# Expand Samples or Expand resemblances

The <ins>Exe environment</ins> matrix does not seem (from **Plots>Draftsman Plot** or **Histogram Plot**) to contain notable outliers and can safely be used without transformation of individual variables. It does however need **Pre-treatment>Normalise Variables** – rename it <ins>Abiotic norm</ins>. To expand this data matrix to the dimensions of 108 samples $\times$ 6 variables, with <ins>Abiotic norm</ins> as the active sheet take **Tools>Expand Samples**>(Expand as data worksheet: <ins>Exe nematodes bi-monthly</ins>) & (Match original labels to factor: <ins>site</ins>). The fourth-root form of the biotic data matrix could equally well have been used in place of the original nematode sheet – what is needed from it is the size of expanded matrix needed, and the structure of samples over the sites, from the factor <ins>site</ins> whose levels 1, …, 19 are matched up with the labels 1, ..., 19 of the normalised environmental sheet. The expanded environmental matrix is then entered to a Euclidean distance resemblance calculation, to give <ins>Euclid expanded</ins>. The same construction can be achieved by first taking Euclidean distance on the <ins>Abiotic norm</ins> data matrix, to give a resemblance matrix renamed <ins>Euclid</ins>, and then entering this as the active matrix in **Tools>Expand**>(Expand as resemblance worksheet: <ins>B-C 4rt</ins>) & (Match original labels to factor: <ins>site</ins>) to obtain exactly the same model (abiotic) matrix <ins>Euclid expanded</ins>.

Now with active sheet <ins>B-C 4rt</ins> a further run of **Analyse>RELATE**>(Secondary data•Resemblance /model matrix: <ins>Euclid expanded</ins>) gives a much larger $\rho$ of 0.72 (highly significant, of course, at p<0.01% for the 9999 permutations of this run), indicating the very good fit of the individual bi-monthly samples to the alternative model of sites differences, structured by these abiotic variables. 

[![ScreenshotPage248a.png](https://learninghub.primer-e.com/uploads/images/gallery/2024-10/scaled-1680-/screenshotpage248a.png)](https://learninghub.primer-e.com/uploads/images/gallery/2024-10/screenshotpage248a.png)