', 'Mean Sq']</code> and that helps me calculate the <strong>reliability of the model (cv)</strong></p>