A marine biologist is investigating the relationship between the depth DDD (in metres) of a coral reef and the condition score S S\,S of the coral (ranked from 1 to 7, where 7 is the most degraded and 1 is the most pristine). She suspects that coral located at greater depths is more prone to degradation. She collects data from 7 different sites, as shown in the table below:
\begin{center} \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline Depth D(m) & 4.5 & 12.8 & 8.2 & 22.1 & 2.3 & 35.6 & 17.4 \\ \hline Condition RankS & 3 & 4 & 2 & 7 & 1 & 6 & 5 \\ \hline \end{tabular} \end{center}
Calculate Spearman's rank correlation coefficient (rsr_srs) for these data.
Stating your hypotheses clearly and using a one-tailed test at the 5% level of significance, interpret your coefficient. (The critical value for n=7n=7n=7 at the 5% level is 0.7143).
State a reason why Spearman's rank correlation coefficient might be more appropriate than the product moment correlation coefficient (PMCC) for this specific dataset.
