ukey"</span>, 
               type <span class="op">=</span> <span class="fl">3</span><span class="op">)</span>

<span class="va">tukey_factorial</span></code></pre></div>
<p>Notice that doing this hasn't changed the pattern of the ANOVA results, the p-values for the main effects and interactions are very slightly different but the overall conclusions remain the same. This is likely because the violations of normality was quite mild and there is a large sample size, however, with the transformation we can b