out labels. This reflects our point in the beginning about how many tests of homogeneity typically require sample labels. On the other hand, the environmental health book describes a formalizable description of homogeneity, namely the clause about statistical properties of any one part looking the same as another.</p>
<p>Mathematically, the description above says that given a dataset <span class="math inline">\(\{\mathbf{x}_1,\ldots,\mathbf{x}_N\} \subset \mathbb{R}^P\)</span>, for it to be homogeneous it s