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:
| Depth DDD (m) | 4.5 | 12.8 | 8.2 | 22.1 | 2.3 | 35.6 | 17.4 |
| Condition Rank SSS | 3 | 4 | 2 | 7 | 1 | 6 | 5 |
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.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.